Test Scene Design for Physically Based Rendering
TTest Scene Design for Physically Based Rendering
Elias Brugger, Christian Freude, Michael WimmerTU Wien
Abstract
Physically based rendering is a discipline in computergraphics which aims at reproducing certain light andmaterial appearances that occur in the real world.Complex scenes can be difficult to compute for render-ing algorithms. This paper introduces a new compre-hensive test database of scenes that treat different lightsetups in conjunction with diverse materials and dis-cusses its design principles. A lot of research is focusedon the development of new algorithms that can dealwith difficult light conditions and materials efficiently.This database delivers a comprehensive foundation forevaluating existing and newly developed renderingtechniques. A final evaluation compares different re-sults of different rendering algorithms for all scenes.The full data set can be downloaded from
Zenodo andindividual scenes can be accessed via a dedicated webrepository . Physically Based Rendering (PBR) is a discipline in com-puter graphics that aims at producing images that re-semble the real world as accurate as possible. PBR isintegral to photorealism in movies and games as wellas architectural and industrial visualization.In general, the techniques of PBR aim to simulate thelighting conditions as they appear in reality. Therefore,rendering such images requires simulation of light,which is often computationally expensive and timeconsuming. Generally, PBR consists of several tech-niques that have to play together to achieve a realisticimage, most importantly path tracing and associated
Monte Carlo Integration are fundamental methods forcreating such images. [PJH16]Different
Monte Carlo -based algorithms exist to ren-der physically correct images, each of them having https://zenodo.org/ , 10.5281/zenodo.4002021 https://odpr.cg.tuwien.ac.at advantages and drawbacks depending on the scenesetup. Research work is focused to improve the ef-ficiency of Monte Carlo Rendering . Newly developedapproaches need to be compared and evaluated againstalready existing ones. The problem is that there aremany different scattered scenes available but there isno commonly used database for evaluation and testing,this makes it difficult to compare methods.The goal of this paper is to deliver a step towardsa more consistently designed scene database for theevaluation of different aspects of PBR and
Monte CarloRendering . Since there can be considerable differencesin efficiency and capabilities between the different al-gorithms, the scenes are designed to include a varietyof challenging cases that try to enhance and show thecharacteristics of such algorithms.This paper will discuss the individual test scenesand the underlying design principles and also includesrendered examples using a selection of different al-gorithms. Additional sections regarding Monte Carlo(MC) rendering are included in the appendix. The nextsection will give an overview of existing test scenedatabases and related work.
The database described in this paper lays a comprehen-sive foundation for testing light and material phenom-ena. For further testing with more complex models,material, and light setups, refer to the PBR databasecreated and gathered by Morgan McGuire [McG17]. Itcontains several complex scenes with large amountsof polygons as well as a variety of different materialsand light setups.Another comprehensive and more complex databasewas created and gathered by Benedikt Bitterli [Bit16].This database contains 32 different scenes rangingfrom simple scenes to complex scenes with complexlight setup and 3D objects. Partially overlapping scenescan be found in the PBR database by Wenzel et al.[MP18]. This dataset features extensive representa-tions of outdoor vegetation with a variety of unique1 a r X i v : . [ c s . G R ] A ug lant models as well as scenes with large portions ofglass materials.An initial approach on scene creation for Global Illu-mination can be found in the paper
Global IlluminationTest Scenes by Smits et al. [SJ01]. The scenes containelementary 3D objects and monochrome light setupsto show basic phenomena of light transport.An analytical approach on
Global Illumina-tion scenes can be found in the paper
TestingMonte-Carlo global illumination methods with ana-lytically computable scenes by Szirmay-Kalos et al.[SKKA01], which investigates the correctness of
Global Illumination algorithms. Because
Monte CarloRendering uses random sampling, correct or incorrectresults (because of implementation errors) are oftennot noticeable. As a solution, scenes with knownexact solutions are used to verify the algorithms.Another approach on verification of PBR algorithmscan be found in the paper
Verification of PhysicallyBased Rendering Algorithms by Ulbricht et al. [UWP06].This paper discusses several state of the art approachesto verify the correctness of light transport simulationas well as advantages and disadvantages of them.The database discussed in this paper, in contrast,should give a more structured and comprehensive setof test scenes used to observe a variety of phenomenain PBR without focus on physical or analytical correct-ness. Moreover, the modular library containing the 3Dobjects delivers the possibility to adjust the existingscenes or even create completely new ones.
In this chapter, the main motivation of this paper, thecreation of a scene database, will be discussed andpresented in detail. Twenty scenes were created out ofa library of different objects including different lightingsituations, simple objects, and more complex objectswith different material setups. Since not all algorithmsachieve the same result with the same render time,it is interesting to observe the different lighting andmaterial conditions in order to choose an appropriatealgorithm that delivers a good result and does not taketoo long in terms of render time. The evaluation partof this paper will compare render results of different integrator s (algorithms like bidirectional path tracing or Metropolis light transport ) in terms of render timeand visual quality.The render engine that is used to render the scenes is mitsuba , developed by Jakob Wenzel [Jak10] in 2010.As this is the most common render system for scientificpurposes, it is an appropriate choice to observe realisticmaterials and light conditions and show difficulties andissues common in the field of PBR. mitsuba is a comprehensive renderer that combinesmultiple techniques from important research workin
Physically Based Rendering . Many inspirations inthe system come from the book [PJH16] that was in-troduced earlier. Important integrator s and materialproperties will be explained later. The material presetsare based on real-world measurements according tothe mitsuba documentation [Jak14]. The documenta-tion is an extensive collection of all the materials andlight emitters that come with the render system, fur-thermore it contains the usage and constraints of thedifferent components. The scenes have been modeledin Blender 2.79 with the mitsuba plugin. Conveniently,the scenes can be exported as XML file, as the native mitsuba application operates with this file system.
There are several criteria that accompanied the cre-ation of the test scenes. The first and most importantone was to design them as representative and expres-sive as possible. That means that the advantages anddrawbacks of the different algorithms can be well dis-tinguished based on the renderings. More specifically,the idea was to use different advanced materials likeglass and rough surfaces in order to increase the com-plexity of the calculations and to challenge the algo-rithms.Moreover, the scenes feature typical phenom-ena/effects characteristic to PBR. However, certainscenes are designed to particularly concentrate on feweffects. Refractions and reflections play an importantrole in realistic synthesized images. Translucent andreflective materials are not perfectly smooth in reality,that means that they have certain surface irregularities.Several scenes feature such surfaces. The difference isthat rough materials generally demand more complexcalculations, because light scatters more in the scene.More sophisticated scenes feature materials withSubsurface scattering (SSS), which can only be ren-dered with a few of the available algorithms. SSS ma-terials are considerably relevant to PBR, because – inthe real world – many objects are partially translucent.In regard to participating media , some scenes featureatmospheric-like particles, which is a challenge for anyalgorithm but is also integral to realistic renderings.Several scenes also feature complex geometry in2onjunction with refractive and reflective materials.This will generally challenge the calculations of lightpaths, especially when it comes to resolving caustics.That is where certain integrator s have an advantagecompared to basic algorithms like path tracing . Table1 shows a list with the scenes and the correspondingeffects they focus on.
Figure 1: Simple scene with a water glass and a mirrorcausing different caustics and reflections. Renderedwith Primary Sample Space Metropolis Light Transport(PSSMLT) and
Independent sampler with 2048 samplesper pixel (Samples per pixel (spp)).Figure 1 shows a simple scene with a water glassand a bent mirror. It was made primarily to showcomplex caustics of the glass material and the mirror.The glass has a common glass material and severalindents on the side. The mirror to the right is bentand applied with a copper material preset. The groundhas a common metallic material with a high roughnesscoefficient (see Section 2.3.1). The scene involves asphere light in the top left of the scene. The spherelight itself is a spherical shape with a material definedas area emitter (see Section 2.2.1), this is a typical setupfor any kind of realistic light source in mitsuba .The glass itself is relatively hard to render becausethe light that penetrates the glass causes many reflec-tions in several different directions. In order to sim-ulate the real world as accurate as possible, the 3Dobjects have to have several properties. The glass is de-fined as an object with an inner material. mitsuba ma-terials allow to set properties for materials that arein the exterior and in the interior (exterior is the sideof the normal directions) of the outer boundary. Incase of the glass, the exterior is defined as air and theinterior as a glass with a typical index of refraction,while the glass material itself is a
Smooth dielectric ma- terial [Jak14] (see Section 2.2.2). The renderer needs toknow these parameters to compute the correct reflec-tion angles, and depending on the preset, the materialshave different indices of refraction.The ground of the scene appears relatively grainy,that is because the surface material has a high rough-ness coefficient, which means a widespread light scat-tering in the scene. The scene was primarily designedto test different integrator s and to evaluate which ofthem can handle caustics well. It appears that the caus-tics coming from the mirror are less grainier than thosecoming from the glass.
An area emitter is a light source that emits light viathe exterior surface of an arbitrary shape. Unlike someother lights definable in the mitsuba renderer, areaemitters generally cast soft shadows. [Jak14]
Figure 2: The red arrow is the incident light ray, theblue arrow depicts the reflected ray and the greenarrow shows the refracted light through the glass ma-terial. [Jak14]Figure 2 shows a geometric interpretation of the
Smooth dielectric material in mitsuba . It defines a ma-terial with a perfectly smooth surface, that means thatthe BSDF scatters light in discrete directions (as op-posed to rough surfaces with a continuum of resultinglight rays). The green arrow in Figure 2 shows thechange of direction of the incoming light (red arrow)depending on the index of refraction. The blue arrowshows the portion of the light that is reflected on thesurface. Figure 3 shows a scene with four glass spheres with acrown glass material preset arranged in a row which isprimarily designed to show light propagation throughglass materials as well as caustics of spherical shapes.3cene RefrSpec RefrGl Reflec Caust SoftSh ColBl PartM Cgeom SSS2.2 (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88)
Table 1: An overview of the different aspects covered by each scene. Bold check marks indicate primary effectsand normal check marks indicate secondary effects which are not in the main focus of the respective scenes.RefrSpec – Refraction specular, RefrGl – Refraction glossy, Reflec – Reflection, Caust – Caustics, SoftSh – Softshadows, ColBl – Color bleeding, PartM –
Participating media , Cgeom – Complex geometry, SSS – SubsurfacescatteringFigure 3: Glass spheres arranged as pendulum to showlight propagation and caustics. Rendered with PSSMLTand
Independent sampler with 1024 spp. It simulates a light pendulum that transmits the in-coming light from the first until the last sphere. Anarea light connected to a common plane serves as lightsource. It is slightly raised to have the light directionoriented towards the ground. As a result, the lightnot only shines straight through the spheres, it alsocauses the spheres to throw caustics onto the ground.The light propagation of spheres is shown in detail inFigure 6. However, the arrangement of the spheresleads to light being bundled at most for the first sphere.The subsequent spheres gradually receive less lightfrom the previous one. Interesting to observe are thecaustics that appear on the ground. They come fromthe spheres but do not have a typical spherical shapeas it is common for such shapes. This comes from the4ariation of light directly falling on the ground andthe intersection with subsequent spheres. This leadsto light being refracted in another direction.A glossy bent mirror is placed behind the pendulum.It has a copper material with little roughness. Thisis achieved through a
Rough conductor material that,unlike the
Smooth conductor material , has surface scat-tering as seen in Figure 4. Interestingly, the grounditself is not as grainy as the ground in Figure 1 al-though the surface has the same material with equalroughness. This may come from the complexity of theglass portions in the scene and from the shape andintensity of the light source.
Figure 4: Light (red arrow) falling onto a surface withtiny fluctuations results in a reflected continuum ofscattered light (blue array). [Jak10]The
Rough conductor material describes a micro-facet distribution of a surface. The implementationin mitsuba is based on the paper
Microfacet Modelsfor Refraction through Rough Surfaces by Walter etal. [WMLT07]. Microfacets describe surfaces withmicro geometry. For instance a metal surface in thereal world is not perfectly smooth but it has tiny sur-face fluctuations. The microfacet model attempts tosimulate such surfaces through varying surface nor-mals. The light computation for rough surfaces gener-ally takes longer than for perfectly smooth materials[Jak14].
Figure 5 shows a similar scene like before. This time,different shapes are arranged in a row. The light sourceis a plane emitting from the top left of the arrangement.As different glass shapes throw different caustics, thisis an appropriate setup to compare some commonshapes. In order to give the light rays an appearance,a participating medium was put around the arrange-ment. The bounding box of the medium can be seen Figure 5: Different glass shapes arranged causing dif-ferent caustic shapes. Rendered with PSSMLT and
Independent sampler with 1024 spp.on the ground where the hard edges appear. The innersurface appears a bit darker because of the light beinggradually absorbed/reflected by the particles in themedium. Participating media is good for showing howlight rays are cast through space. This can be observedwell by looking at the light cones that emerge fromunderneath the sphere and the glass lens in the middle.The glass cube and the glass bowl have caustics aswell but the bundling of the light rays is too weak toappear in the medium, but they can be observed onthe ground. The size difference of the light cone of thesphere and the lens is remarkable. This is because ofthe different diameters. This phenomenon can be seenin Figure 6.Figure 6: Light propagation through a translucentsphere. [SKP07]5 .5 Scene – Sphere and lenses
Figure 7: Glass sphere and glass lenses forwardinglight rays differently. Rendered with PSSMLT and
In-dependent sampler with 1024 spp.The scene in Figure 7 consists of a larger glass sphereand two tinier lenses. The main focus in this sceneis to show the properties of light bundling and whatshapes are designed to achieve it. The backgroundagain features a bent mirror with a
Rough conductormaterial . The light source comes from the top left ofthe scene. The main focus here is on the light rays thatare propagated through the glass materials.The glass sphere transmits a relatively large amountof the incoming light to the first lens. The lens thencasts the incoming portions of light onto the last lens.It is noticeable that the light intensity differs consid-erably. When looking at the ground to the left of therendering, it can be observed that due to the transmis-sion and refraction of the light rays through the glassmaterials, the light gradually intensifies. On the rightside of the last lens on the ground, the light intensityis at its peak.
The scene in Figure 8 was designed to show caustics ofwaves in a medium like water. An area light is placedon the top and behind the objects. Furthermore, a glasssphere is placed in the middle as well as two diffusespheres on the sides.The colored spheres and the walls on the side of therendering have a
Smooth diffuse material [Jak14]. Itcan be described as a perfectly diffuse material witheven distribution of light in any direction (see Section2.6.1). This material leads to light reflections that areindependent from the point of view [Jak14].Specifically hard to render are the caustics comingfrom the waves of the water. The colored objects in the Figure 8: Glass sphere in water with waves causingdifferent complex caustics. Rendered with PSSMLTand
Independent sampler with 1024 spp.scene should help visualize the distribution of the re-flected light. Color bleeding resulting from the spherescan be seen underneath the glass sphere. In the realworld, there are generally no perfectly smooth diffusematerials, but this was set up out of simplicity.
Figure 9: Light distribution of
Smooth diffuse mate-rial . The red arrow is the incident light and the bluecontinuum is the scattered light on the surface. [Jak14]The
Smooth diffuse material is a surface materialthat reflects and scatters light independently from thepoint of view, as seen in Figure 9.
The scene in Figure 10 shows similar effects like before.A room with a rough diffuse material is filled withwater. The water is a deformed plane that simulateswaves. Furthermore, a common glass sphere is placedin the middle. On the left there is also a glass prism aswell as a glass lens on the right side.In this case, a participating medium was added forthe portions underneath the water surface to showthe light rays that are thrown onto the ground. Thetwo colored diffuse spheres in the corners in the back-6igure 10: Room filled with water with three differentglass shapes transmitting light into a partially partici-pating medium. Rendered with PSSMLT and
Indepen-dent sampler with 1024 spp.ground appear less saturated because of the causticsand the participating medium .Already known are the typical caustics of the spherein the middle as well as the caustics of the lens. Theprism has a more uncommon behavior in respect oflight refraction and reflection, regardless, the lightrays that are refracted are almost not visible in themedium. This is similar to the scene in Figure 5, wherethe caustics of the box and the bowl are not visibleeither, apart from the light that hits the ground.The portions of the water throwing caustics arelarger and more detailed. It is noticeable that the fur-ther away the appearances of the caustics are from thelight source, the more blurred they become. This canbe seen when comparing the caustics directly under-neath the surface and the appearances on the ground.Naturally this depends on the edginess of the waves.Relatively choppy waves result in short focal pointswhereas broad waves result in longer focal points. Thisis the same principle as it can be observed when com-paring the caustics of a lens and a sphere.
The scene in Figure 11 shows a scene set up to showcolor bleeding, which is a common effect in realisticcomputer graphics because of the exchange of indirectlight between objects in the scene. The idea behind isbased on the scene of the cornell boxes from the originalpaper
Modeling the Interaction of Light between DiffuseSurfaces by Goral et al. [GTGB84].A modification to the original rendering was madein terms of object shapes and the assignment of colors.In this case a green box and a red sphere are placedin front of a mirror on the back wall. The plane area Figure 11: Scene showing emphasized color bleedingeffect. Rendered with PSSMLT and
Independent sam-pler with 1024 spp.light throws light onto the back side of the box andsphere. This causes the reflections to mainly throwcolored reflections onto the back side of the room,which can be seen as green and red reflections aroundthe light source. The mirror on the back wall haslittle roughness applied so the scattering of the lightsupports the visualization of color bleeding.
Figure 12: Two high polygon objects with glass mate-rial, the left one with no roughness and the right onewith moderate roughness. Rendered with PSSMLT and
Independent sampler with 1024 spp.In the scene shown in Figure 12, a high polygonobject was used to simulate two different glass mate-rials. The left version has a common glass materialwith no roughness at all (
Smooth dielectric material ),whereas the right one has a
Rough dielectric mate-rial [Jak14] (see Section 2.9.1). The complex objectitself has around half a million polygons. A red diffusesphere was placed inside each of the objects to empha-size the impacts of roughness. On top of each objectthere is an area light that casts light through the glass.7hile the light rays for the
Smooth dielectric mate-rial reflect in discrete directions, the light rays for the
Rough dielectric material scatter in a continuum. Onthe one hand, the light gets scattered on the exteriorof the surface, on the other hand, the light that passesthe surface also results in a continuum of scatteredlight. In case of the rendering, this results in causticson the ground being more visible for the left object.Additionally, the light that is scattered within the rightobject is much more present than for the left one be-cause the roughness makes it collect more light insidethe surface, specifically visible on the ground.
Figure 13: Light distribution of
Rough dielectric ma-terial . The incident light (red arrow) gets reflectedin a continuum (blue array) as well as refracted in acontinuum through the surface (green array). [Jak14]As well as the rough version of the conductor mate-rial, the
Rough dielectric material (see Figure 13) is alsobased on the theory from the paper
Microfacet Modelsfor Refraction through Rough Surfaces [WMLT07] andimplements specific microfacet distributions for glassmaterials. [Jak14]
Figure 14: High polygon object with
Dipole-based sub-surface scattering material. Rendered with
Path tracer and
Independent sampler with 1024 spp. This scene shows again a complex object slightlymodified by adding fissures all over it. The materialis designed to show the properties of an SSS material.In order to apply SSS in mitsuba , the base materialhas to be either a
Smooth plastic material or a
Roughplastic material . In case of the scene in Figure 14, thematerial is a
Smooth plastic material , which is morecomplex than the materials used so far (see Section2.10.1). With SSS, materials like porcelain or wax canbe simulated. Typically, light shining on such objectsnot only reflects it directly on the surface but it alsolets portions of light through the surface. The innermedium of the object can be adjusted to have differentscattering and absorption coefficients as well. This canbe used to control how much light eventually shinesthrough the object. It is clear that, the more solid anobject is the less light will appear on the other side.To emphasize the effect of an SSS material, an arealight is placed behind the object. It can be seen thatportions of the object are considerably bright becausethe thickness at this location is low.Mentionable is that SSS can be simulated in twoways in mitsuba . The first one is an approximation(see Section 2.10.2) of the medium that normally isin the interior of the object. The second option is toactually set a participating medium in the interior ofthe object. The main advantage of the approximationmethod is a better performance but at costs of accuracy.
Participating media is the preferable option to simulatereal SSS, but it usually has a higher render time.
Figure 15: Light distribution of
Smooth plastic mate-rial
The incident light (red arrow) results in a reflec-tion on the surface (blue arrow) and several scatteringevents within the subsurface (black arrow and greenarrays/arrow). [Jak14]The
Smooth plastic material simulates a surface witha subsurface, as seen in Figure 15. It simulates a diffusesurface with a dielectric coating surrounding it. Asa result, there are generally many internal scatteringevents. On the one hand, the light gets reflected (blue8rrow) when it hits the dielectric coating, on the otherhand, the remaining portion of the light (black arrow)goes through the surface and hits the diffuse base layer.This triggers the internal scattering process (greenarrays and arrows within the subsurface). [Jak14]
This SSS model is implemented in mitsuba and has itsorigins in radiative transport [EVNT01] and medicalphysics [Pl12]. The implementation is based on thearticle
A practical model for subsurface light transport by Jensen et al. [JMLH01]. [Jak14]The
Smooth plastic material (see Section 2.10.1) inconjunction with the
Dipole-based subsurface scatter-ing model , an approximate simulation of SSS can beachieved. This is done by setting the diffuse reflectanceparameter of the plastic material to zero and have thedipole plugin calculate the diffuse part instead. [Jak14]
Figure 16: High polygon object with
Dipole-based sub-surface scattering material with additional water out-flow coming from above. Rendered with
Path tracer and
Independent sampler with 1024 spp.The scene in Figure 16 is a modified version of thescene in Figure 14. This time, a simulated water out-flow has been placed above the complex object. Theidea behind it is to observe how light behaves in com-bination with water and a subsurface material under-neath. An area light is placed behind the complexobject as well.Since the scene contains only materials with zeroroughness – apart from the ground – the light pro-cessing is relatively straight forward and simple torender. This is the reason why there is almost no grainin the rendering compared to other scenes. The wa-ter itself has a relatively low resolution in terms of polygon count to simplify the scene. Regardless, thewater appears fairly realistic although the viscosity ofthe water seems to be higher, which is rather atypical.Also mind the little caustics in the bottom right cornercoming from the water slipping off of the object sur-face. Because only a few integrator s are able to renderscenes containing subsurface materials, caustics areoften difficult to render. This problem will be treatedmore detailed later on.As an example, this scene has been rendered withthe common path tracer integrator . This integrator usually has troubles rendering caustics and therefore integrator s like bidirectional path tracer are commonlyused. The issue with the bidirectional method is thatit cannot handle SSS materials in mitsuba [Jak14], asthis is the case in this scene.
Figure 17: More complex scene showing the propertiesof lenses of difference thickness resulting in differentray propagations. Rendered with PSSMLT and
Inde-pendent sampler with 1024 spp.The scene in Figure 17 shows a setup designed toshow the effects of applying a different thickness toconvex lenses. Two light sources are placed in the topleft corner and in the bottom left corner.To catch as much light as possible, the light sourcesare surrounded by geometry, this makes it possibleto control the size of the light cone. The first lens inthe top left portion of the rendering receives almostall of the incoming light from the top light source.As the lens propagates the incoming light rays ontothe bent mirror in about the middle part of the ren-dering, the rays once more get bundled to constructa relatively narrow focal point. The straight mirrorat the mid top receives the scattered light from thebent mirror and reflects it towards a lens with a higherthickness. It is noticeable that the light reaching the9ast lens is already considerably low. Regardless, thelens bundles the light once more to throw a causticwith a slightly higher light intensity onto a high poly-gon object, which shows the effect of a convex lenswith a higher thickness.The lens in the bottom left corner and the corre-sponding mirror on the right side is built to transferlight towards the side of the last lens that is describedabove. This results in several tiny transmitted raysemerging from the top right of the lens and converg-ing towards the top right of the rendering. Interestingto observe are the considerably long focal points of thelights rays transmitting the lens. The color from thelight being reflected by the bent mirror is destined toshow clearly what portions of the light get reflected towhat location. In order to achieve light rays appearingin a scene, again a participating medium was setup tofacilitate this intent. Considerably interesting are thecaustics resulting from the bottom left lens, since itappears to throw a variety of light rays from differentdirections.
Figure 18: Lenses with different thickness depictingthe effect such material and shape convey. Renderedwith PSSMLT and
Independent sampler with 1024 spp.Figure 18 depicts the effect of glass lenses with dif-ferent thicknesses. The left one is a bit thicker than theright one, which results in a different magnificationand focal point. Previously we have seen the effect inthe shape and form of caustics. This time, a more directapproach was taken to show how lenses manipulateincoming light.The thicker lens to the left appears to magnify theobjects in the back more than the right one. Con-sidering the graphical interpretation of light passingthrough a lens in Figure 6, this means that it dependson the shape, the thickness, and the curvature of the lens, how much the light will be refracted. This leadsto the effect that images in thicker lenses appear biggerin size. It is recognizable that the objects placed alongthe borders of the lenses appear deformed. The thickerthe lens, the more distorted objects become around theborders.
Figure 19: Multiple mirrors showing the impact ofthe bounces parameter for integrator s. Rendered withPSSMLT and
Independent sampler with 1024 spp.The scene in Figure 19 was primarily designed toshow the effect of the path depth parameter in the mitsuba integrator s. The path depth parameter is ageneral parameter that can be adjusted for any inte-grator . The amount of the bounces control how manyray intersections happen per pixel (path depth). Thiscan be observed in the rendering, the scene was ren-dered using a depth of 32 to show the effect of maximalpath depth. This fact is noticeable when looking atthe tiny black shaded square located in the mirror to-wards the top of the rendering. This indicates that thealgorithm stopped computing and no further light isprocessed here. If the path depth is high enough or
Russian Roulette is employed, the unfilled area in themirror would eventually get fully resolved.
Russian Roulette is a
Monte Carlo technique usedfor reducing variance originally introduced by Kirk etal. [AK90]. Basically it stops tracing rays if there isless than a minimum of contribution to the pixel value.[PJH16]Additionally, a high polygon object with a goldmaterial preset has been placed to increase the com-plexity of the scene. Furthermore, two convex lensesare placed around the door to increase light complex-ity. The room itself consists of a door that is slightlyopened. Outside the room, an area light is located toemit light towards the door crack as well as an area10ight inside the room which can be seen in the firstmirrored instance. Usually, light coming from a tinycrack is difficult to catch for certain integrator s becauserandomly shooting a ray towards the crack and lightsource is rare (
Path tracer has difficulties resolvingsuch lighting situation). The rough diffuse material ofthe room increases the complexity of the scatteringsas well.
Figure 20: Glass prism which has interesting light re-flections and transmissions. Rendered with PSSMLTand
Independent sampler with 1024 spp.Figure 20 shows a scene set up to describe the be-havior of light falling onto a glass prism. The initialidea was to evaluate the correctness of light being re-fracted and reflected depending on the wavelengthsof physical light. Although mitsuba has an option toinvolve physical light with a discrete set of the wave-length spectrum, this paper and specifically this scenedoes not observe the behavior of different wavelengths,because the application would need some parameterschanged and recompiled to enable this property. Fur-thermore, a vertical row of spheres is placed inside theprism to produce additional light reflection and refrac-tion. It may appear as if the light rays pass throughsome participating medium , but the illuminated areason the ground simply come from the direct and indirectlight. At the right hand side of the rendering there is aconvex glass lens stuck in the ground, which collectsthe incoming light and throws a variety of caustics.Regardless, interesting refractions and reflections oflight can be observed in the scene. Like in the previouslens test scene, a light with high intensity was placedon the left side. It is also surrounded by geometry thathelps the light shine in a narrower cone than usual. Itis noticeable that one portion of the light gets reflectedon the first intersection with the prism surface and the other portion gets transmitted through the glassmaterial. Also mind the direction the whole bundle oflight rays take when passing through the prism. Theglass material has a typical index of refraction of 1.49,which is around an index of crown glass. The arrange-ment of the spheres in the middle of the prism have afocusing effect on the rays. The light bundle exitingthe prism would normally have a lower intensity, sincethe spheres bundle the rays in the prism, the light ap-pears brighter. Furthermore, it can be slightly seenthat the glass spheres cast the typical sphere caustics.Considerably interesting are the caustics thrown fromthe lens on the right side.
Figure 21: Light setup showing the different shad-ows cast from different light sources. Rendered withPSSMLT and
Independent sampler with 1024 spp.The scene in Figure 21 is designed to show the dif-ferences between the most common light sources in mitsuba . The first one is a common area light in formof a sphere, the middle one is a spot light, and the lastone is a directional light typically for the sun.Because of the properties of area lights defined in mitsuba , this type of light source leads to objects cast-ing soft shadows [Jak14]. This is noticeable when ob-serving the darkest portions of the shadows of theobjects. The sharpness of the shadow boundary is de-pendent on the distance to the casting object. Closeto the object the shadow boundary is sharp and fur-ther away it is more blurred. The same behavior canbe seen for the other objects, whereas the area lightshadow for the cylinder is barely visible because of theother lights overlapping it.The spotlight is defined to have a certain linearfalloff for the intensity [Jak14], however since the lightemits from a single point in space, this type of light11ource does not cast soft shadows. This can be seenin the rendering when observing the blue light fallingonto the objects. The shadows construct a perspec-tively distorted shape but the sharpness of the shadowsremains constant.The third light (green tint) is a direct light emitter, asdefined in mitsuba [Jak14]. Typically, it simulates thesun like it exists in reality, which emits light rays in aspecific direction. The common effect of a light sourcelike the sun can be seen in the rendering by observingthe shadows that the green light casts. Particularly,the shadows from the sphere and the cylinder appearto have a constant shape over distance. Soft shadowsdo not occur for this type of light source either.Another interesting aspect is the difference of thematerials of the objects. Whereas the complex objectleft has almost no grain, the red diffuse sphere and therough metal cylinder exhibit a large amount of it aswell as the shadows. This is because of the complex-ity of the surface material. The complex object hasa smooth material, which makes it easier to render,whereas the red sphere and the cylinder have a diffusematerial with moderate roughness that scatters thelight to a greater extent.
Figure 22: Light coming from a tiny crack of the doorresulting in several light scattering events. Renderedwith PSSMLT and
Independent sampler with 1024 spp.The scene in Figure 22 was specifically made to testthe behavior of light coming from a door that is almostclosed. The idea behind it was to observe a varietyof soft shadows being cast all over the scene and tohave a relatively simple setup of materials that simul-taneously lead to a quick convergence and a visuallypleasing result. The glass and mirror materials in thescene do not have any roughness, this is to decrease complexity overall and to put the focus on the lightdistribution through the door. The scene was renderedwith the same amount of spp (1024) as most of the otherscenes, yet the result is already considerably good com-pared to other renderings. This is also because of theperfectly smooth glass and mirror surfaces. Severalgrainy portions can be observed on the right side ofthe cube where the light source from the door appearsand on the back side of the sphere when looking atthe right mirror. Interesting to observe are the cubeshadows cast on the left wall on the left hand side ofthe rendering.
Figure 23: Light coming from outside and scatteredthrough a simulated window shutter causing soft shad-ows. Rendered with PSSMLT and
Independent sampler with 1024 spp.The scene in Figure 23 is, similarly to previous scene,designed to show soft shadows and glass materials.This time the light comes from a window involving ashutter object that breaks and scatters the incomingrays. Additionally to an area light in form of a planeplaced outside the window, the world environment isset to have a constant monochrome light. This can beseen when looking at the right-hand side around thewindow. The bright brownish light that appears onthe back wall comes from the area light source.The effect of the decreased sharpness of soft shad-ows over distance can be distinctly seen when lookingat the light projections at the back wall. Apart fromthe shadows getting more blurred, the further the lighttravels also the intensity of the reflected light graduallydecreases. It is noteworthy that the light intensity inthe mirror on the left side is higher than the intensitydirectly on the back wall. This happens because ofthe specularity of the room. The roughness is consid-erably high but is not independent from the point of12iew. The light reflecting from the diffuse back wallgets reflected by the mirror, which eventually reflectsit back to the camera with a higher intensity. This isdue to the angle towards the light source and thereforean angle that is closer around the perfect reflectionangle of the wall.A high polygon model is located on top of the cube.It is noteworthy that the graininess of the complexmodel differs considerably compared to the glass cube.There are more reflections outside and inside the highpolygon object and therefore the scene is more difficultto render. Compared to the scene before (see Figure22), this one has also been rendered with PSSMLT with1024 samples per pixel. Yet, the scene overall looksmore grainy also because of the higher light intensitycoming from outside.
Figure 24: Scene with large SSS portions and morerealistic light setup. Rendered with
Path tracer and
Independent sampler with 1024 spp.The scene in Figure 24 was specifically designedto show behavior of large portions of materials withSSS in a more realistic light setting. Therefore, twohigh polygon objects are placed in the scene, one is asimulated wax candle and the other is the known highpolygon object from previous scenes. The candle wickis lit and supports to show the impact of light on thesubsurface material. Typically for candles, the lightgoes through the top of the lit surface and graduallydecreases towards the bottom.The light source coming from outside is a constantenvironment tinted slightly blueish. This should sim-ulate indirect environment lighting. Additionally tothe light from outside, a lamp in the room was placedabove the objects to give the scene more depth andseveral light scatterings. Hard to render are the glass spheres located insidethe water glass. They have a glass material with a mod-erate roughness, and therefore the graininess for thisportion of the rendering is considerably high comparedto the rest of the image.
Figure 25: Complex portion of subsurface materialin conjunction with rough glass surfaces. Renderedwith
Extended volumetric path tracer and
Independentsampler with 1024 spp.Figure 25 shows a scene with several different mate-rials put together. Generally, this scene was designedwith a more artistic and more complex approach inmind. The cloth blanket that covers objects under-neath has an SSS material applied to simulate morerealistic clothing. The high polygon object to the lefthas a gold material applied. Underneath the blanket,in the middle of the scene, there is a glass box witha red diffuse sphere inside and the object to the rightis a water glass. Behind in the back of the scene, amirror with moderate roughness distributes the lightthat shines onto the blanket from behind. Anotherlight is placed above to allow the water and lenses tothrow visible caustics. Additionally to these objectsa water outflow was put above the scene mainly tolet the water throw caustics on the ground. Anotherrough glass sphere is placed on top of the glass to theright to emphasize light scattering inside the blanket.In that respect, it is also noticeable that the bottomof the blanket is highlighted from the scattered lightinside.The scene was rendered with the
Extended volumet-ric path tracer (volpath) [Jak14] integrator . Also mindthe relatively sharp and smooth portions of the render-ing that do not belong to glass caustics. This is a wellknown problem for volpath. Yet, for 1024 samples per13ixel, the caustics on the bottom of the image comingfrom the water drops and the lens are considerablygood but still grainy in comparison when renderedwith an integrator like PSSMLT. It is noticeable for theblanket that there are several cloth folds that generallyreceive less light from the internal scattering eventsand therefore convey a better perception of depth. Alsointeresting is to show SSS with parameters that aretypical for cloth and how little is visible through thehighly scattering material.
Figure 26: Room filled with water and objects with asphere light in the middle. Rendered with
Extendedvolumetric path tracer and
Independent sampler with1024 spp.The scene in Figure 26 is a constellation of objectswith different materials arranged around an area lightin form of a sphere. Starting with the first object, abent mirror with a slightly rough copper material isplaced behind the sphere light to enable diffuse lightscatterings. On the left side, a red diffuse sphere withina larger glass sphere is placed. To give the scene amore complex material setup, a wax candle with anSSS material was added. Besides the high polygonwax candle, the raven head was added as well and hasbeen applied with a gold material. The last object isa simple cylinder with a metal texture with moderateroughness.Additionally, a water mesh fills the room so abouthalf of the height of the objects are located inside. It isnoticeable that for the red sphere, the reflection of thelight source is not as intense. This comes from a lightportion getting reflected by the outer glass sphere andthe other portion hitting the red diffuse material. Theroughness of the bent mirror ensures that there aremany light scattering events that take place over the scene. This increases complexity in terms of renderingtime and visual quality. The volpath integrator hasbeen used to render the image. The issue is that thescene has an SSS material and simultaneously thereare many caustics that need to be rendered. This leadsto the problem that integrator s like PSSMLT wouldnot work because of the implementation in mitsuba .The deficit of volpath not being able to handle causticswell, is noticeable when looking at the darker portionsof the rendering. The perceivable variance is very highand the image as a whole looks very grainy.
This chapter deals with the evaluation of the scenesthat are described in Chapter 2. Depending on thescene, the integrator s achieve considerably differentresults within the same render time. Each scene eval-uation will contain five (four in special cases) renderresults from a selection of the most relevant integrator s.The algorithms partially sample light very differentlyand comparing on the basis of equal spp would hide thesampling overhead of the different algorithms. Thisis the reason why the results from the renderings arecompared with render time. Perfectly accurate consen-sus in render time is not possible, but the differencesin time are around plus/minus ten seconds.
The following will give brief descriptions about the integrator s as well as the abbreviations that are usedin the evaluation.
Path tracer (PT)
The
Path tracer is a basic pathtracer implementation that shoots random rays fromthe camera into the scene. It is a good choice when thescene contains only simple lighting with no obstaclesalong the light paths. [Jak14]It uses
Multiple Importance Sampling to reduce vari-ance in the image.
Multiple Importance Sampling is atechnique in
Monte Carlo -sampling that uses the ideaof taking samples from multiple different probabilitydensity functions p ( x ) (like described in Section A.2.5),in the hope that one of the distributions resembles theshape of the integrand. [PJH16] Simple volumetric path tracer (VOLPATH SIM-PLE)
Simple volumetric path tracer implements a basicvolumetric path tracer that is used to render volumesin scenes ( participating media , SSS materials). It doesnot make use of
Multiple Importance Sampling . [Jak14]
Extended volumetric path tracer (VOLPATH)
This integrator implements a volumetric path tracerand it also uses
Multiple Importance Sampling . In re-spect of surfaces, it behaves like the standard
Pathtracer [Jak14]
Bidirectional path tracer (BDPT)
The BDPT isimplemented as proposed by Veach and Guibas [VG95],in conjunction with
Multiple Importance Sampling . Thebasic idea is to start two random ray paths in one step.One ray starts from the camera and one from an emitteras described in Section A.2.5. BDPT usually is consid-erably slower than
Path tracing for the same amountof samples but generally results in images with muchless perceivable variance. [Jak14]
Photon mapper (PM)
The
Photon mapper imple-mentation is based on the idea proposed by Jensen[Jen96]. The calculation of light is separated into threeclasses. Diffuse, caustic, and volumetric maps are builtseparately. A ray tracing pass follows that estimatesthe radiance using the photon maps.
Progressive photon mapper (PPM)
This inte-grator implements
Progressive photon mapping byHachisuka et al. [HOJ08]. It is based on
Photon map-ping but it progressively calculates and shows the re-sults as the passes continue indefinitely until eventu-ally all variance vanishes.
Stochastic progressive photon mapper (SPPM)
This integrator implements SPPM as proposed byHachisuka et al. [HJ09]. It is an extension of
Pro-gressive photon mapping that has better performancewhen it comes to motion blur, depth of field or glossyreflections.
Primary Sample Space Metropolis Light Trans-port (PSSMLT)
This rendering technique was de-veloped by Kelemen et al. [KSK01], based on
MarkovChain Monte Carlo Integration [Has70]. Usually, al-gorithms like path tracing compute images by ran-domly shooting light paths into the scene. PSSMLTbenefits from the fact that it tries to find most rele-vant light paths. If a relevant path is discovered alsoneighbored paths are evaluated and involved in the calculation. Generally, this improves the render timeconsiderably and complex light situations give a betterresult. [Jak14]
Metropolis Light Transport, Path Space Metropo-lis Light Transport (MLT)
MLT is similar toPSSMLT. Both integrator s search for light paths thatcarry a high amount of light energy. PSSMLT does thisby using another rendering technique. MLT insteadworks directly on the light carrying paths and there-fore has more information available. This allows di-rected search for certain classes of light paths. [Jak14]
Energy Redistribution Path tracing (ERPT)
This integrator by Cline et al. [CTE05] uses
Pathtracing in conjunction with techniques of
MetropolisLight Transport . With the use of a standard bidirec-tional path tracer, a set of seed paths is generated. AnMLT Markov Chain is then started for each path thatredistributes the energy of the samples over a largerarea.
Irradiance caching (IRRCACHE)
Irradiancecaching is a meta-integrator that works on top ofother integrator s. It was developed by Ward andHeckbert [WRC88]. It calculates and caches irradianceinformation at several scene locations and fills theother locations through interpolation. This can behelpful if results would otherwise look blotchy (oftenused with photon mapping).
The reference in Figure 27 was rendered with PSSMLTwith 2048 samples per pixel (spp). The result of the path tracer (PT) integrator was used as a benchmarkin terms of render time. The images where renderedin about 1.6 minutes. Concerning soft shadows (bot-tom row), PT had difficulties delivering good results.BDPT resulted in considerably lower perceived vari-ance. PSSMLT and PM also had difficulties renderingsoft shadows and resulted in a lower visual qualitythan BDPT. The best results were achieved by ERPT.The glass portions (Figure 27 middle and top row)of the scene are hard to render. Both PT and BDPThad troubles resolving these parts. PSSMLT and ERPTachieved the best results while PM delivered a resultthat is too dark overall. However, PM resolved thecaustic on left side of the glass (on the ground) betterthan the other integrator s. This can be seen in Figure27 PM top row, it shows considerably less perceivablevariance than the other results.15igure 27: Reference rendered with PSSMLT (Independent Sampler) at 2048 spp. Comparison images (Indepen-dent Sampler) rendered in 1.6 minutes.As a conclusion, it can be stated that there is no integrator that performed well in all aspects. WhilePM had better results on portions of the ground, theglass was considerably better for PSSMLT and ERPT.Both PT and BDPT had difficulties in most cases.
The reference in Figure 28 was rendered with PSSMLTwith 1024 samples per pixel. All comparison imageswere rendered in 1.3 minutes. The PT has problemsresolving the caustics that are thrown by the spheres.Also the bent mirror in the background (which haslittle roughness) has a considerably high perceivablevariance. While the BDPT achieves good results onthe portions of the ground (shadows and caustics) thebent mirror also has a high perceivable variance andis not visually better than the result from PT.PSSMLT resolves all aspects better than the other in-tegrator s. MLT and ERPT resolve the ground similarlylike PSSMLT but have problems rendering the bottompart of the bent mirror (Figure 28 top row). This canbe seen as little light peaks all over the bottom of themirror.
The reference in Figure 29 was rendered with PSSMLTwith 1024 samples per pixel. The comparison imageswere rendered in 1.6 minutes. The BDPT renderedthe scene considerably well. If compared to the resultfrom PSSMLT (which achieved the visually best result),there is not much difference. Little drawbacks can be seen in terms of higher perceivable variance for theBDPT.VOLPATH SIMPLE did not achieve good results,the integrator had issues finding the light carryingpaths as well as light scattered inside the volume ofthe participating medium . The PM did not work well,it did not catch the caustics on the ground and it hadproblems resolving scattered light inside the volume.The results from ERPT are behind PSSMLT and BDPTbecause the perceivable variance is even higher but itresolves the caustics and volume visually better thanPM and VOLPATH SIMPLE.
The reference in Figure 30 was rendered with PSSMLTwith 1024 samples per pixel. The comparison imageswere rendered in 2.0 minutes. Like in the previousscenes, the PT has issues resolving caustics and ingeneral light paths that are considerably complex. Thisresults again in high perceivable variance all over thescene. The BDPT achieves relatively smooth resultson the ground portions but not for the bent mirror inthe background (more grainy).PSSMLT again achieves the visually best resultamong all integrator s although MLT resolves the lensesa bit better (Figure 30 MLT middle row). MLT has sev-eral light phenomena/caustics that are not present inthe reference image. While ERPT does a good job forthe lenses and ground portions, it does not resolve thebottom of the mirror, neither does MLT.16igure 28: Reference rendered with PSSMLT (Independent Sampler) at 1024 spp. Comparison images (Indepen-dent Sampler) rendered in 1.3 minutes.Figure 29: Reference rendered with PSSMLT (Independent Sampler) at 1024 spp. Comparison images (Indepen-dent Sampler) rendered in 1.6 minutes.Figure 30: Reference rendered with PSSMLT (Independent Sampler) at 1024 spp. Comparison images (Indepen-dent Sampler) rendered in 2.0 minutes. 17igure 31: Reference rendered with PSSMLT (Independent Sampler) at 1024 spp. Comparison images (Indepen-dent Sampler) rendered in 2.6 minutes.
The reference in Figure 31 was rendered with PSSMLTwith 1024 samples per pixel. The comparison imageswere rendered in 2.6 minutes. The scene lighting inconjunction with the waves on the ground makes thisscene difficult to render. The PT achieves results withhigh perceivable variance. However, in comparison tothe BDPT it occurs to resolve light paths better.PSSMLT has little issues and resolves the causticsrelatively well. PM results in a considerably darkerscene when trying to catch the light and caustics fromthe water, all other parts (the diffuse spheres) are simi-lar to the other results. ERPT achieves the best resultwhen it comes to caustics even though there are lightartifacts all over the water, however, the caustics gener-ally exhibit less perceivable variance than for PSSMLT.
The reference in Figure 32 was rendered with PSSMLTwith 1024 samples per pixel. The comparison imageswere rendered in 3.2 minutes. The VOLPATH integra-tor did not achieve good results, the noise is very high.The PM was used with IRRCACHE but had problemsresolving certain parts as well, especially for caustics.PSSMLT had no problems rendering the scene. Theperceivable variance seems to be the lowest amongall integrator s. MLT results in appropriate causticsas well on the one hand, on the other hand, it showsmany individual light features all over the scene. Alsothe scene overall looks a bit darker than for the other integrator s. ERPT did not create any artifacts but theperceivable variance seems to be still higher than for PSSMLT and MLT.
The reference in Figure 33 was rendered with PSSMLTwith 1024 samples per pixel. The comparison imageswere rendered in 3.4 minutes. The PT shows highperceivable variance in the resulting image. BDPT aswell as PSSMLT delivered very similar results. BDPTonly had more issues resolving the mirror in the back-ground that shows slightly higher perceivable variancethan for PSSMLT (Figure 33 mirror in bottom and midrow).The PM overall resulted in an image with high per-ceivable variance comparable to the result from thePT. The ERPT achieved good results as well and is sim-ilar to the results from BDPT and PSSMLT, however,the scene overall looks slightly blurry. To conclude,the BDPT is probably preferable here because it hasslight benefits in terms of memory usage compared toPSSMLT.
The reference in Figure 34 was rendered with PSSMLTwith 1024 samples per pixel. The comparison imageswere rendered in 3.5 minutes. The PT had troublesrendering the caustics from the smooth glass objecton the left side as well as from the rough glass objecton the right side. In both cases, the perceivable vari-ance is higher compared to other integrator s. BDPTdid a considerably better job at rendering the caustics.However, it also has the same issues when it comesto rendering the interior lighting of the glass material18igure 32: Reference rendered with PSSMLT (Independent Sampler) at 1024 spp. Comparison images (Indepen-dent Sampler) rendered in 3.2 minutes.Figure 33: Reference rendered with PSSMLT (Independent Sampler) at 1024 spp. Comparison images (Indepen-dent Sampler) rendered in 3.4 minutes.Figure 34: Reference rendered with PSSMLT (Independent Sampler) at 1024 spp. Comparison images (Indepen-dent Sampler) rendered in 3.5 minutes. 19nd exhibits high perceivable variance, especially forthe rough glass object.PSSMLT achieved good results overall. It does wellon caustics and the rough glass parts. Yet, the BDPTresolves the caustics a bit better (Figure 34 bottom row).The PSSMLT has a lower perceivable variance for thebottom part of the rough glass (Figure 34 middle row)but the BDPT has a lower perceivable variance for thetop part of the rough glass (Figure 34 top row).The PM exhibits similar perceivable variance likethe PT and is not suitable for this scene. The renderingfrom the ERPT has the lowest perceivable variancefor the rough glass object but exhibits artifacts forthe smooth glass object on the left side. It seems thatPSSMLT achieved the best result overall.
The reference in Figure 34 was rendered with the PTwith 1024 samples per pixel. The comparison imageswere rendered in 2.5 minutes. Only PT, VOLPATH,VOLPATH SIMPLE and PM are able to capture SSSmaterials. The results from the different integrator s arealmost equal. PT, VOLPATH SIMPLE and VOLPATHachieve the same result in terms of visual quality andmemory usage. PM results in a very similar image butit uses slightly more memory for the calculations.
The reference in Figure 36 was rendered with PT(Independent Sampler) with 1024 samples per pixel.The comparison images were rendered in 2.8 minutes.Again the PT, the VOLPATH integrator s and PM areable to capture the SSS materials in a scene. The re-sults from PT, VOLPATH and VOLPATH SIMPLE hadsimilar results. One more closeup visual inspection,the PM seems to have achieved the best results over-all. It has the lowest perceivable variance and it couldresolve the SSS material under the water better thanthe other integrator s. The reference in Figure 37 was rendered with PSSMLTwith 1024 samples per pixel. the comparison imageswere rendered in 2.6 minutes. VOLPATH SIMPLE andVOLPATH achieved similar results, both having highperceivable variance overall however. PSSMLT, MLTand ERPT have similar results as well. The most differ-ence can be seen for the complex glass object (Figure37 middle row) and the thick lens (Figure 37 top row). The results from MLT are generally too dark. The re-sult from ERPT has a better approximation but still hasproblems resolving the complex glass object. Overall,the PSSMLT achieved the best results.
The reference in Figure 38 was rendered with PSSMLTwith 1024 samples per pixel. The comparison imageswere rendered in 2.7 minutes. PT, BDPT, PSSMLT andSPPM achieved very similar results. SPPM deliveredan image that appears sharper than for the other inte-grator s. The results from the PT, BDPT and PSSMLTare slightly blurry. The image rendered with PM isgenerally too bright and the perceivable variance ishigh as well. PSSMLT had no advantage for this scene,the light energy is considerably uniform over the sceneso PT and BDPT are preferable in terms of memoryusage here. SPPM delivers the best result but also hasthe highest memory usage.
The reference in Figure 39 was rendered with PSSMLTwith 1024 samples per pixel. The comparison imageswere rendered in 2.8 minutes. As expected, the PT hadtroubles rendering the scene because of the relativelycomplex light setup. The perceivable variance is con-siderably high, as well as for BDPT which has the sameissues. Yet, BDPT still exhibits slightly lower perceiv-able variance than PT. Surprisingly, PSSMLT also hastroubles with the scene and also exhibits considerablevariance but still has a better visual quality than PTand BDPT.The MLT version was rendered with 300 samples perpixel and stopped when the expected render time wasreached. The ground and wall portions of the scenehave much less perceivable variance than for the other integrator s. However, MLT could not correctly resolvethe interior of the complex glass object (Figure 39 MLTmiddle row). Also it could not resolve the mirror part(Figure 39 top row) like the other integrator s. It occursas if the path depth is too low although it has beenrendered with 32 bounces or the MLT did not haveenough time to sample these areas. ERPT achieved asimilar visual quality like PSSMLT but with slightlyless perceivable variance overall.
The reference in Figure 40 was rendered with PSSMLTwith 1024 samples per pixel. The comparison images20igure 35: Reference rendered with PT (Independent Sampler) at 1024 spp. Comparison images (IndependentSampler) rendered in 2.5 minutes.Figure 36: Reference rendered with PT (Independent Sampler) at 1024 spp. Comparison images (IndependentSampler) rendered in 2.8 minutes. 21igure 37: Reference rendered with PT (Independent Sampler) at 1024 spp. Comparison images (IndependentSampler) rendered in 2.6 minutes.Figure 38: Reference rendered with PSSMLT (Independent Sampler) at 1024 spp. Comparison images (Indepen-dent Sampler) rendered in 2.7 minutes.Figure 39: Reference rendered with PSSMLT (Independent Sampler) at 1024 spp. Comparison images (Indepen-dent Sampler) rendered in 2.8 minutes. 22igure 40: Reference rendered with PSSMLT (Independent Sampler) at 1024 spp. Comparison images (Indepen-dent Sampler) rendered in 2.1 minutes.were rendered in 2.1 minutes. PT, PM and SPPMhad considerable problems catching light paths in thisscene. Especially, in case of PM, the scene looks toodark overall.The results from the BDPT were better than for thePT, but the perceivable variance is still high. PSSMLTresolved the ground of the scene and the caustics fromthe lens relatively well (Figure 40 PSSMLT middle row).However, also PSSMLT had troubles resolving the light-ing within the glass materials.
The reference in Figure 41 was rendered with PSSMLTwith 1024 samples per pixel. The comparison imageswere rendered in 1.8 minutes. Regarding the objects,especially the red sphere and the metal cylinder (Figure41 top row), the PT and PM resulted in images withthe lowest perceivable variance.Other than that, the results from all integrator s arevery similar. Preferable is the PM because it has thelowest perceivable variance overall. However, theshadow of the red sphere gets resolved better withERPT (Figure 41 ERPT top row) than for the other integrator s. The reference in Figure 42 was rendered with PSSMLTwith 1024 samples per pixel. The comparison imageswere rendered in 3.2 minutes. PT again exhibits themost overall perceivable variance of all integrator sbecause of the complex light setup (light coming froma door that is slightly opened). BDPT delivers a better image than PT in terms of variance overall. PSSMLT iscomparable to the result from BDPT but resolves lightpaths a bit better (less perceivable variance) as seen inFigure 42 in the bottom row.The PM had troubles resolving the mirror areawhich results in regions that are too dark and withhigh perceivable variance. ERPT resolves the area inthe left mirror better than PSSMLT (Figure 42 bottomrow). Also the perceivable variance overall is slightlylower with ERPT than with PSSMLT.
The reference in Figure 43 was rendered with PSSMLTwith 1024 samples per pixel. The comparison imageswere rendered in 2.5 minutes. The results are similarto those of the previous scene. PT has little perceiv-able variance on the wall parts of the room (Figure 43PT top and bottom row). BDPT has less perceivablevariance than PT. As in the case of the complex glassobject (Figure 43 middle row), it resolves the lightingin the interior slightly better than PSSMLT. MLT hastroubles resolving the lighting of the interior of thecomplex glass object as well, even more than PSSMLT.Also MLT has a few outliers (bright blotches like in themiddle row on the back wall) spread all over the scene,which are not present for the other results. ERPT hassimilar results like PSSMLT and BDPT but exhibitshigher perceivable variance for the complex glass ob-ject.23igure 41: Reference rendered with PSSMLT (Independent Sampler) at 1024 spp. Comparison images (Indepen-dent Sampler) rendered in 1.8 minutes.Figure 42: Reference rendered with PSSMLT (Independent Sampler) at 1024 spp. Comparison images (Indepen-dent Sampler) rendered in 3.2 minutes.Figure 43: Reference rendered with PSSMLT (Independent Sampler) at 1024 spp. Comparison images (Indepen-dent Sampler) rendered in 2.5 minutes. 24igure 44: Reference rendered with PT (Independent Sampler) at 1024 spp. Comparison images (IndependentSampler) rendered in 2.5 minutes.
The reference in Figure 44 was rendered with PSSMLTwith 1024 samples per pixel. The comparison imageswere rendered in 2.5 minutes. PT, VOLPATH SIMPLE,VOLPATH and PM have very similar results. VOL-PATH SIMPLE has slightly more perceivable varianceoverall than the other results. PM has problems re-solving the glass materials in the scene (Figure 44 PMbottom row), generally they are too dark.
The reference in Figure 45 was rendered with VOL-PATH with 1024 samples per pixel. The comparisonimages were rendered in 3.0 minutes. PT and VOL-PATH has very similar results (because VOLPATH usesPT for surfaces). The perceivable variance is relativelyhigh for the caustics on the ground coming from thewater drops and lenses (Figure 45 middle row). VOL-PATH SIMPLE generally has very similar results likePT and VOLPATH as well but it has troubles renderingthe top of the complex object with the gold material(Figure 45 bottom row), it appears too dark and withhigh perceivable variance. PM achieved very similarresults compared to VOLPATH and PT as well and ithas no obvious advantages or disadvantages exceptfrom the slightly higher memory usage.
The reference in Figure 46 was rendered with VOL-PATH with 1024 samples per pixel. The comparisonimages were rendered in 2.8 minutes. This scene ex-hibits difficult light paths so all of the integrator s haddifficulties rendering the scene. PT, VOLPATH SIMPLEand VOLPATH all show very similar results. However,the scene looks very grainy overall because of the PTnot being capable of finding relevant light paths. Theproblem is, that an SSS material exists in the scene andit cannot be rendered with integrator s like PSSMLTwhich may resolve the light situation considerably bet-ter. The IRRCACHE integrator was used in conjunctionwith PM as well but did not deliver a better result thanthe others. The scene looks darker overall and theperceivable variance is high as well.
In the previous chapter we have seen that the discussed integrator s have different advantages and disadvan-tages depending on the scene setup. In conclusion, wewill recapitulate the most important aspects that cameto light in the evaluation chapter.The PT integrator generally has problems renderingcomplex light conditions, this may result in high per-ceivable variance because the algorithm (randomizedrays) has problems sampling important light paths suf-ficiently. Furthermore, this issue also affects rendering25igure 45: Reference rendered with VOLPATH (Independent Sampler) at 1024 spp. Comparison images(Independent Sampler) rendered in 3.0 minutes.Figure 46: Reference rendered with VOLPATH (Independent Sampler) at 1024 spp. Comparison images(Independent Sampler) rendered in 2.8 minutes. 26f glass materials and caustics – more advanced in-tegrator s like PSSMLT might be the better choice forthat. Interestingly, certain light and material condi-tions may lead to less perceivable variance than BDPT,as is the case in Figure 31, mainly because PT usedfar more spp than BDPT and most of the objects havediffuse materials which are easy to render.In general, BDPT has difficulties rendering translu-cent materials like glass as well. However, it seemsto be the better choice than PT (with exceptions likementioned before). Under certain light and materialconditions, BDPT might come close to the visual qual-ity of PSSMLT, see Figure 42 for an example. Certainconditions can also result in BDPT being able to resolvecaustics slightly better than PSSMLT like in Figure 34.The PSSMLT integrator generally delivers good re-sults when dealing with difficult light paths, as is thecase with translucent materials in conjunction withdiffuse surfaces (for example light going through thewater surface, hitting the ground and going throughthe water again until eventually the camera catchesthe light).MLT generally delivers similar results like PSSMLT,however, it might also render caustics with less per-ceivable variance. For smooth glass materials it alsogenerally has advantages in visual quality compared toPSSMLT. As in the case of Figure 30, MLT may deliverresults with odd behavior (MLT bottom row) which dif-fer considerably from the other results. Figure 32 alsoshows that it might result in glass materials appearingdarker in the rendering, this might come from the timelimitation for the algorithm to converge, a good exam-ple concerning this issue can also be seen in Figure39, where the glass materials are also darker and themirror part is not completely resolved compared to theother results.PM often delivers visual quality that is below theresults from BDPT in the same render time. Glassmaterials also seem to be darker than from other inte-grator s (for instance in Figure 31), this may be becauseof the limited render time. PM converges to the refer-ence when enough photons are stored in the photonmaps, ideally tending to an indefinite amount. As a dis-advantage, PM generally requires considerably morememory than other integrator s, but it delivers goodresults if enough time is available to render the scene.PM might not work well for scenes with participatingmedia like in Figure 29.The ERPT integrator is generally a good choice forscenes, especially for glass materials and complex caus-tics. However, it has difficulties rendering participatingmedia and its visual quality is below the results from PSSMLT and BDPT. Furthermore, it can result in vi-sually blurry renderings, as in the case of Figure 33.Interestingly, as in the case of Figure 34, the roughglass material appears to have the lowest perceivablevariance among the tested integrator s, but the smoothglass material appears to have the highest perceivablevariance.VOLPATH SIMPLE and VOLPATH seem to have, incomparison to other integrator s like PSSMLT, more dif-ficulties rendering participating media . The differencewhen rendering SSS (dipole-based subsurface scatter-ing) materials is not noticeable compared to the resultsfrom PT or PM like in Figure 35, this is expected be-cause VOLPATH is basically a PT with the possibilityto render participating media . SPPM seems not to be agood choice in general, although it might deliver betterresults in rare cases, like in Figure 38.The designed scenes for this paper should showwhere integrator s exhibit large differences in the re-sults. Mentionable are the scenes in Figures 29, 30, 31,32, 34, 39 due to the large variations in the renderings.The scenes are all available in XML format, they canconveniently be loaded and rendered in mitsuba . Addi-tionally, the
Blender files are published, which containthe scene setups and a library containing the linkedobjects. When adding new objects to a scene, it ispreferable to link the blend files instead of appending,so the material parameters can be adjusted from a sin-gle point of reference, but the objects can also be madelocal to test different parameters only in that scene.The scenes have been tested with
Blender mit-suba version 0.5.0 and mitsuba Blender plugin version0.5.1.
Acknowledgments
Research reported in this paper was supported by Aus-trian Science Fund (FWF): ORD 61
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A Appendix
A.1 Physically Based Rendering
A.1.1
Related Work
In this section, historic approaches and developmentswill be presented, concluding with recent techniquesthat are used in the field of Physically Based Rendering(PBR). Early render systems did not have the appro-priate methods and algorithms to synthesize realisticimages. Rendering an image was very costly bothin terms of hardware resources and algorithmic com-plexity. First advancements on a more realistic light-ing approach has been achieved by Turner Whitted[Whi80] by using the idea of ray tracing to computethe distribution of light in scenes in a more realisticway. Another important step towards higher realismwas made by Goral et al. [GTGB84] by investigatingthe light exchange between surfaces in scenes. Thisled to the approach of radiosity in computer graphics,which can compute the distribution of light in a scene.However, algorithms based on radiosity were hard tohandle because of the underlying computations. Af-ter several years of research work on radiosity , pathtracing has been introduced. [Kaj86] Path tracing simulates the distribution of light in ascene with help of
Monte Carlo Integration to approxi-mate the fundamental light transport equation (Lighttransport equation (LTE)). Scenes could be renderedwith an even more physically realistic approach thanever before. However, also path tracing would takea large amount of computation resources because ofthe high complexity of the underlying algorithms, sorendering scenes at that time took long and was costlyin terms of the needed hardware. In following years,more and more research work has been done to im-prove algorithms based on path tracing . [PJH16]Great efforts have been made by Eric Veach [Vea98]in terms of research on
Monte Carlo Integration . He de-veloped bidirectional path tracing as well as
Metropolislight transport which led to huge increases in efficiencyand lower rendering times. [PJH16]Over the years many improvements and new ap-proaches in the field of path tracing -based algorithmsled to a variety of improvements on the integraltools. The following will cover related work on otherdatabases and papers with PBR background.
A.2 Basics of PBR
In the following, the most important aspects of physi-cally based rendering systems will be discussed. Almost29ll of them make use of ray-tracing algorithms thatsimply cast rays into a scene which interact with allthe objects involved [PJH16]. Since PBR aims at real-ism, different combinations of materials and objectsin the scene can result in complex lighting conditionsthat need to be calculated both fast and in high visualquality.A great compendium for the theoretical backgroundand practical implementations for PBR can be foundin the book
Physically based rendering: From theoryto implementation: Third edition , written by Pharr etal. [PJH16]. It delivers the necessary knowledge forimplementing such rendering system. Most of thefollowing information is also extracted from this book.
A.2.1 Light Distribution 1D example
In principle, the amount of light reflected from a pointtowards the camera has to be calculated. To achievethis, all the incident light at this point must be com-puted. Objects in real life usually emit light via dif-ferent shapes, to simplify things the following willcontain just a point light (that uniformly casts lightrays in all directions), which does not exist in realitybut can be used to observe this issue on a more abstractlevel. Figure 47 shows a simple graphical interpreta-tion of a ray from a point light hitting a surface. Theintensity of the light reflection on the surface point p towards the camera is what we want to calculate.[PJH16]Figure 47: Geometric interpretation of light comingfrom a point light, where p denotes the point on thesurface and r denotes the distance to the point light.The angle θ between r and the normal at p denotes theincidence angle of the light. [PJH16]Because light in the real world does not perfectlyreflect on surfaces but is scattered in different direc-tions, there are several models that simulate this effect. Given the information about the location and normalof the intersection point and the location and proper-ties of the light source, the specific material propertiesnow define how the incident light is scattered. Theso called bidirectional reflectance distribution function (Bidirectional reflectance distribution function (BRDF))is often used to define these material properties. Thelight traveling towards the camera from that point hasto be calculated by multiplying the incident light tothe surface point p with the corresponding BRDF ofthe surface. [PJH16] A.2.2 Indirect Light Transport
With the use of rays [Whi80], also indirect reflectionsand transmissions can be simulated. Whitted’s methodand path tracing solve the light transport equation withdifferent accuracy, Whitted ray tracing uses simpli-fied terms for the render equation.
Path tracing solvesthe full equation by sending out many recursive raysper pixel (more on that later on). That means thatat an intersection point another sub-ray will be castto capture light that is incident to that point. Theserecursive steps make sure that the rendered image in-volves all the mutual reflections of the objects in thescene. However, Whitted’s method only accounts forrecursive evaluation of perfect refraction and reflec-tion. [PJH16]
A.2.3 LTE
As mentioned before, the light transport equation (Equation 2) is the fundamental equation that has tobe solved in order to achieve correct results in syn-thesized images. It models all reflections at a pointon a surface, including emission coming directly fromthe surface and the distribution of incoming light atthat point. The fact that physical realism involves tak-ing into account all objects in the scene that radiateor transmit light, the recursive (because of sub-paths) light transport equation has to be solved to achieve global illumination , however this makes the numericalevaluation difficult. [PJH16]One important principle when using the light trans-port equation is energy conservation . In terms of pointson surfaces, the outgoing radiance from that pointmust be equal to the emitted radiance minus the ab-sorbed energy plus the incoming light that is scatteredby the surface. This is derived from the general formulaof the conservation of power (Equation 1.1 [PJH16]),where ϕ o denotes the outgoing energy, ϕ i the incom-ing energy, ϕ e the emitted energy and ϕ a the absorbed30nergy. [PJH16] ϕ o − ϕ i = ϕ e − ϕ a (1)Eventually, the light transport equation for surfaces(Equation 1.2 [PJH16]) is as follows L o ( p , ω o ) = L e ( p , ω o ) + ∫ S f ( p , ω o , ω i ) L i ( p , ω i )| cosθ i | dω i (2)where the first term describes the emitted light andthe integral describes the incoming light that is scat-tered on that surface point. A.2.4 Monte Carlo Integration solves the LTE
The following will give a brief overview on
MonteCarlo Integration , which is fundamental for path trac-ing , since the underlying light transport equation can-not be computed analytically but only numericallyusing this method.
Monte Carlo Integration involves computations thatapproximate the integral of a given function by aver-aging randomly chosen samples. In the context of pathtracing , this idea is applied by letting the algorithmgo over one pixel several times, each time computinga random sample (light path). Statistically, averagingthe different values from different runs will convergeto the correct value. [PJH16]In detail,
Monte Carlo Integration aims at solving anarbitrary integral, in terms of 1D let it be ∫ ba f ( x ) dx .The expected value of the Monte Carlo Estimator E [ F n ] (Equation 1.3 [PJH16]) estimates this integral. E [ F N ] = E (cid:20) b − aN N (cid:213) i = f ( X i ) (cid:21) (3)where X i ∈ [ a , b ] and the probability is uniformlydistributed and N denotes the number of random sam-ples. In order to reduce variance from the integration,the underlying probability density function p ( x ) canbe chosen heuristically to address this issue ( Impor-tance Sampling ). This leads to the adapted estimator(Equation 1.4 [PJH16]). E [ F N ] = E (cid:20) N N (cid:213) i = f ( X i ) p ( X i ) (cid:21) (4)The estimator can easily be used with higher dimen-sions, making it the only practical numerical methodthat converges high dimensional integrals indepen-dently from the dimensionality, that means the size of the dimension does not have impact on the perfor-mance of Monte Carlo Integration .One negative aspect is that the error behaves in-versely proportional to the amount of samples in away that if the error should be halved, four times asmany samples have to be evaluated. Graphically, ap-proximation errors from the integration result in noisypixels that are either too dark or too bright. [PJH16]
A.2.5 Advanced sampling methods
Path tracing was the first algorithm that solves thefull light transport equation numerically. However, itcan lead to partially very grainy images due to highvariance in more complex lighting conditions [PJH16].The following will give a brief overview on more ad-vanced sampling techniques that are generally betterthan pure path tracing in terms of render quality andconvergence time.
Next Event Estimation (NEE)
Next Event Estima-tion is a sampling technique that aims at reducing vari-ance of
Monte Carlo -sampling. Basically, NEE achievesthis by searching for direct light sources at any path in-tersection. This can improve render performance andquality considerably when applied at every surfaceintersection of the path. [KNK + Importance Sampling
Importance Sampling is amethod for
Monte Carlo Integration to reduce varianceand convergence as well. The
Monte Carlo Estimator from Equation 4 has the property that it convergesfaster if the samples are taken from a probability den-sity function that is similar to f ( x ) in the integrand.Graphically, this means, the focus is on areas with high(relevant) values and therefore, calculations are fasterand variance of the image decreases. [PJH16] Bidirectional path tracer (BDPT)
BDPT is an ex-tension to the common path tracing algorithm. It wasdeveloped independently by Lafortune and Willems[LW98] and Veach and Guibas [VG95]. It is called bidi-rectional because it does not only cast rays going outfrom the camera but also from the light sources. Basi-cally, the algorithm knows all intersection points andattempts to connect pairs of them for each camera/lightpath. It then evaluates if a connection between pairsof intersections is not interrupted by another object.If this is the case, the corresponding path is added tothe light estimation. BDPT generally speeds up the31onvergence of the light computation while also deliv-ering less variance with fewer samples per pixel than path tracing . [PJH16]BDPT has the advantage that the search for a rele-vant light source is easier unlike for
Path tracing . Astandard
Path tracer shoots random rays into the scenetrying to find light sources. Because it is very rare tofind light sources with random rays in scenes with dif-ficult light setups (for instance a light that is partiallycovered), resulting images often exhibit high variance.BDPT simplifies this process and generally deliversimages with less variance. The basic differences oflight sampling between
Path tracing and BDPT can beseen in Figure 48.
Metropolis Light Transport, Path Space Metropo-lis Light Transport (MLT)
MLT was first proposedby Veach and Guibas [VG97] in 1997. In contrast tothe other methods, MLT is not based on the
MonteCarlo method, specifically it creates samples that arestatistically correlated. Basically, MLT sequentiallyshoots rays into the scene. Each subsequent ray is amutation of the previous one using
Markov chain tech-niques (the next sample state is dependent on the pre-vious one). The main advantage of this method is thatif a light path with high relevance is found, the follow-ing rays will search for further relevant paths in theneighborhood. The amount of searches in a region istherefore dependent on the relevance of the particularregion in the scene. The basic principle of this methodcan be seen in Figure 48. This means that MLT is con-siderably good for scenes with difficult light situationslike caustics where many light rays are located in smallareas. However, MLT does have performance deficien-cies when it comes to relatively simple and balancedlight conditions. [PJH16]There are several other sampling strategies that havedifferent advantages and disadvantages, however thiswill not be covered in detail. Especially, BDPT andMLT will be interesting related to the scene data setin the next chapter, because the light setups often re-quire appropriate samplers to achieve good results ina reasonable time. Specifically, there will be scenesthat have complex materials and light setups whichcan be easier or more difficult to sample depending onthe chosen integrator .The reason for this is illustrated by a simplified ex-ample showing a difficult scene setup in Figure 48. Itshows the comparisons of the sampling strategies thatwere mentioned previously. The scenes described inthis paper aim at challenging these strategies in orderto understand their differences and examine potential shortcomings and problems. Difficulties in samplingwill later be seen as variance in the renderings, de-pending on the sampling technique, the algorithmsmay give considerably different results.Figure 48: Graphical interpretations of light samplingvia
Path Tracer , Bidirectional Path Tracer and
MetropolisLight Transport . In the case of the