Radomír Vávra

Template-Based Sampling of Anisotropic BRDFs

BRDFs are commonly used to represent given materials’ appearance in computer graphics and related fields. Although, in the recent past, BRDFs have been extensively measured, compressed, and fitted by a variety of analytical models, most research has been primarily focused on simplified isotropic BRDFs. In this paper, we present a unique database of 150 BRDFs representing a wide range of materials; the majority exhibiting anisotropic behavior. Since time‐consuming BRDF measurement represents a major obstacle in the digital material appearance reproduction pipeline, we tested several approaches estimating a very limited set of samples capable of high quality appearance reconstruction. Initially, we aligned all measured BRDFs according to the location of the anisotropic highlights. Then we propose an adaptive sampling method based on analysis of the measured BRDFs. For each BRDF, a unique sampling pattern was computed, given a predefined count of samples. Further, template‐based methods are introduced based on reusing of the precomputed sampling patterns. This approach enables a more efficient measurement of unknown BRDFs while preserving the visual fidelity for the majority of tested materials. Our method exhibits better performance and stability than competing sparse sampling approaches; especially for higher numbers of samples.

Rapid Material Appearance Acquisition Using Consumer Hardware

A photo-realistic representation of material appearance can be achieved by means of bidirectional texture function (BTF) capturing a material’s appearance for varying illumination, viewing directions, and spatial pixel coordinates. BTF captures many non-local effects in material structure such as inter-reflections, occlusions, shadowing, or scattering. The acquisition of BTF data is usually time and resource-intensive due to the high dimensionality of BTF data. This results in expensive, complex measurement setups and/or excessively long measurement times. We propose an approximate BTF acquisition setup based on a simple, affordable mechanical gantry containing a consumer camera and two LED lights. It captures a very limited subset of material surface images by shooting several video sequences. A psychophysical study comparing captured and reconstructed data with the reference BTFs of seven tested materials revealed that results of our method show a promising visual quality. Speed of the setup has been demonstrated on measurement of human skin and measurement and modeling of a glue dessication time-varying process. As it allows for fast, inexpensive, acquisition of approximate BTFs, this method can be beneficial to visualization applications demanding less accuracy, where BTF utilization has previously been limited.

BRDF Slices: Accurate Adaptive Anisotropic Appearance Acquisition

In this paper we introduce unique publicly available dense an isotropic BRDF data measurements. We use this dense data as a reference for performance evaluation of the proposed BRDF sparse angular sampling and interpolation approach. The method is based on sampling of BRDF subspaces at fixed elevations by means of several adaptively-represented, uniformly distributed, perpendicular slices. Although this proposed method requires only a sparse sampling of material, the interpolation provides a very accurate reconstruction, visually and computationally comparable to densely measured reference. Due to the simple slices measurement and methods robustness it allows for a highly accurate acquisition of BRDFs. This in comparison with standard uniform angular sampling, is considerably faster yet uses far less samples.

Effective Acquisition of Dense Anisotropic BRDF

The development of novel analytical BRDF models, as well as adaptive BRDF sampling approaches, rely on the appropriate BRDF measurement of real materials. The quality of measurements is even more critical when it comes to accurately representing anisotropic materials where the character of anisotropy is unknown (locations of anisotropic highlights, their width, shape, etc.). As currently there is a lack of dense yet noise-free BRDF anisotropic datasets, we introduce such unique measurements of three anisotropic fabric materials. In this paper we discuss a method of dense BRDF data acquisition, post processing, missing values interpolation, and analyze properties of the datasets. Our results are compared with photographs, dense data fitted and generated by two state-of-the art anisotropic BRDF models, and alternative measurements available.

Fast method of sparse acquisition and reconstruction of view and illumination dependent datasets

Although computer graphics uses measured view and illumination dependent data to achieve realistic digital reproduction of real-world material properties, the extent of their utilization is currently limited by a complicated acquisition process. Due to the high dimensionality of such data, the acquisition process is demanding on time and resources. Proposed is a method of approximate reconstruction of the data from a very sparse dataset, obtained quickly using inexpensive hardware. This method does not impose any restrictions on input datasets and can handle anisotropic, non-reciprocal view and illumination direction-dependent data. The methods performance was tested on a number of isotropic and anisotropic apparent BRDFs, and the results were encouraging. The method performs better than the uniform sampling of a comparable sample count and has three main benefits: the sparse data acquisition can be done quickly using inexpensive hardware, the measured material does not need to be extracted or removed from its environment, and the entire process of data reconstruction from the sparse samples is quick and reliable. Finally, the ease of sparse dataset acquisition was verified in measurement experiments with three materials, using a simple setup of a consumer camera and a single LED light. The proposed method has also shown promising performance when applied to sparse measurement and reconstruction of BTFs, mainly for samples with a lower surface height variation. Our approach demonstrates solid performance across a wide range of view and illumination dependent datasets, therefore creating a new opportunity for development of time and cost-effective portable acquisition setups. Graphical abstractDisplay Omitted Author-HighlightsMethod for fast and inexpensive acquisition of anisotropic non-reciprocal BRDFs.Fast and continuous measurement of BRDF slices by a consumer camera and light.Fast reconstruction of anisotropic BRDFs and BTFs from the measured slices.

Adaptive highlights stencils for modeling of multi-axial BRDF anisotropy

Directionally dependent anisotropic material appearance phenomenon is widely represented using bidirectional reflectance distribution function (BRDF). This function needs in practice either reconstruction of unknown values interpolating between sparse measured samples or requires data fidelity preserving compression forming a compact representation from dense measurements. Both properties can be, to a certain extent, preserved by means of analytical BRDF models. Unfortunately, the number of anisotropic BRDF models is limited, and moreover, most require either a demanding iterative optimization procedure dependent on proper initialization or the user setting parameters. Most of these approaches are challenged by the fitting of complex anisotropic BRDFs. In contrast, we approximate BRDF anisotropic behavior by means of highlight stencils and derive a novel BRDF model that independently adapts such stencils to each anisotropic mode present in the BRDF. Our model allows for the fast direct fitting of parameters without the need of any demanding optimization. Furthermore, it achieves an encouraging, expressive visual quality as compared to rival solutions that rely on a similar number of parameters. We thereby ascertain that our method represents a promising approach to the analysis and modeling of complex anisotropic BRDF behavior.

Registration of multi-view images of planar surfaces

This paper presents a novel image-based registration method for high-resolution multi-view images of a planar material surface. Contrary to standard registration approaches, this method aligns images based on a true plane of the materials surface and not on a plane defined by registration marks. It combines the camera calibration and the iterative fitting of desired position and slant of the surface plane, image re-registration, and evaluation of the surface alignment. To optimize image compression performance, we use an error of a compression method as a function evaluating the registration quality. The proposed method shows encouraging results on example visualizations of view- and illumination-dependent textures. In addition to a standard multi-view data registration approach, it provides a better alignment of multi-view images and thus allows more detailed visualization using the same compressed parameterization size.

Minimal sampling for effective acquisition of anisotropic BRDFs

BRDFs are commonly used for material appearance representation in applications ranging from gaming and the movie industry, to product design and specification. Most applications rely on isotropic BRDFs due to their better availability as a result of their easier acquisition process. On the other hand, anisotropic BRDF due to their structure‐dependent anisotropic highlights, are more challenging to measure and process. This paper thus leverages the measurement process of anisotropic BRDF by representing such BRDF by the collection of isotropic BRDFs. Our method relies on an anisotropic BRDF database decomposition into training isotropic slices forming a linear basis, where appropriate sparse samples are identified using numerical optimization. When an unknown anisotropic BRDF is measured, these samples are repeatably captured in a small set of azimuthal directions. All collected samples are then used for an entire measured BRDF reconstruction from a linear isotropic basis. Typically, below 100 samples are sufficient for the capturing of main visual features of complex anisotropic materials, and we provide a minimal directional samples to be regularly measured at each sample rotation. We conclude, that even simple setups relying on five bidirectional samples (maximum of five stationary sensors/lights) in combination with eight rotations (rotation stage for specimen) can yield a promising reconstruction of anisotropic behavior. Next, we outline extension of the proposed approach to adaptive sampling of anisotropic BRDF to gain even better performance. Finally, we show that our method allows using standard geometries, including industrial multi‐angle reflectometers, for the fast measurement of anisotropic BRDFs.

Predicting Visual Perception of Material Structure in Virtual Environments

One of the most accurate yet still practical representation of material appearance is the Bidirectional Texture Function (BTF). The BTF can be viewed as an extension of Bidirectional Reflectance Distribution Function (BRDF) for additional spatial information that includes local visual effects such as shadowing, interreflection, subsurface‐scattering, etc. However, the shift from BRDF to BTF represents not only a huge leap in respect to the realism of material reproduction, but also related high memory and computational costs stemming from the storage and processing of massive BTF data. In this work, we argue that each opaque material, regardless of its surface structure, can be safely substituted by a BRDF without the introduction of a significant perceptual error when viewed from an appropriate distance. Therefore, we ran a set of psychophysical studies over 25 materials to determine so‐called critical viewing distances, i.e. the minimal distances at which the material spatial structure (texture) cannot be visually discerned. Our analysis determined such typical distances typical for several material categories often used in interior design applications. Furthermore, we propose a combination of computational features that can predict such distances without the need for a psychophysical study. We show that our work can significantly reduce rendering costs in applications that process complex virtual scenes.

BRDF Interpolation using Anisotropic Stencils

Fast and reliable measurement of material appearance is crucial for many applications ranging from virtual prototyping to visual quality control. The most common appearance representation is BRDF capturing illuminationand viewing-dependent reflectance. One of the approaches to rapid BRDF measurement captures its subspace, using so called slices, by continuous movements of a light and camera in azimuthal directions, while their elevations remain fixed. This records set of slices in the BRDF space while remaining data are unknown. We present a novel approach to BRDF reconstruction based on a concept of anisotropic stencils interpolating values along predicted locations of anisotropic highlights. Our method marks an improvement over the original linear interpolation method, and thus we ascertain it to be a promising variant of interpolation from such sparse yet very effective measurements. Introduction Efficient material appearance acquisition and representation is one of the ultimate goals in computer graphics. Since the appearance acquisition process demands considerable time and resources, the introduction of more efficient measurement methods is a must. As such approaches rely on a very limited collection of reflectance samples, a reconstruction of the missing non-measured values has to be applied. This paper builds on our previously published appearance measurement based on BRDF slices [1]; however, the original reconstruction method is further extended using the concept of anisotropic stencils. In this paper we study global material reflectance represented by the Bidirectional Reflectance Distribution Function (BRDF) as introduced by Nicodemus et al. [2]. It describes the ratio of energy reflected by material for a certain combination of incoming and outgoing directions. When we assume the separate processing of color channels, the anisotropic BRDF is a four-dimensional function B(θi,φi,θv,φv), whereas the isotropic BRDF is merely three-dimensional, i.e., B(θi,θv, |φi−φv|). The four dimensional anisotropic BRDF can be parameterized by two vectors specified by θ elevation and φ azimuthal angles. The vectors of illumination direction ωi = (θi,φi) = [xi,yi,zi] and view direction ωv = (θv,φv) = [xv,yv,zv]. Anisotropic BRDF unfolded into 2D image is shown in Fig. 1-left. The image consists of toroidal subimages representing azimuthally-dependent (φi,φv) reflectance behavior for fixed view and illumination elevations (θi,θv). Related Work Most BRDF related research is concentrated on isotropic BRDF due to their lower dimensionality and better availability via the MERL database [3]; therefore until recently [4], anisotropic BRDFs were used only sporadically. Although one can directly use recent anisotropic BRDF models for fitting sparse anisotropic Figure 1. The 4D BRDF unfolding into 2D image (left), diagonal (blue) and axial (red) slices in a toroidal BRDF subspace (right). measurements and reconstruction of the underlying BRDF [5], [6], the final result depends heavily either on the selection of initial parameters or on the expert knowledge of material structure and its physical properties. This is even more difficult when multiple anisotropy modes are present. BRDF Slices Therefore, we use the concept of BRDF slices first introduced in [1]. It suggests the reconstruction of each toroidal BRDF subspace (subimage) by means of two slices in azimuthal space as shown in Fig. 1-right. The axial slice sA (shown as red) is measured using rotation of the mutually fixed light and sensor around the sample, while the diagonal slice sD data (shown as blue) is obtained by mutually opposed movements of the light and sensor relative to the sample. Both the camera and light travel full circle around the sample and return to the initial position. This can be formalized using the following equations sA,θi,θv,α (φv) = B(θi,φi = φv−α,θv,φv), (1) sD,θi,θv,β (φv) = B(θi,φi = 2π−φv +β ,θv,φv). where α and β are initial azimuthal differences between directions to camera and light. This method was further generalized to more slices in [7]. Slices for Fast BRDF Measurement The main advantage of BRDF slices is that they can be captured by a continuous rotation of arms holding camera and light, which significantly reduces acquisition time of the appearance data. This was practically shown in [8], where an approximate BRDF/BTF acquisition setup was introduced based on a simple, affordable mechanical gantry containing a consumer camera and two LED lights. Depiction of the initial prototype setup and its ©2016 Society for Imaging Science and Technology IS&T International Symposium on Electronic Imaging 2016 Measuring, Modeling, and Reproducing Material Appearance 2016 MMRMA-356.1 (a) (b) Figure 2. Measurement devices: (a) an initial proof-of-concept device build from a toy-construction set [8], and (b) a fully automatic prototype of a commercial solution. subsequent fully automatic successor are shown in Fig. 2. The device is portable and can be folded down to luggage size. (a) (b) (c) (d) reference data 8 slices reconstruction interpolation (B) Figure 3. A principle of entire BRDF reconstruction from four recorded subspaces [1]: (a) the reference, (b) sparse-sampling of eight slices, (c) reconstructions of elevations where the slices were measured, (d) missing data interpolation. It captures a very limited subset of material surface images by shooting several video sequences in less than four minutes. The BRDF space is sampled only sparsely and the majority of its values are unmeasured. The missing data reconstruction method presented in [7] allows for a fast, inexpensive, acquisition of approximate BRDFs/BTFs (Fig. 3) from two slices per subspace; however, as it uses only a constrained linear interpolation method [1], [7], it provides only an approximate reconstruction of appearance representation as shown in Fig. 4. This effect is most apparent at subspaces with significant difference between illumination and viewing angles, i.e., |θi− θv| > 45 . The anisotropic highlights at such elevations are not perpendicular to the slices and the original orthogonal linear projection method [7] cannot provide proper results. BRDF subspace reconstruction θi/θv = 30/75 o [7] Figure 4. A BRDF subspace reconstruction error for |θi−θv|= 45 . Our Contribution Therefore, in this paper we strive to improve BRDF reconstruction from two slices per subspace. We build on a recent paper [9] predicting locations of anisotropic highlights in the BRDF space. The locations of anisotropic highlights can be predicted [10] on directional surface elements laying in planes orthogonal to the bisector (often denoted as half-way direction ωh = ωi+ωv ||ωi+ωv|| = (θh,φh)) of directions of incidence and reflectance as proposed in [11]. Therefore, anisotropic highlights can be predicted at directions of the bisector orthogonal to the detected anisotropy axis of the material u = [sinφh,cosφh,0], i.e., ωh ·u = 0. An example of predicted locations of anisotropic highlights are shown in Fig. 5, BRDFs and their rendering for four different anisotropy alignment angles φh are shown side-by-side with prediction of locations of one of the anisotropic highlights in directional space. The technique of anisotropic highlights (so called anisotropic stencils) prediction was successfully applied to the efficient modeling of highly anisotropic BRDFs featuring multi-axial anisotropy [12]. The main advantage of such a model is its extremely fast and reliable fitting of anisotropic highlights without the need of using iterative optimization techniques. In the following section we outline a BRDF data interpolation method based on anisotropic stencils, i.e., benefiting from prior analytical knowledge of an anisotropic highlights location. Proposed Interpolation Method Our interpolation method is based on the observation that BRDF values are almost constant along azimuthal angle φh of half-way direction ωh. Therefore, each reconstructed point P in the BRDF subspace can be interpolated from the point on diagonal slice (A) and the point on axial slice (B) with the same φh as shown in Fig. 6-right. We will derive equations to find coordinates in azimuthal space (φi,φv) for both points. First, let us remind basic equations for conversions between the spherical and Cartesian coordinates: x = sin(θ) · cos(φ), θ = arccos(z) y = sin(θ) · sin(φ), φ = arctan ( y x ) z = cos(θ) . (2) ©2016 Society for Imaging Science and Technology IS&T International Symposium on Electronic Imaging 2016 Measuring, Modeling, and Reproducing Material Appearance 2016 MMRMA-356.2 (a) rendering (b) BRDF (c) stencils