Fatih Calakli

SSD: Smooth Signed Distance Surface Reconstruction

We introduce a new variational formulation for the problem of reconstructing a watertight surface defined by an implicit equation, from a finite set of oriented points; a problem which has attracted a lot of attention for more than two decades. As in the Poisson Surface Reconstruction approach, discretizations of the continuous formulation reduce to the solution of sparse linear systems of equations. But rather than forcing the implicit function to approximate the indicator function of the volume bounded by the implicit surface, in our formulation the implicit function is forced to be a smooth approximation of the signed distance function to the surface. Since an indicator function is discontinuous, its gradient does not exist exactly where it needs to be compared with the normal vector data. The smooth signed distance has approximate unit slope in the neighborhood of the data points. As a result, the normal vector data can be incorporated directly into the energy function without implicit function smoothing. In addition, rather than first extending the oriented points to a vector field within the bounding volume, and then approximating the vector field by a gradient field in the least squares sense, here the vector field is constrained to be the gradient of the implicit function, and a single variational problem is solved directly in one step. The formulation allows for a number of different efficient discretizations, reduces to a finite least squares problem for all linearly parameterized families of functions, and does not require boundary conditions. The resulting algorithms are significantly simpler and easier to implement, and produce results of quality comparable with state‐of‐the‐art algorithms. An efficient implementation based on a primal‐graph octree‐based hybrid finite element‐finite difference discretization, and the Dual Marching Cubes isosurface extraction algorithm, is shown to produce high quality crack‐free adaptive manifold polygon meshes.

One-shot scanning using De Bruijn spaced grids

In this paper we present a new “one-shot” method to reconstruct the shape of dynamic 3D objects and scenes based on active illumination. In common with other related prior-art methods, a static grid pattern is projected onto the scene, a video sequence of the illuminated scene is captured, a shape estimate is produced independently for each video frame, and the one-shot property is realized at the expense of space resolution. The main challenge in grid-based one-shot methods is to engineer the pattern and algorithms so that the correspondence between pattern grid points and their images can be established very fast and without uncertainty. We present an efficient one-shot method which exploits simple geometric constraints to solve the correspondence problem. We also introduce De Bruijn spaced grids, a novel grid pattern, and show with strong empirical data that the resulting scheme is much more robust compared to those based on uniform spaced grids.

Robust one-shot 3D scanning using loopy belief propagation

A structured-light technique can greatly simplify the problem of shape recovery from images. There are currently two main research challenges in design of such techniques. One is handling complicated scenes involving texture, occlusions, shadows, sharp discontinuities, and in some cases even dynamic change; and the other is speeding up the acquisition process by requiring small number of images and computationally less demanding algorithms. This paper presents a “one-shot” variant of such techniques to tackle the aforementioned challenges. It works by projecting a static grid pattern onto the scene and identifying the correspondence between grid stripes and the camera image. The correspondence problem is formulated using a novel graphical model and solved efficiently using loopy belief propagation. Unlike prior approaches, the proposed approach uses non-deterministic geometric constraints, thereby can handle spurious connections of stripe images. The effectiveness of the proposed approach is verified on a variety of complicated real scenes.

High Resolution Surface Reconstruction from Multi-view Aerial Imagery

This paper presents a novel framework for surface reconstruction from multi-view aerial imagery of large scale urban scenes, which combines probabilistic volumetric modeling with smooth signed distance surface estimation, to produce very detailed and accurate surfaces. Using a continuous probabilistic volumetric model which allows for explicit representation of ambiguities caused by moving objects, reflective surfaces, areas of constant appearance, and self-occlusions, the algorithm learns the geometry and appearance of a scene from a calibrated image sequence. An online implementation of Bayesian learning precess in GPUs significantly reduces the time required to process a large number of images. The probabilistic volumetric model of occupancy is subsequently used to estimate a smooth approximation of the signed distance function to the surface. This step, which reduces to the solution of a sparse linear system, is very efficient and scalable to large data sets. The proposed algorithm is shown to produce high quality surfaces in challenging aerial scenes where previous methods make large errors in surface localization. The general applicability of the algorithm beyond aerial imagery is confirmed against the Middlebury benchmark.

SSD-C: Smooth Signed Distance Colored Surface Reconstruction

In this chapter we address the problem of reconstructing the surface geometry, topology, and color map of a 3D scene from a finite set of colored oriented points. These data sets are nowadays obtained using a variety of techniques, including multi-view stereo reconstruction methods from multiple 2D images. We describe a novel variational method which reduces the problem to the solutions of sparse systems of linear equations. We first use the point positions and orientation vectors to reconstruct the geometry and topology of a watertight surface represented as an adaptively tessellated polygon mesh. The method then smoothly extrapolates the color information from the points to the surface. Experimental evidence is presented to show that the resulting method produces high quality polygon meshes with smooth color maps which accurately approximate the source colored oriented points.

Unsynchronized structured light

Various Structured Light (SL) methods are used to capture 3D range images, where a number of binary or continuous light patterns are sequentially projected onto a scene of interest, while a digital camera captures images of the illuminated scene. All existing SL methods require the projector and camera to be hardware or software synchronized, with one image captured per projected pattern. A 3D range image is computed from the captured images. The two synchronization methods have disadvantages, which limit the use of SL methods to niche industrial and low quality consumer applications. Unsynchronized Structured Light (USL) is a novel SL method which does not require synchronization of pattern projection and image capture. The light patterns are projected and the images are captured independently, at constant, but possibly different, frame rates. USL synthesizes new binary images as would be decoded from the images captured by a camera synchronized to the projector, reducing the subsequent computation to standard SL. USL works both with global and rolling shutter cameras. USL enables most burst-mode-capable cameras, such as modern smartphones, tablets, DSLRs, and point-and-shoots, to function as high quality 3D snapshot cameras. Beyond the software, which can run in the devices, a separate SL Flash, able to project the sequence of patterns cyclically, during the acquisition time, is needed to enable the functionality.

Characterizing a Debris Field Using Digital Mosaicking and CAD Model Superimposition from Underwater Video

Abstract Identifying submerged objects is critical for several disciplines such as marine archaeology and search and rescue. However, identifying objects in underwater searches presents many challenges, particularly if the only data available to analyze is poor-quality video where the videographer did not plan for photogrammetric techniques to be utilized. In this paper, we discuss the use of adaptive sampling of the underwater video to extract sharp still images for stitching and analysis, and creating mosaicked images by identifying and matching local scale-invariant feature transform features using computationally efficient algorithms. Computer aided design models of suspected aircraft components were superimposed, and a feature common in multiple mosaicked images was used to identify a common feature between purported objects to assess goodness of fit. The superimposition method was replicated using landing gear from a reference aircraft and a rope of known dimensions, and favorably compared against the remotely operated vehicle (ROV) analysis results.

Identification of a putative man-made object from an underwater crash site using CAD model superimposition

In order to identify an object in video, a comparison with an exemplar object is typically needed. In this paper, we discuss the methodology used to identify an object detected in underwater video that was recorded during an investigation into Amelia Earharts purported crash site. A computer aided design (CAD) model of the suspected aircraft component was created based on measurements made from orthogonally rectified images of a reference aircraft, and validated against historical photographs of the subject aircraft prior to the crash. The CAD model was then superimposed on the underwater video, and specific features on the object were geometrically compared between the CAD model and the video. This geometrical comparison was used to assess the goodness of fit between the purported object and the object identified in the underwater video.