Shape from shading and photometric stereo are two fundamental problems in computer vision aimed at reconstructing surface depth given either a single image taken under a known light source or multiple images taken under different illuminations from the same viewing angle. Whereas the former uses partial differential equation techniques to solve the image irradiance equation, the latter can be expressed as a linear system of equations in surface derivatives when three or more images are given. Therefore, it seems that current photometric stereo techniques do not extract all possible depth information from each image by itself. Extending our previous results on this problem, we consider the more realistic perspective projection of surfaces during the photographic process. Under this assumption, there is a unique weak solution (Lipschitz continuous) to the problem at hand, solving the well-known convex/concave ambiguity of the shape from shading problem. The main contribution of this paper is based on a new differential approach for multi-image photometric stereo. Most of the existing works on this topic do not directly address this problem. The common approach is to estimate the gradient field of the surface by minimizing some functional and integrate it afterwards to find the depth and hence the geometry of the object. Our new differential approach allows us to solve the problem directly, while dealing with images having missing parts. The mathematical well-posedness of the new formulation allows a fast numerical algorithm based on a combination of fast marching and fast sweeping methods.

Shape from shading (SFS) is one of the most fundamental problems in Computer Vision: reconstruction of the three-dimensional (3D) shape of photographed objects given a single input image. Image formation is then modelled based on assumptions on illumination and light reflectance. Solving the 3D shape from the model is useful for many applications. SFS has been extended, for example, to several input images of the same scene taken under different lighting conditions, known as photometric stereo. The aim of the session is to introduce state-of-the-art models and algorithms in the field, and to discuss future directions of research.

Photometric stereo is a fundamental approach in computer vision. At its core lies a set of image irradiance equations each taken with a different illumination. The vast majority of studies in this field have assumed orthography as the projection model. This paper re-examines the basic set of equations of photometric stereo, under an assumption of perspective projection. We show that the resulting system is linear (as is the case under the orthographic model; Nevertheless, the unknowns are different in the perspective case). We then suggest a simple reconstruction algorithm based on the perspective formulae, and compare it to its orthographic counterpart on synthetic as well as real images. This algorithm obtained lower error rates than the orthographic one in all of the error measures. These findings strengthen the hypothesis that a more realistic set of assumptions, the perspective one, improves reconstruction significantly.

Shape-from-shading (SFS) is a fundamental problem in computer vision. The vast majority of research in this field have assumed orthography as its projection model. This paper reexamines the basis of SFS, the image irradiance equation, under an assumption of perspective projection. The paper also shows that the perspective image irradiance equation depends merely on the natural logarithm of the depth function (and not on the depth function itself), and as such it is invariant to scale changes of the depth function. We then suggest a simple reconstruction algorithm based on the perspective formula, and compare it to existing orthographic SFS algorithms. This simple algorithm obtained lower error rates than legacy SFS algorithms, and equated with and sometimes surpassed state-of-the-art algorithms. These findings lend support to the assumption that transition to a more realistic set of assumptions improves reconstruction significantly.

Detection of feature points in images is an important preprocessing stage for many algorithms in computer vision. We address the problem of detection of feature points in video sequences of 3D scenes, which could be mainly used for obtaining scene correspondence. The main feature we use is the zero crossing of the intensity gradient argument. We analytically show that this local feature corresponds to specific constraints on the local 3D geometry of the scene, thus ensuring that the detected points are based on real 3D features. We present a robust algorithm that tracks the detected points along a video sequence, and suggest some criteria for quantitative evaluation of such algorithms. These criteria serve in a comparison of the suggested operator with two other feature trackers. The suggested criteria are generic and could serve other researchers as well for performance evaluation of stable point detectors.

This paper presents biological evidence for camouflage breaking using the convexity of the intensity function. Some animals use apatetic coloring especially to prevent their detection by gray-level convexity. This implies that other animals might be able to break camouflage based on gray-level convexity. We demonstrate the effectiveness of convexity-based camouflage breaking using an operator ("D/sub arg/") for detection of 3D convex or concave gray levels. Its high robustness and the biological motivation make D/sub arg/ particularly suitable for camouflage breaking. As will be demonstrated, the operator is able to break very strong camouflage, which might delude even human viewers. Being nonedge-based, the performance of the operator is juxtaposed with that of a representative edge-based operator in the task of camouflage breaking. Better performance is achieved by D/sub arg/ for animal as well as military camouflage breaking.