| Oren, M., Nayar, S.K. A theory of specular surface geometry International Journal of Computer Vision 1996 (24):105-124 [pdf] |
| Atheoretical framework is introduced for the perception of specular surface geometry.Whenan observer moves in three-dimensional space, real scene features such as surface markings remain stationary with respect to the surfaces they belong to. In contrast, a virtual feature which is the specular reflection of a real feature, travels on the surface. Based on the notion of caustics, a feature classification algorithm is developed that distinguishes real and virtual features from their image trajectories that result from observer motion. Next, using support functions of curves, a closed-form relation is derived between the image trajectory of a virtual feature and the geometry of the specular surface it travels on. It is shown that, in the 2D case, where camera motion and the surface profile are coplanar, the profile is uniquely recovered by tracking just two unknown virtual features. Finally, these results are generalized to the case of arbitrary 3D surface profiles that are traveled by virtual features when camera motion is not confined to a plane. This generalization includes a number of mathematical results that substantially enhance the present understanding of specular surface geometry. An algorithm is developed that uniquely recovers 3D surface profiles using a single virtual feature tracked from the occluding boundary of the object. All theoretical derivations and proposed algorithms are substantiated by experiments. |
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| Faugeras, O.D., Luong, Q.-T. , Maybank, S.J. Camera Self-Calibration: Theory and Experiments 1992 :321-334 [html] |
| The problem of finding the internal orientation of a camera (camera calibration) is extremely important for practical applications. In this paper a complete method for calibrating a camera is presented. In contrast with existing methods it does not require a calibration object with a known 3D shape. The new method requires only point matches from image sequences. It is shown, using experiments with noisy data, that it is possible to calibrate a camera just by pointing it at the environment... |
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| Riesenhuber, M., Poggio, T. Computational Models of Object Recognition in Cortex: A Review 2000 [pdf] |
| Review des principales tendances dans les théories de reconnaissance d'objet: d'une part les théories centrées sur l'extraction de données structurées indépendantes du point de vue, d'autre part les théories centrées sur l'utilisation en parallèle d'une collection de vues de différents points de vue, dans une approche soit feedforward soit top-down (avec hypothèses, tests, etc). Les études biologiques semblent indiquer que le CNS humain fonctionne avec une collection de vues et en feedforward. |
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| Olver, J.P., Sapiro, G., Tannenbaum, A. Differential Invariant Signatures and Flows in Computer Vision: A Symmetry Group Approach 1993 [html] |
| Computer vision deals with image understanding at various levels. At the low level, it addresses issues such us planar shape recognition and analysis. Some classical results on differential invariants associated to planar curves are relevant to planar object recognition under different views and partial occlusion, and recent results concerning the evolution of planar shapes under curvature controlled diffusion have found applications in geometric shape decomposition, smoothing, and analysis, as well as in other image processing applications. In this work we first give a modern approach to the theory of differential invariants, describing concepts like Lie theory, jets, and prolongations. Based on this and the theory of symmetry groups, we present a high level way of defining invariant geometric flows for a given Lie group. We then analyze in detail different subgroups of the projective group, which are of special interest for computer vision. We classify the corresponding invariant flows and show that the geometric heat flow is the simplest possible one. This uniqueness result, together with previously reported results which we review in this paper, confirms the importance of this class of flows. |
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| Tarel, J.-P. Global 3D Planar Reconstruction with Uncalibrated Cameras and Rectified Stereo Geometry Machine Graphics \& Vision 1997 (6)4:393-418 [html] |
| L'idée de la reconstruction 3D par patches, et de prendre des régions planaires comme éléments de base à associer sur les images stéréo, au lieu d'associer des points. La transformation des régions est connue, est donc en intégrant les équations sur les surfaces on obtient des estimations plus robustes. |
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| Gros, P. Introduction géométrique à la vison par ordinateur 2000 |
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| Lee, D.D., Seung, H.S. Learning the Parts of Objects by Non-negative Matrix Factorization Nature 1999 (401):788 [pdf] |
| Is perception of the whole based on perception of its parts? There is psychological and physiological evidence for parts-based representations in the brain, and certain computational theories of object recognition rely on such representations. But little is known about how brains or computers might learn the parts of objects. Here we demonstrate an algorithm for non-negative matrix factorization that is able to learn parts of faces and semantic features of text. This is in contrast to other methods, such as principal components analysis and vector quantization, that learn holistic, not parts-based, representations. Non-negative matrix factorization is distinguished from the other methods by its use of non-negativity constraints. These constraints lead to a parts-based representation because they allow only additive, not subtractive, combinations. When non-negative matrix factorization is implemented as a neural network, parts-based representations emerge by virtue of two properties: the firing rates of neurons are never negative and synaptic strengths do not change sign. |
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| Nayar, S.K., Xi-Sheng, F., Boult, T. Separation of reflection components using color and polarization International Journal of Computer Vision 1997 (21)3:163-186 [pdf] |
| Specular reflections and interreflections produce strong highlights in brightness images. These highlights can cause vision algorithms for segmentation, shape from shading, binocular stereo, and motion estimation to produce erroneous results. A technique is developed for separating the specular and diffuse components of reflection from images. The approach is to use color and polarization information, simultaneously, to obtain constraints on the reflection components at each image point. Polarization yields local and independent estimates of the color of specular reflection. The result is a linear subspace in color space in which the local diffuse component must lie. This subspace constraint is applied to neighboring image points to determine the diffuse component. In contrast to previous separation algorithms, the proposed method can handle highlights on surfaces with substantial texture, smoothly varying diffuse reflectance, and varying material properties. The separation algorithm is applied to several complex scenes with textured objects and strong interreflections. The separation results are then used to solve three problems pertinent to visual perception; determining illumination color, estimating illumination direction, and shape recovery. |
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