Algebraic Functions For Recognition

In the general case, a trilinear relationship between three perspective views is shown to exist. The trilinearity result is shown to be of much practical use in visual recognition by alignment --- yielding a direct method that cuts through the computations of camera transformation, scene structure and epipolar geometry. The proof of the central result may be of further interest as it demonstrates certain regularities across homographies of the plane and introduces new view invariants. Experiments on simulated and real image data were conducted, including a comparative analysis with epipolar intersection and the linear combination methods, with results indicating a greater degree of robustness in practice and a higher level of performance in re-projection tasks.

Surface Reflectance Estimation and Natural Illumination Statistics

Humans recognize optical reflectance properties of surfaces such as metal, plastic, or paper from a single image without knowledge of illumination. We develop a machine vision system to perform similar recognition tasks automatically. Reflectance estimation under unknown, arbitrary illumination proves highly underconstrained due to the variety of potential illumination distributions and surface reflectance properties. We have found that the spatial structure of real-world illumination possesses some of the statistical regularities observed in the natural image statistics literature. A human or computer vision system may be able to exploit this prior information to determine the most likely surface reflectance given an observed image. We develop an algorithm for reflectance classification under unknown real-world illumination, which learns relationships between surface reflectance and certain features (statistics) computed from a single observed image. We also develop an automatic feature selection method.

How do Humans Determine Reflectance Properties under Unknown Illumination?

Under normal viewing conditions, humans find it easy to distinguish between objects made out of different materials such as plastic, metal, or paper. Untextured materials such as these have different surface reflectance properties, including lightness and gloss. With single isolated images and unknown illumination conditions, the task of estimating surface reflectance is highly underconstrained, because many combinations of reflection and illumination are consistent with a given image. In order to work out how humans estimate surface reflectance properties, we asked subjects to match the appearance of isolated spheres taken out of their original contexts. We found that subjects were able to perform the task accurately and reliably without contextual information to specify the illumination. The spheres were rendered under a variety of artificial illuminations, such as a single point light source, and a number of photographically-captured real-world illuminations from both indoor and outdoor scenes. Subjects performed more accurately for stimuli viewed under real-world patterns of illumination than under artificial illuminations, suggesting that subjects use stored assumptions about the regularities of real-world illuminations to solve the ill-posed problem.

Recognition of Surface Reflectance Properties from a Single Image under Unknown Real-World Illumination

This paper describes a machine vision system that classifies reflectance properties of surfaces such as metal, plastic, or paper, under unknown real-world illumination. We demonstrate performance of our algorithm for surfaces of arbitrary geometry. Reflectance estimation under arbitrary omnidirectional illumination proves highly underconstrained. Our reflectance estimation algorithm succeeds by learning relationships between surface reflectance and certain statistics computed from an observed image, which depend on statistical regularities in the spatial structure of real-world illumination. Although the algorithm assumes known geometry, its statistical nature makes it robust to inaccurate geometry estimates.

Sparse Representations for Fast, One-Shot Learning

Humans rapidly and reliably learn many kinds of regularities and generalizations. We propose a novel model of fast learning that exploits the properties of sparse representations and the constraints imposed by a plausible hardware mechanism. To demonstrate our approach we describe a computational model of acquisition in the domain of morphophonology. We encapsulate phonological information as bidirectional boolean constraint relations operating on the classical linguistic representations of speech sounds in term of distinctive features. The performance model is described as a hardware mechanism that incrementally enforces the constraints. Phonological behavior arises from the action of this mechanism. Constraints are induced from a corpus of common English nouns and verbs. The induction algorithm compiles the corpus into increasingly sophisticated constraints. The algorithm yields one-shot learning from a few examples. Our model has been implemented as a computer program. The program exhibits phonological behavior similar to that of young children. As a bonus the constraints that are acquired can be interpreted as classical linguistic rules.

The Role of Knowledge in Visual Shape Representation

This report shows how knowledge about the visual world can be built into a shape representation in the form of a descriptive vocabulary making explicit the important geometrical relationships comprising objects' shapes. Two computational tools are offered: (1) Shapestokens are placed on a Scale-Space Blackboard, (2) Dimensionality-reduction captures deformation classes in configurations of tokens. Knowledge lies in the token types and deformation classes tailored to the constraints and regularities ofparticular shape worlds. A hierarchical shape vocabulary has been implemented supporting several later visual tasks in the two-dimensional shape domain of the dorsal fins of fishes.

Perceiving Illumination Inconsistencies in Scenes

The human visual system is adept at detecting and encoding statistical regularities in its spatio-temporal environment. Here we report an unexpected failure of this ability in the context of perceiving inconsistencies in illumination distributions across a scene. Contrary to predictions from previous studies [Enns and Rensink, 1990; Sun and Perona, 1996a, 1996b, 1997], we find that the visual system displays a remarkable lack of sensitivity to illumination inconsistencies, both in experimental stimuli and in images of real scenes. Our results allow us to draw inferences regarding how the visual system encodes illumination distributions across scenes. Specifically, they suggest that the visual system does not verify the global consistency of locally derived estimates of illumination direction.