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91
Numerical Shape from Shading and Occluding Boundaries
 Artifical Intelligence
, 1981
"... An iterative method for computing shape from shading using occluding boundary information is proposed. Some applications of this method are shown. We employ the stereographic plane to express the orientations of surface patches, rather than the more commonly.used gradient space. Use of the stereogra ..."
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Cited by 191 (14 self)
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An iterative method for computing shape from shading using occluding boundary information is proposed. Some applications of this method are shown. We employ the stereographic plane to express the orientations of surface patches, rather than the more commonly.used gradient space. Use of the stereographic plane makes it possible to incorporate occluding boundary information, but forces us to employ a smoothness constraint different from the one previously proposed. The new constraint follows directly from a particular definition of surface smoothness. We solve the set of equations arising from the smoothness constraints and the imageirradiance equation iteratively, using occluding boundary information to supply boundary conditions. Good initial values are found at certain points to help reduce the number of iterations required to reach a reasonable solution. Numerical experiments show that the method is effective and robust. Finally, we analyze scanning electron microscope (SEM) pictures using this method. Other applications are also proposed. 1.
A physical Approach to Color Image Understanding
, 1990
"... In this paper, we present an approach to color image understanding that can be used to segment and analyze sur faces with color variations due to highlights and shading. The work is based on a theorythe Dichromatic Reflec tion Modelwhich describes the color of the reflected light as a mixture ..."
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Cited by 171 (10 self)
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In this paper, we present an approach to color image understanding that can be used to segment and analyze sur faces with color variations due to highlights and shading. The work is based on a theorythe Dichromatic Reflec tion Modelwhich describes the color of the reflected light as a mixture of light from surface reflection (highlights) and body reflection (object color). In the past, we have shown how the dichromatic theory can be used to separate a color image into two intrinsic reflection images: an image of just the highlights, and the original image with the highlights removed. At that time, the algorithm could only be applied to handsegmented images. This paper shows how the same reflection model can be used to include color image segmentation into the image analysis. The result is a color image understanding system, capable of generating physical descriptions of the reflection processes occurring in the scene. Such descriptions include the intrinsic reflection images, an image segmenta tion, and symbolic information about the object and highlight colors. This line of research can lead to based image understanding methods that are both more reliable and more useful than traditional methods.
Algorithms for the Satisfiability (SAT) Problem: A Survey
 DIMACS Series in Discrete Mathematics and Theoretical Computer Science
, 1996
"... . The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computeraided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, compute ..."
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Cited by 127 (3 self)
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. The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computeraided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and practical techniques have been developed for solving SAT. In this survey, we present a general framework (an algorithm space) that integrates existing SAT algorithms into a unified perspective. We describe sequential and parallel SAT algorithms including variable splitting, resolution, local search, global optimization, mathematical programming, and practical SAT algorithms. We give performance evaluation of some existing SAT algorithms. Finally, we provide a set of practical applications of the sat...
Generative models for discovering sparse distributed representations
 Philosophical Transactions of the Royal Society B
, 1997
"... We describe a hierarchical, generative model that can be viewed as a nonlinear generalization of factor analysis and can be implemented in a neural network. The model uses bottomup, topdown and lateral connections to perform Bayesian perceptual inference correctly. Once perceptual inference has b ..."
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Cited by 120 (5 self)
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We describe a hierarchical, generative model that can be viewed as a nonlinear generalization of factor analysis and can be implemented in a neural network. The model uses bottomup, topdown and lateral connections to perform Bayesian perceptual inference correctly. Once perceptual inference has been performed the connection strengths can be updated using a very simple learning rule that only requires locally available information. We demonstrate that the network learns to extract sparse, distributed, hierarchical representations.
The variational approach to shape from shading
 Computer Vision, Graphics, and Image Processing
, 1986
"... We develop a systematic approach to the discovery of parallel iterative schemes for solving the shapefromshading problem on a grid. A standard procedure for finding such schemes is outlined, and subsequently used to derive several new ones. The shapefromshading problem is known to be mathematica ..."
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Cited by 111 (1 self)
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We develop a systematic approach to the discovery of parallel iterative schemes for solving the shapefromshading problem on a grid. A standard procedure for finding such schemes is outlined, and subsequently used to derive several new ones. The shapefromshading problem is known to be mathematically equivalent to a nonlinear firstorder partial differential equation in surface elevation. To avoid the problems inherent in methods used to solve such equations, we follow previous work in reformulating the problem as one of finding a surface orientation field that minimizes the integral of the brightness error. The calculus of variations is then employed to derive the appropriate Euler equations on which iterative schemes can be based. The problem of minimizing the integral of the brightness error term is ill posed, since it has an infinite number of solutions in terms of surface orientation fields. A previous method used a regularization technique to overcome this difficulty. An extra term was added to the integral to obtain an approximation to a solution that was as smooth as possible. We point out here that surface orientation has to obey an integrability constraint if it is to correspond to an underlying smooth surface. Regularization methods do not guarantee that the surface orientation recovered satisfies this constraint. see also "Shape from Shading" MIT Press.
Calculating the Reflectance Map
, 1978
"... It appears that the development of machine vision may benefit from a detailed understanding of the imaging process. The reflectance map, showing scene radiance as a function of surface gradient, has proved to be helpful in this endeavor. The reflectance map depends both on the nature of the surface ..."
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Cited by 103 (8 self)
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It appears that the development of machine vision may benefit from a detailed understanding of the imaging process. The reflectance map, showing scene radiance as a function of surface gradient, has proved to be helpful in this endeavor. The reflectance map depends both on the nature of the surface layers of the objects being imaged and the distribution of light sources. Recently, a unified approach to the specification of surface reflectance in terms of both incident and reflected beam geometry has been proposed The reflecting properties of a surface are specified in terms of the bidirectional reflectancedistribution function (BRDF). Here we derive the reflectance map in terms of the BRDF and the distribution of source radiance. A number of special cases of practical importance are developed in detail. The significance of this approach to the understanding of image formation is
Interpreting Line Drawings as ThreeDimensional Surfaces
, 1981
"... Understanding how line drawings convey tridimensionality is of fundamental importance in explaining surface perception when photometry is either uninformative or too compex to model analytically. We put forward here a computational model for interpreting line drawings as threedimensional surfaces, ..."
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Cited by 82 (2 self)
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Understanding how line drawings convey tridimensionality is of fundamental importance in explaining surface perception when photometry is either uninformative or too compex to model analytically. We put forward here a computational model for interpreting line drawings as threedimensional surfaces, based on constraints on local surface orientation along extremal and discontinuity boundaries. Specific techniques are described for two key processes recovering the threedimensional conformation of a space curve (e.g., a surface boundary) from its twodimensional projection in an image, and interpolating smooth surfaces from orientation constraints along extremal boundaries. The relevance of the model to a general theory of lowlevel vision is discussed.
The Measurement of Highlights in Color Images
, 1988
"... In this paper, we present anapproach to colorimage understandingthat accountsforcolorvariationsdue to highlights and shading. We demonstrate that the reflected light from every point on a dielectric object. such as plastic, can be described asa linearcombination of the object color and the highligh ..."
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Cited by 81 (6 self)
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In this paper, we present anapproach to colorimage understandingthat accountsforcolorvariationsdue to highlights and shading. We demonstrate that the reflected light from every point on a dielectric object. such as plastic, can be described asa linearcombination of the object color and the highlight color. The colors of all light rays reflected from one object then form a planar cluster in the color space.The shapeof this cluster is determined by the object and highlight colors and by the object shape and illumination geometry. We present a method that exploits the difference between object color and highlight color to separate the color of every pixel into a matte component and a highlight component.This generates two intrinsic images, one showing the scene without highlights, and the other one showing only the highlights. The intrinsic images may be a useful tool for a variety of algorithms in computer vision. such as stereo vision, motion analysis, shape from shading,and shapefrom highlights. Ourmethod combines the analysis of matte and highlight reflection with a sensor model that accounts for camera limitations. This enables us to successfully run our algorithm on real images taken in a laboratory setting. We show and discuss the results.
On Designing a Visual System (Towards a Gibsonian computational model of vision)
 Journal of Experimental and Theoretical AI
, 1989
"... This paper contrasts the standard (in AI) "modular" theory of the nature of vision with a more general (labyrinthine) theory of vision as involving multiple functions and multiple relationships with other subsystems of an intelligent system. ..."
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Cited by 59 (41 self)
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This paper contrasts the standard (in AI) "modular" theory of the nature of vision with a more general (labyrinthine) theory of vision as involving multiple functions and multiple relationships with other subsystems of an intelligent system.