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141
Stereo matching using belief propagation
, 2003
"... In this paper, we formulate the stereo matching problem as a Markov network and solve it using Bayesian belief propagation. The stereo Markov network consists of three coupled Markov random fields that model the following: a smooth field for depth/disparity, a line process for depth discontinuity, ..."
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Cited by 350 (4 self)
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In this paper, we formulate the stereo matching problem as a Markov network and solve it using Bayesian belief propagation. The stereo Markov network consists of three coupled Markov random fields that model the following: a smooth field for depth/disparity, a line process for depth discontinuity, and a binary process for occlusion. After eliminating the line process and the binary process by introducing two robust functions, we apply the belief propagation algorithm to obtain the maximum a posteriori (MAP) estimation in the Markov network. Other lowlevel visual cues (e.g., image segmentation) can also be easily incorporated in our stereo model to obtain better stereo results. Experiments demonstrate that our methods are comparable to the stateoftheart stereo algorithms for many test cases.
A Method for enforcing integrability in shape from shading algorithms
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1988
"... Several recently developed techniques for reconstructing surface shape from shading information estimate surface slopes without ensuring that they are integrable. This paper presents an approach for enforcing integrability, a particular implementation of the approach, an example of its application ..."
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Cited by 284 (6 self)
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Several recently developed techniques for reconstructing surface shape from shading information estimate surface slopes without ensuring that they are integrable. This paper presents an approach for enforcing integrability, a particular implementation of the approach, an example of its application to extending an existing shapefromshading algorithm, and experimental results showing the improvement that results from enforcing integrability. A possibly nonintegrable estimate of surface slopes is represented by a finite set of basis functions, and integrability is enforced by calculating the orthogonal projection onto a vector subspace spanning the set of integrable slopes. This projection maps closed convex sets into closed convex sets and, hence, is attractive as a constraint in iterative algorithms. The same technique is also useful for noniterative algorithms since it provides a leastsquares fit of integrable slopes to nonintegrable slopes in one pass of the algorithm. The special case of Fou
Bayesian Modeling of Uncertainty in LowLevel Vision
, 1990
"... The need for error modeling, multisensor fusion, and robust algorithms i becoming increasingly recognized in computer vision. Bayesian modeling is a powerful, practical, and general framework for meeting these requirements. This article develops a Bayesian model for describing and manipulating the d ..."
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Cited by 204 (17 self)
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The need for error modeling, multisensor fusion, and robust algorithms i becoming increasingly recognized in computer vision. Bayesian modeling is a powerful, practical, and general framework for meeting these requirements. This article develops a Bayesian model for describing and manipulating the dense fields, such as depth maps, associated with lowlevel computer vision. Our model consists of three components: a prior model, a sensor model, and a posterior model. The prior model captures a priori information about he structure of the field. We construct this model using the smoothness constraints from regularization to define a Markov Random Field. The sensor model describes the behavior and noise characteristics of our measurement system. We develop a number of sensor models for both sparse and dense measurements. The posterior model combines the information from the prior and sensor models using Bayes ' rule. We show how to compute optimal estimates from the posterior model and also how to compute the uncertainty (variance) in these estimates. To demonstrate the utility of our Bayesian framework, we present three examples of its application to real vision problems. The first application is the online extraction of depth from motion. Using a twodimensional generalization of the Kalman filter, we develop an incremental algorithm that provides a dense online estimate of depth whose accuracy improves over time. In the second application, we use a Bayesian model to determine observer motion from sparse depth (range) measurements. In the third application, we use the Bayesian interpretation f regularization to choose the optimal smoothing parameter for interpolation. The uncertainty modeling techniques that we develop, and the utility of these techniques invarious applications, support our claim that Bayesian modeling is a powerful and practical framework for lowlevel vision.
The BasRelief Ambiguity
 IN THE PROCEEDINGS OF CVPR97.
, 1997
"... Since antiquity, artisans have created attened forms, often called "basreliefs," which give an exaggerated perception of depth when viewed from a particular vantage point. This paper presents an explanation of this phenomena, showing that the ambiguity in determining the relief of an obje ..."
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Cited by 168 (12 self)
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Since antiquity, artisans have created attened forms, often called "basreliefs," which give an exaggerated perception of depth when viewed from a particular vantage point. This paper presents an explanation of this phenomena, showing that the ambiguity in determining the relief of an object is not con ned to basrelief sculpture but is implicit in the determination of the structure of any object. Formally, if the object's true surface is denoted by z true = f(x � y), then we define the "generalized basrelief transformation" asz = f(x � y)+ x + y � with a corresponding transformation of the albedo. For each image of a Lambertian surface f(x � y) produced by a point light source at in nity, there exists an identical image of a basrelief produced by a transformed light source. This equality holds for both shaded and shadowed regions. Thus, the set of possible images (illumination cone) is invariant over generalized basrelief transformations. When = =0(e.g. a classical basrelief sculpture), we show that the set of possible motion elds are also identical. Thus, neither small unknown motions nor changes of illumination can resolve the basrelief ambiguity. Implications of this ambiguity on structure recovery and shape representation are discussed.
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 145 (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...
Height and gradient from shading
 International Journal of Computer Vision
, 1990
"... Abstract: The method described here for recovering the shape of a surface from a shaded image can deal with complex, wrinkled surfaces. Integrability can be enforced easily because both surface height and gradient are represented (A gradient field is integrable if it is the gradient of some surface ..."
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Cited by 135 (1 self)
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Abstract: The method described here for recovering the shape of a surface from a shaded image can deal with complex, wrinkled surfaces. Integrability can be enforced easily because both surface height and gradient are represented (A gradient field is integrable if it is the gradient of some surface height function). The robustness of the method stems in part from linearization of the reflectance map about the current estimate of the surface orientation at each picture cell (The reflectance map gives the dependence of scene radiance on surface orientation). The new scheme can find an exact solution of a given shapefromshading problem even though a regularizing term is included. The reason is that the penalty term is needed only to stabilize the iterative scheme when it is far from the correct solution; it can be turned off as the solution is approached. This is a reflection of the fact that shapefromshading problems are not illposed when boundary conditions are available, or when the image contains singular points. This paper includes a review of previous work on shape from shading and photoclinometry. Novel features of the new scheme are introduced one at a time to make it easier to see what each contributes. Included is a discussion of implementation details that are important if exact algebraic solutions of synthetic shapefromshading problems are to be obtained. The hope is that better performance on synthetic data will lead to better performance on real data.
Illumination cones for recognition under variable lighting: Faces
 In Proc. IEEE Conf. on Comp. Vision and
, 1998
"... Due to illumination variability, the same object can appear dramatically di erent even when viewed in xed pose. To handle this variability, an object recognition system must employ a representation that is either invariant to, or models this variability. This paper presents an appearancebased metho ..."
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Cited by 115 (15 self)
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Due to illumination variability, the same object can appear dramatically di erent even when viewed in xed pose. To handle this variability, an object recognition system must employ a representation that is either invariant to, or models this variability. This paper presents an appearancebased method formodeling the variability due to illumination in the images of objects. The method di ers from past appearancebased methods, however, in that a small set of training images is used to generate a representation { the illumination cone { which models the complete set of images of an object with Lambertian re ectance under an arbitrary combination of point light sources at in nity. This method isboth an implementation and extension (an extension in that it models cast shadows) of the illumination cone representation proposed in[3]. The method is tested on a database of 660 images of 10 faces, and the results exceed those of popular existing methods. 1
Synthesizing Bidirectional Texture Functions for RealWorld Surfaces
, 2001
"... In this paper, we present a novel approach to synthetically generating bidirectional texture functions (BTFs) of realworld surfaces. Unlike a conventional twodimensional texture, a BTF is a sixdimensional function that describes the appearance of texture as a function of illumination and viewing d ..."
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Cited by 72 (6 self)
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In this paper, we present a novel approach to synthetically generating bidirectional texture functions (BTFs) of realworld surfaces. Unlike a conventional twodimensional texture, a BTF is a sixdimensional function that describes the appearance of texture as a function of illumination and viewing directions. The BTF captures the appearance change caused by visible smallscale geometric details on surfaces. From a sparse set of images under different viewing /lighting settings, our approach generates BTFs in three steps. First, it recovers approximate 3D geometry of surface details using a shapefromshading method. Then, it generates a novel version of the geometric details that has the same statistical properties as the sample surface with a nonparametric sampling method. Finally, it employs an appearance preserving procedure to synthesize novel images for the recovered or generated geometric details under various viewing/lighting settings, which then define a BTF. Our experimental results demonstrate the effectiveness of our approach. CR Categories: I.2.10 [Artificial Intelligence]: Vision and Scene Understandingmodeling and recovery of physical attributes I.3.7 [Computer Graphics]: Threedimensional Graphics and Realismcolor, shading, shadowing, and texture I.4.8 [Image Processing]: Scene Analysiscolor, photometry, shading Keywords: Bidirectional Texture Functions, Reflectance and Shading Models, Texture Synthesis, ShapefromShading, Photometric Stereo, ImageBased Rendering.
A Simple Algorithm for Shape from Shading
, 1992
"... In this paper we describe a simple shape from shading algorithm which recovers depth from a brightness image, typically in fewer than ten iterations. This algorithm, which is a simplification of the algorithm of Oliensis and Dupuis, is based on a minimum downhill principle which guarantees continuou ..."
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Cited by 72 (3 self)
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In this paper we describe a simple shape from shading algorithm which recovers depth from a brightness image, typically in fewer than ten iterations. This algorithm, which is a simplification of the algorithm of Oliensis and Dupuis, is based on a minimum downhill principle which guarantees continuous surfaces and stable results. The algorithm is applicable to a broad variety of objects and reflectance maps. 1 Introduction Until the recent publications of Oliensis and Dupuis [[5],[6],[7]] most researchers in shape from shading were convinced that recovering depth from a brightness image necessarily required some regularization technique in order to guarantee a physically plausible surface [4]. It also seemed evident that only an iterative process with typically several thousand iterations would lead to a good approximation of the true surface. Linear methods [8] with an elegant solution in the Fourier domain form an exception to that rule, but they can only be applied to a limited numb...