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Variational principles, Surface Evolution, PDE's, level set methods and the Stereo Problem
 IEEE TRANSACTIONS ON IMAGE PROCESSING
, 1999
"... We present a novel geometric approach for solving the stereo problem for an arbitrary number of images (greater than or equal to 2). It is based upon the denition of a variational principle that must be satisfied by the surfaces of the objects in the scene and their images. The EulerLagrange equati ..."
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Cited by 225 (23 self)
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We present a novel geometric approach for solving the stereo problem for an arbitrary number of images (greater than or equal to 2). It is based upon the denition of a variational principle that must be satisfied by the surfaces of the objects in the scene and their images. The EulerLagrange equations which are deduced from the variational principle provide a set of PDE's which are used to deform an initial set of surfaces which then move towards the objects to be detected. The level set implementation of these PDE's potentially provides an efficient and robust way of achieving the surface evolution and to deal automatically with changes in the surface topology during the deformation, i.e. to deal with multiple objects. Results of an implementation of our theory also dealing with occlusion and vibility are presented on synthetic and real images.
Complete Dense Stereovision using Level Set Methods
 in Proc. 5th European Conf. on Computer Vision
, 1998
"... We present a novel geometric approach for solving the stereo problem for an arbitrary number of images (greater than or equal to 2). It is based upon the denition of a variational principle that must be satised by the surfaces of the objects in the scene and their images. The EulerLagrange equation ..."
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Cited by 123 (3 self)
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We present a novel geometric approach for solving the stereo problem for an arbitrary number of images (greater than or equal to 2). It is based upon the denition of a variational principle that must be satised by the surfaces of the objects in the scene and their images. The EulerLagrange equations which are deduced from the variational principle provide a set of PDE's which are used to deform an initial set of surfaces which then move towards the objects to be detected. The level set implementation of these PDE's potentially provides an efficient and robust way of achieving the surface evolution and to deal automatically with changes in the surface topology during the deformation, i.e. to deal with multiple objects. Results of an implementation of our theory also dealing with occlusion and vibility are presented on synthetic and real images.
Phenomenological description of bidirectional surface reflection
 JOSA A
, 1998
"... General surface scattering is characterized through the bidirectional reflection distribution function (BRDF). The BRDF is a function of the directions of the incident and remitted beams and thus depends on four parameters. Under very general assumptions one shows that the BRDF is invariant under in ..."
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Cited by 25 (0 self)
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General surface scattering is characterized through the bidirectional reflection distribution function (BRDF). The BRDF is a function of the directions of the incident and remitted beams and thus depends on four parameters. Under very general assumptions one shows that the BRDF is invariant under interchange of the incident and remitted beams, the socalled Helmholtz reciprocity. For isotropic surfaces the BRDF depends only on the absolute value of the difference between the azimuths of the incident and remitted beams. Since these exhaust the symmetries, the BRDF is a very complicated function. For many applications it would be advantageous to be able to summarize empirical data or to smooth and/or interpolate (often even extrapolate) BRDF data. We present a principled way to do this, exactly respecting the symmetry properties. © 1998 Optical
Cyclopean geometry of binocular vision
"... The geometry of binocular projection is analyzed in relation to the primate visual system. An oculomotor parameterization that includes the classical vergence and version angles is defined. It is shown that the epipolar geometry of the system is constrained by binocular coordination of the eyes. A l ..."
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Cited by 18 (10 self)
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The geometry of binocular projection is analyzed in relation to the primate visual system. An oculomotor parameterization that includes the classical vergence and version angles is defined. It is shown that the epipolar geometry of the system is constrained by binocular coordination of the eyes. A local model of the scene is adopted in which depth is measured relative to a plane containing the fixation point. These constructions lead to an explicit parameterization of the binocular disparity field involving the gaze angles as well as the scene structure. The representation of visual direction and depth is discussed with reference to the relevant psychophysical and neurophysiological literature. © 2008 Optical Society of America OCIS codes: 330.1400, 330.2210. 1.
Visual Space Distortion
 Biological Cybernetics
, 1997
"... We are surrounded by surfaces that we perceive by visual means. Understanding the basic principles behind this perceptual process is a central theme in visual psychology, psychophysics and computational vision. In many of the computational models employed in the past, it has been assumed that a metr ..."
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Cited by 13 (12 self)
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We are surrounded by surfaces that we perceive by visual means. Understanding the basic principles behind this perceptual process is a central theme in visual psychology, psychophysics and computational vision. In many of the computational models employed in the past, it has been assumed that a metric representation of physical space can be derived by visual means. Psychophysical experiments, as well as computational considerations, can convince us that the perception of space and shape has a much more complicated nature, and that only a distorted version of actual, physical space can be computed. This paper develops a computational geometric model that explains why such distortion might take place. The basic idea is that, both in stereo and motion, we perceive the world from multiple views. Given the rigid transformation between the views and the properties of the image correspondence, the depth of the scene can be obtained. Even a slight error in the rigid transformation parameters c...
1 Cyclorotation Models for Eyes and Cameras
"... Abstract—The human visual system obeys Listing’s law, which means that the cyclorotation of the eye (around the line of sight) can be predicted from the direction of the fixation point. It is shown here that Listing’s law can be conveniently formulated in terms of rotation matrices. The function th ..."
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Cited by 5 (2 self)
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Abstract—The human visual system obeys Listing’s law, which means that the cyclorotation of the eye (around the line of sight) can be predicted from the direction of the fixation point. It is shown here that Listing’s law can be conveniently formulated in terms of rotation matrices. The function that defines the observed cyclorotation is derived in this representation. Two polynomial approximations of the function are developed, and the accuracy of each model is evaluated by numerical integration over a range of gaze directions. The error of the most simple approximation, for typical eye movements, is less than half a degree. It is shown that, given a set of calibrated images, the effect of Listing’s law can be simulated in a way that is physically consistent with the original camera. This is important for robotic models of human vision, which typically do not reproduce the mechanics of the oculomotor system. Index Terms—Biological control systems, visual system, robot kinematics. I.
Statistics Explains Geometrical Optical Illusions
, 2001
"... It is proposed in this paper that many geometrical optical illusions, as well as illusionary patterns due to motion signals in line drawings, are due to the statistics of visual computations. The interpretation of image patterns is preceded by a step where image features such as lines, intersections ..."
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Cited by 4 (1 self)
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It is proposed in this paper that many geometrical optical illusions, as well as illusionary patterns due to motion signals in line drawings, are due to the statistics of visual computations. The interpretation of image patterns is preceded by a step where image features such as lines, intersections of lines, or local image movement must be derived. That is, these features must be estimated from the input data. However, noise in the image intensity and its derivatives causes problems in the estimation of the features; in particular, it causes bias. As a result, the locations of features are perceived erroneously and the appearance of the patterns is altered. The bias occurs with any visual processing of line features; under average conditions it is not large enough to be noticeable, but illusionary patterns are such that the bias is highly pronounced. In general, this bias cannot be avoided, and any vision system, biological or artificial, must cope with it. This work reveals a general uncertainty principle governing the workings of vision systems. A consequence of this principle is the prediction of a large class of geometric optical illusions.
MUSIC ANALYSIS AND KOLMOGOROV COMPLEXITY
"... The goal of music analysis is to find the most satisfying explanations for musical works. It is proposed that this can best be achieved by attempting to write computer programs that are as short as possible and that generate representations that are as detailed as possible of the music to be explain ..."
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The goal of music analysis is to find the most satisfying explanations for musical works. It is proposed that this can best be achieved by attempting to write computer programs that are as short as possible and that generate representations that are as detailed as possible of the music to be explained. The theory of Kolmogorov complexity suggests that the length of such a program can be used as a measure of the complexity of the analysis that it represents. The analyst therefore needs a way to measure the length of a program so that this length reflects the quality of the analysis that the program represents. If such an effective measure of analysis quality can be found, it could be used in a system that automatically finds the optimal analysis for any passage of music. Measuring program length in terms of number of sourcecode characters is shown to be problematic and an expression is proposed that overcomes some but not all of these problems. It is suggested that the solutions to the remaining problems may lie either in the field of concrete Kolmogorov complexity or in the design of languages specialized for expressing musical structure. 1.
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART B: CYBERNETICS 1 Cyclorotation Models for Eyes and Cam
"... Abstract—The human visual system obeys Listing’s law, which means that the cyclorotation of the eye (around the line of sight) can be predicted from the direction of the fixation point. It is shown here that Listing’s law can conveniently be formulated in terms of rotation matrices. The function tha ..."
Abstract
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Abstract—The human visual system obeys Listing’s law, which means that the cyclorotation of the eye (around the line of sight) can be predicted from the direction of the fixation point. It is shown here that Listing’s law can conveniently be formulated in terms of rotation matrices. The function that defines the observed cyclorotation is derived in this representation. Two polynomial approximations of the function are developed, and the accuracy of each model is evaluated by numerical integration over a range of gaze directions. The error of the simplest approximation for typical eye movements is less than half a degree. It is shown that, given a set of calibrated images, the effect of Listing’s law can be simulated in a way that is physically consistent with the original camera. This condition is important for robotic models of human vision, which typically do not reproduce the mechanics of the oculomotor system. Index Terms—Biological control systems, robot kinematics, visual system. I.
Spectrum analysis of motion parallax in a 3D cluttered scene and
"... application to egomotion ..."
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