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 Euler-Lagrange 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.

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 Euler-Lagrange 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.

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 so-called 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

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.

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...

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.

Abstract—The human visual system obeys Listing’s law, which means that the cyclo-rotation 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 cyclo-rotation 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.

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.

This paper presents the visual measurement of physical object properties that characterize the perceived object including: size, shape, surface properties, cover reflectance properties, distance, and motion. We provide an overview of complete set of local spatial, spectral and temporal measurements. From local visual measurements and a physical model of the visual stimulus formation, we derive complete sets of photometric, geometrical, and temporal invariants to counteract unwanted transformations in the observation including: illumination spectrum and intensity, scene setting causing shadow, shading and highlight effects, and variation due to object position, pose and distance. Experiments show the different invariants to be highly discriminative, while maintaining invariance properties. The presented framework for invariant measurement is well-founded in physics as well as in measurement science. Hence, the local visual measurements and their invariant representations are considered theoretically better founded than existing methods for the measurement of invariant features.

The geometry of binocular projection is analyzed in relation to the primate visual system. An oculomotor parameterization, which 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. 1