Recovering Heading for Visually-Guided Navigation

We present a model for recovering the direction of heading of an observer who is moving relative to a scene that may contain self-moving objects. The model builds upon an algorithm proposed by Rieger and Lawton (1985), which is based on earlier work by Longuet-Higgens and Prazdny (1981). The algorithm uses velocity differences computed in regions of high depth variation to estimate the location of the focus of expansion, which indicates the observer's heading direction. We relate the behavior of the proposed model to psychophysical observations regarding the ability of human observers to judge their heading direction, and show how the model can cope with self-moving objects in the environment. We also discuss this model in the broader context of a navigational system that performs tasks requiring rapid sensing and response through the interaction of simple task-specific routines

Edge Detection

For both biological systems and machines, vision begins with a large and unwieldy array of measurements of the amount of light reflected from surfaces in the environment. The goal of vision is to recover physical properties of objects in the scene, such as the location of object boundaries and the structure, color and texture of object surfaces, from the two-dimensional image that is projected onto the eye or camera. This goal is not achieved in a single step; vision proceeds in stages, with each stage producing increasingly more useful descriptions of the image and then the scene. The first clue about the physical properties of the scene are provided by the changes of intensity in the image. The importance of intensity changes and edges in early visual processg has led to extensive research on their detection, description and .use, both in computer and biological vision systems. This article reviews some of the theory that underlies the detection of edges, and the methods used to carry out this analysis

Implementation of a Theory of Edge Detection

This report describes the implementation of a theory of edge detection, proposed by Marr and Hildreth (1979). According to this theory, the image is first processed independently through a set of different size filters, whose shape is the Laplacian of a Gaussian, ***. Zero-crossings in the output of these filters mark the positions of intensity changes at different resolutions. Information about these zero-crossings is then used for deriving a full symbolic description of changes in intensity in the image, called the raw primal sketch. The theory is closely tied with early processing in the human visual systems. In this report, we first examine the critical properties of the initial filters used in the edge detection process, both from a theoretical and practical standpoint. The implementation is then used as a test bed for exploring aspects of the human visual system; in particular, acuity and hyperacuity. Finally, we present some preliminary results concerning the relationship between zero-crossings detected at different resolutions, and some observations relevant to the process by which the human visual system integrates descriptions of intensity changes obtained at different resolutions

The Computation of the Velocity Field

The organization of movement in the changing retinal image provides a valuable source of information for analyzing the environment in terms of objects, their motion in space and their three-dimensional structure. A description of this movement is not provided to our visual system directly, however; it must be inferred from the pattern of changing intensity that reaches the eye. This paper examines the problem of motion measurement, which we formulate as the computation of an instantaneous two-dimensional velocity field from the changing image. Initial measurements of motion take place at the location of significant intensity changes, as suggested by Marr and Ullman (1981). These measurements provide only one component of local velocity, and must be integrated to compute the two-dimensional velocity field. A fundamental problem for this integration stage is that the velocity field is not determined uniquely from information available in the changing image. We formulate an additional constraint of smoothness of the velocity field, based on the physical assumption that surfaces are generally smooth, which allows the computation of a unique velocity field. A theoretical analysis of the conditions under which this computation yields the correct velocity field suggests that the solution is physically plausible. Empirical studies show the predictions of this computation to be consistent with human motion perception

Computations Underlying the Measurement of Visual Motion

The organization of movement in a changing image provides a valuable source of information for analyzing the environment in terms of objects, their motion in space, and their three-dimensional structure. This movement may be represented by a two-dimensional velocity field that assigns a direction and magnitude of velocity to elements in the image. This paper presents a method for computing the velocity field, with three main components. First, initial measurements of motion in the image take place at the location of significant changes, which give rise to zero-crossings in the output of the convolution of the image with a *** operator. The initial motion measurements provide the component of velocity in the direction perpendicular to the local orientation of the zero-crossing contours. Second, these initial measurements are integrated along contours to compute the two-dimensional velocity field. Third, an additional constraint of smoothness of the velocity field, based on the physical constraint that surfaces are generally smooth, allows the computation of a unique velocity field. The details of an algorithm are presented, with results of the algorithm applied to artificial and natural image sequences

The Computational Study of Vision

The computational approach to the study of vision inquires directly into the sort of information processing needed to extract important information from the changing visual image---information such as the three-dimensional structure and movement of objects in the scene, or the color and texture of object surfaces. An important contribution that computational studies have made is to show how difficult vision is to perform, and how complex are the processes needed to perform visual tasks successfully. This article reviews some computational studies of vision, focusing on edge detection, binocular stereo, motion analysis, intermediate vision, and object recognition

The Analysis of Visual Motion: From Computational Theory to Neuronal Mechanisms

This paper reviews a number of aspects of visual motion analysis in biological systems from a computational perspective. We illustrate the kinds of insights that have been gained through computational studies and how these observations can be integrated with experimental studies from psychology and the neurosciences to understand the particular computations used by biological systems to analyze motion. The particular areas of motion analysis that we discuss include early motion detection and measurement, the optical flow computation, motion correspondence, the detection of motion discontinuities, and the recovery of three-dimensional structure from motion

The Measurement of Visual Motion

The analysis of visual motion divides naturally into two stages: the first is the measurement of motion, for example, the assignment of direction and magnitude of velocity to elements in the image, on the basis of the changing intensity pattern; the second is the use of motion measurements, for example, to separate the scene into distinct objects, and infer their three-dimensional structure. In this paper, we present a computational study of the measurement of motion. Similar to other visual processes, the motion of elements is not determined uniquely by information in the changing image; additional constraint is required to compute a unique velocity field. Given this global ambiguity of motion, local measurements from the changing image, such as those provided by directionally-selective simple cells in primate visual cortex, cannot possibly specify a unique local velocity vector, and in fact, specify only one component of velocity. Computation of the full two-dimensional velocity field requires the integration of local motion measurements, either over an area, or along contours in the image. We will examine possible algorithms for computing motion, based on a range of additional constraints. Finally, we will present implications for the biological computation of motion