Optical flow cannot be computed locally, since only one independent measurement is available from the image sequence at a point, while the flow velocity has two components. A second constraint is needed. A method for finding the optical flow pattern is presented which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image. An iterative implementation is shown which successfully computes the optical flow for a number of synthetic image sequences. The algorithm is robust in that it can handle image sequences that are quantized rather coarsely in space and time. It is also insensitive to quantization of brightness levels and additive noise. Examples are included where the assumption of smoothness is violated at singular points or along lines in the image.

A motion sequence may be represented as a single pattern in x-y-t space; a velocity of motion corresponds to a three-dimensional orientation in this space. Motion sinformation can be extracted by a system that responds to the oriented spatiotemporal energy. We discuss a class of models for human motion mechanisms in which the first stage consists of linear filters that are oriented in space-time and tuned in spatial frequency. The outputs of quadrature pairs of such filters are squared and summed to give a measure of motion energy. These responses are then fed into an opponent stage. Energy models can be built from elements that are consistent with known physiology and psychophysics, and they permit a qualitative understanding of a variety of motion phenomena.

This paper provides a review of shape analysis methods. Shape analysis methods play an important role in systems for object recognition, matching, registration, and analysis. Researchin shape analysis has been motivated, in part, by studies of human visual form perception systems.

In this paper we show that the optical flow, a 2-D field that can be associated with the variation of the image brightness pattern, and the 2-D motion field, the projection on the image plane of the 3-D velocity field of a moving scene, are in general different, unless very special conditions are satisfied. The optical flow, therefore, is ill-suited for computing structure from motion and for reconstructing the 3-D velocity field, problems that require an accurate estimate of the 2-D motion field. We then suggest a different use of the optical flow. We argue that stable qualitative properties of the 2-D motion field give useful information about the 3-D velocity field and the 3-D structure of the scene, and that they can be usually obtained from the optical flow. To support this approach we show how the (smoothed) optical flow and 2-D motion field, interpreted as vector fields tangent to flows of planar dynamical systems, may have the same qualitative properties from the point of view of the theory of structural stability of dynamical systems. () Massachusetts Institute of Technology 1986 This report describes research done within the Artificial Intelligence Laboratory. Support for the A.I. Laboratory's artificial intelligence research is provided in part by the Advanced Research Projects Agency of the Depart- ment of Defense under Oilice of Naval Research contract N00014-S5-K-0124. Support for this research is also provided by a grant from the Oilice of Naval Research, Engineering Psychology Division and by gift of the Artificial Intelligence Center of Hughes Aircraft Corporation to T. Poggio.

This thesis describes some new approaches to the representation and analysis of visual motion, as perceived by a biological or machine visual system. We begin by discussing the computation of image motion fields, the projection of motion in the three-dimensional world onto the two-dimensional image plane. This computation is notoriously difficult, and there are a wide variety of approaches that have been developed for use in image processing, machine vision, and biological modeling. We show that a large number of the basic techniques are quite similar in nature, differing primarily in conceptual motivation, and that they each fail to handle a set of situations that occur commonly in natural scenery. The central theme of the thesis is that the failure of these algorithms is due primarily to the use of vector fields as a representation for visual motion. We argue that the translational vector field representation is inherently impoverished and error-prone. Furthermore, there is evidence that a ...

Abstract-Optical flow can be used to locate dynamic occlusion boundaries in an image sequence. We derive an edge detection algorithm sensitive to changes in flow fields likely to be associated with occlusion. The algorithm is patterned after the Marr-Hildreth zero-crossing detectors currently used to locate boundaries in scalar fields. Zero-crossing detectors are extended to identify changes in direction and/or magnitude in a vector-valued flow field. As a result, the detector works for flow boundaries generated due to the relative motion of two overlapping surfaces, as well as the simpler case of motion parallax due to a sensor moving through an otherwise stationary environment. We then show how the approach can be extended to identify which side of a dynamic occlusion boundary corresponds to the occluding surface. The fundamental principal involved is that at an occlusion boundary, the image of the surface boundary moves with the image of the occluding surface. Such information is important in interpreting dynamic scenes. Results are demonstrated on optical flow fields automatically computed from real image sequences. Index Terms-Dynamic occlusion, dynamic scene analysis, edge detection, optical flow, visual motion. I.

How does the visual system generate percepts of moving forms? How does this happen when the forms are emergent percepts, such as illusory contours or segregated textures, and the motion percept is apparent motion between the emergent forms? We develop a neural model of form-motion interactions to explain and simulate parametric properties of psychophysical motion data and to make predictions about how the parallel cortical processing streams V1 ! MT and V1 ! V2 ! MT control form-motion interactions. The model explains how an illusory contour can move in apparent motion to another illusory contour or to a luminance-derived contour; how illusory contour persistence relates to the upper ISI threshold for apparent motion; and how upper and lower ISI thresholds for seeing apparent motion between two flashes decrease with stimulus duration and narrow with spatial separation (Korte's laws). The model accounts for these data by suggesting how the persistence of a boundary segmentation in the V...

In order to estimate the motion of an object, the visual system needs to combine multiple local measurements, each of which carries some degree of ambiguity. We present a model of motion perception whereby measurements from dierent image regions are combined according to a Bayesian estimator: the estimated motion maximizes the posterior probability assuming a prior favoring slow and smooth velocities. In reviewing a large number of previously published phenomena we nd that the Bayesian estimator predicts a wide range of psychophysical results. This suggests that the seemingly complex set of illusions arise from a single computational strategy that is optimal under reasonable assumptions. 1 Introduction Estimating motion in scenes containing multiple, complex motions remains a dicult problem for computer vision systems, yet is performed eortlessly by human observers. Motion analysis in such scenes imposes conicting demands on the design of a vision system (Braddick, 1993)....

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Recent approaches to estimating two-dimensional image motion and to modeling the perception of image motion have achieved success with Bayesian formulations. With a Bayesian approach, the goal is to compute the posterior probability distribution of velocity, which is proportional to a likelihood function and a prior. The likelihood function describes the probability of observing the image data given the image velocity; surprisingly, there is still disagreement about the right likelihood function to use. Here we derive a likelihood function by starting from a generative model. We assume that the scene translates, conserving image brightness, while the image is equal to the projected scene plus noise. We discuss the connection between the resulting likelihood function and existing models of motion analysis. We show that the likelihood can be calculated by a population of units whose response properties are similar to \motion energy" units. This suggests that a population o...