A theory of edge detection is presented. The analysis proceeds in two parts.(1) Intensity changes, which occur in a natural image over a wide range of scales, are detected separately at different scales. An appropriate filter for this purpose a t a given scale is found to be the second derivative of a Gaussian, and it is shown th a t, provided some simple conditions are satisfied, these prim ary filters need not be orientation-dependent. Thus, intensity changes a t a given scale are best detected by finding the zero values of V2G(x, y)* I(x, y) for image I, where G(x, y) is a two-dimen sional Gaussian distribution and V2 is the Laplacian. The intensity changes thus discovered in each of the channels are then represented by oriented primitives called zero-crossing segments, and evidence is given th a t this representation is complete. (2) Intensity changes in images arise from surface discontinuities or from reflectance or illumination bound aries, and these all have the property th a t they are spatially localized. Because of this, the zero-crossing segments from the different channels are not independent, and rules are deduced for combining them into a description of the image. This description is called the raw primal sketch. The theory explains several basic psychophysical findings, and the opera tion of forming oriented zero-crossing segments from the output of centre-surround V2G filters acting on the image forms the basis for a physiological model of simple cells (see .

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When moving toward a stationary scene, people judge their heading quite well from visual information alone. Much experimental and modeling work has been presented to analyze how people judge their heading for stationary scenes. However, in everyday life, we often move through scenes that contain moving objects. Most models have difficulty computing heading when moving objects are in the scene, and few studies have examined how well humans perform in the presence of moving objects. In this study, we tested how well people judge their heading in the presence of moving objects. We found that people perform remarkably well under a variety of conditions. The only condition that affects an observer's ability to judge heading accurately consists of a large moving object crossing the observer's path. In this case, the presence of the object causes a small bias in the heading judgments. For objects moving horizontally with respect to the observer, this bias is in the object's direction of motion. These results present a challenge for computational models.The task ofnavigating through a complex environment requires the visual system to solve a variety of problems related to three-dimensional (3-D) observer motion and object motion. To reach a desired destination, people must accurately judge their direction of motion. To avoid hitting objects in the scene, they must be able to judge the position of stationary objects and the position and 3-D motion of objects moving relative to themselves. Because we often move through scenes that contain moving objects, our heading judgments ideally should not be affected by the presence of these objects. For example, a driver on a busy street must make accurate headingjudgments in the presence of other moving cars and pedestrians. It is clear from psychophysical experiments that, for translational motion, people can accurately judge their heading when approaching stationary scenes (Crowell & Banks, 1993;Crowell, Royden, Banks, Swenson, & Sekuler, 1990;Rieger & Toet, 1985;van den Berg, 1992;Warren & Hannon, 1988, 1990. However, little has been done to measure human ability to judge heading in the presence of moving objects. Furthermore, most computational models have been designed to make heading judgments given stationary scenes. The presence ofmoving objects in the scene adversely affects their performance. In this paper, we present experiments that test whether the presence of moving objects similarly affects human ability to judge heading. To illustrate the difficulties involved in judging heading in the presence of moving objects, we first describe some of the computational models that have been put forth to compute heading from visual input. Most of these models have been developed to solve the problem of computing both the translation and the rotation components of motion for an observer moving through a stationary scene. We will focus our discussion on models that are the most biologically plausible. Following the discussion of computational modeling, we briefly summarize previou...

Experienced drivers performed simple steering maneuvers in the absence of continuous visual input. Experiments conducted in a driving simulator assessed drivers' performance of lane corrections during brief visual occlusion and examined the visual cues that guide steering. The dependence of steering behavior on heading, speed, and lateral position at the start of the maneuver was measured. Drivers adjusted steering amplitude with heading and performed the maneuver more rapidly at higher speeds. These dependencies were unaffected by a 1.5-s visual occlusion at the start of the maneuver. Longer occlusions resulted in severe performance degradation. Two steering control models were developed to account for these findings. In the 1st, steering actions were coupled to perceptual variables such as lateral position and heading. In the 2nd, drivers pursued a virtual target in the scene. Both models yielded behavior that closely matches that of human drivers.

We presep~t 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 cn earlier work by Longuet-Higgins and Prazdny (198i). The algorithm uses velocity differences computed in regions of high depth variation to estimate the location of the focus of ezpan3ion, 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 selfmoving 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.@Massachusetts Institute of Technology" (1991)

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We present a set of psychophysical experiments that measure the accuracy of perceived threedimensional (3-D)structure derived from relative motion in the changing two-dimensional image. The experiments are motivated in part by a computational model proposed by Ullman (1984), called the incremental rigidity scheme, in which an accurate 3-D structure is built up incrementally, by considering images of moving objects over an extended time period. Our main conclusions are: First, the human visual system can derive an accurate model of the relative depths of moving points, even in the presence of noise in their image positions; second, the accuracy of the 3-D model improves with time, eventually reaching a plateau; and third, the 3-D structure currently perceived appears to depend on previous 3-D models. Through computer simulations, we relate the results of our psychophysical experiments with the predictions of Ullman's model.A valuable source of three-dimensional (3-D) information is provided by the relative motions of elements in the changing two-dimensional (2-D) image. The remarkable ability of the human visual system to recover 3-D structure from motion was explored in many early perceptual studies (e.g., Braunstein, 1976;Gibson & Gibson, 1957;Green, 1961;Johansson, 1973Johansson, , 1978Rogers & Graham, 1979;Ullman, 1979;Wallach & O'Connell, 1953;White & Mueser, 1960). These studies revealed that the human system can recover the structure of rigid and nonrigid objects, under perspective and orthographic projection, and in the absence of all other cues to 3-D structure. Early perceptual work was typically focused on the recovery of qualitative aspects of an object's structure, such as its apparent rigidity, volume, or coherence. More recently, studies have addressed, quantitatively, the accuracy of perceived 3-D structure (e.g., Braunstein, Hoffman, Shapiro, Andersen, & Bennett, 1987; Dosher, Landy, & Sperling, 1989;Lappin & Fuqua, 1983; Loomis & Eby, 1988 Sperling, Landy, Dosher, & Perkins, 1989;Todd, 1982Todd, , 1984Todd, , 1985.In this paper, we present a set of psychophysical experiments in which we have examined both the accuracy We thank Tomaso Poggio, Shimon Ullman, and Whitman Richards for valuable comments on this paper, and Mike Landy for useful discussions. This report describes research done within the Artificial In- The experiments were motivated in part by a computational model proposed by Ullman (1984), called the incremental rigidity scheme, in which an accurate 3-D structure is built up incrementally, as images of moving objects are considered over an extended time period. If this model captures some aspects of the human recovery of structure from motion, then two critical predictions arise. First, the accuracy of perceived structure should increase over an extended time period comparable to that of the model, and second, the current perception of structure should strongly influence later perceptions. Also, in contrast to previous structure-from-motion models, the incremental rigidity scheme e...