Constructing and representing visual objects.

The objects we see are not given in the images at the eyes, but must be constructed by the human visual system. Indeed, damage to specific brain regions often leads to specific impairments of visual abilities (for example, the perception of shape, color or motion). Human vision constructs the various properties of visual objects, not independently of each other, but in a highly coordinated fashion. The construction of one visual property strongly influences the constructions of other properties. Visual shape is an important construction for successfully recognizing objects. There is growing consensus that human vision represents shapes in terms of component parts and their spatial relationships. These parts and their spatial relationships provide a powerful first index into one's visual memory of shapes.

Salience of visual parts.

Many objects have component parts, and these parts often differ in their visual salience. In this paper we present a theory of part salience. The theory builds on the minima rule for defining part boundaries. According to this rule, human vision defines part boundaries at negative minima of curvature on silhouettes, and along negative minima of the principal curvatures on surfaces. We propose that the salience of a part depends on (at least) three factors: its size relative to the whole object, the degree to which it protrudes, and the strength of its boundaries. We present evidence that these factors influence visual processes which determine the choice of figure and ground. We give quantitative definitions for the factors, visual demonstrations of their effects, and results of psychophysical experiments.

Unity of perception.

Perceptual scientists have recently enjoyed success in constructing mathematical theories for specific perceptual capacities, capacities such as stereovision, auditory localization, and color perception. Analysis of these theories suggests that they all share a common mathematical structure. If this is true, the elucidation of this structure, the study of its properties, the derivation of its consequences, and the empirical testing of its predictions are promising directions for perceptual research. We consider a candidate for the common structure, a candidate called an "observer". Observers, in essence, perform inferences; each observer has a characteristic class of perceptual premises, a characteristic class of perceptual conclusions, and its own functional relationship between these premises and conclusions. If observers indeed capture the structure common to perceptual capacities, then each capacity, regardless of its modality or manner of instantiation, can be described as some observer. In this paper we develop the definition of an observer. We first consider two examples of perceptual capacities: the measurement of visual motion, and the perception of depth from visual motion. In each case, we review a formal theory of the capacity and abstract its structural essence. From this essence we construct the definition of observer. We then exercise the definition in discussions of transduction, perceptual illusions, perceptual uncertainty, regularization theory, the cognitive penetrability of perception, and the theory neutrality of observation.

Minimum points and views for the recovery of three-dimensional structure.

Mathematical analyses of motion perception have established minimum combinations of points and distinct views that are sufficient to recover three-dimensional (3D) structure from two-dimensional (2D) images, using such regularities as rigid motion, fixed axis of rotation, and constant angular velocity. To determine whether human subjects could recover 3D information at these theoretical levels, we presented subjects with pairs of displays and asked them to determine whether they represented the same or different 3D structures. Number of points was varied between two and five; number of views was varied between two and six; and the motion was fixed axis with constant angular velocity, fixed axis with variable velocity, or variable axis with variable velocity. Accuracy increased with views, decreased with points, and was greater with fixed-axis motion. Subjects performed above chance levels even when motion was eliminated, indicating that they exploited regularities in addition to those in the theoretical analyses.

Yield and Seed Quality of Soybean Cultivars Infected with Sclerotinia sclerotiorum.

Sclerotinia stem rot (SSR) is one of the most important diseases of soybean in the United States. Five maturity group III cultivars, Asgrow A3304 STS (A3304), Pioneer Brand 9342 (P9342), Pioneer Brand 9381 (P9381), Probst, and Yale, grown in fields in east-central Illinois, were used to determine the relationship of SSR incidence to yield, 100-seed weight, seed protein and oil content, visual seed quality, and seed germination. In addition, the number of sclerotia in seed samples and the seedborne incidence of Sclerotinia sclerotiorum were determined. For each cultivar, at least 23 two-row plots, 3 m long, that represented a range of SSR incidence from low to high, were used to count the number of plants with and without SSR stem symptoms and were used to estimate yields and evaluate seed quality. Disease incidence ranged from 2 to 45% for Probst, 0 to 65% for P9381, 0 to 68% for P9342, 1 to 93% for Yale, and 0 to 95% for A3304. Regression of yields on SSR incidences for each cultivar was significant (P < 0.05); for every 10% increase in SSR incidence, yields were reduced by 147, 194, 203, 254, and 263 kg/ha for Probst, A3304, P9342, Yale, and P9381, respectively. Disease incidence was negatively correlated (P < 0.05) with seed germination for all cultivars but Probst, and to oil content and seed weight for P9381 and Yale. Disease incidence was positively correlated (P < 0.05) with seed quality for all cultivars and to the number of sclerotia in harvested seeds for P9342, P9381, and Probst. The seedborne incidence of S. sclerotiorum was 0.3, 0.3, 0.3, 0.4 and 0.7% in A3304, P9381, Yale, Probst, and P9342, respectively, and represents a significant potential for further spread of this pathogen and disease.

Selected Soybean Plant Introductions with Partial Resistance to Sclerotinia sclerotiorum.

Sclerotinia stem rot, caused by Sclerotinia sclerotiorum, is a major soybean (Glycine max) disease in north-central regions of the United States and throughout the world. Current sources of resistance to Sclerotinia stem rot express partial resistance, and are limited in number within soybean germ plasm. A total of 6,520 maturity group (MG) 0 to IV plant introductions (PIs) were evaluated for Sclerotinia stem rot resistance in the United States and Canada in small plots or in the greenhouse from 1995 to 1997. Selected PIs with the most resistance were evaluated for resistance in the United States and Canada in replicated large plots from 1998 to 2000. The PIs in the MG I to III tests in Urbana, IL were evaluated for agronomic traits from 1998 to 2000. The selected PIs also were evaluated with an excised leaf inoculation and petiole inoculation technique. After the 1995 to 1997 evaluations, all but 68 PIs were eliminated because of their susceptibility to Sclerotinia stem rot. In field tests in Urbana, higher disease severity in selected MG I to III PIs was significantly (P< 0.05) associated with taller plant heights and greater canopy closure. All other agronomic traits evaluated were not associated or were inconsistently associated with disease severity. MG I to III PIs 153.282, 189.931, 196.157, 398.637, 417.201, 423.818, and 561.331 had high levels of resistance and had canopies similar to the resistant checks. The resistance ratings from the petiole inoculation technique had a high and significant (P< 0.01) correlation with disease severity in the MG I and II field tests. The partially resistant PIs identified in this study can be valuable in incorporating Sclerotinia stem rot resistance into elite germ plasm.

Inferring local surface orientation from motion fields.

The problem of inferring local surface orientation from changing images is studied computationally by deriving conditions under which the motion information is sufficient for an information processing system, biological or otherwise, to infer unique descriptions of the local surface orientation. The analysis is based on shape-from-motion proposition, which states, that given the first spatial derivatives of the orthographically projected velocity and acceleration fields of a rigidly rotating regular surface, then the angular velocity and the surface normal at each visible point on that surface are uniquely determined up to a reflection. The proof proceeds in two steps. First it is shown that surface tilt and one component of the angular velocity are uniquely determined by the first spatial derivatives of the velocity field. Then it is shown that surface slant and the remaining two components of the angular velocity are uniquely determined if the first spatial derivatives of the acceleration field are also available.

The generic-viewpoint assumption and illusory contours.

Visual images are ambiguous. Any image, or collection of images, is consistent with an infinite number of possible scenes in the world. Yet we are generally unaware of this ambiguity. During ordinary perception we are generally aware of only one, or perhaps a few of these possibilities. Human vision evidently exploits certain constraints--assumptions about the world and images formed of it--in order to generate its perceptions. One constraint that has been widely studied by researchers in human and machine vision is the generic-viewpoint assumption. We show that this assumption can help to explain the widely discussed fact that outlines of blobs are ineffective inducers of illusory contours. We also present a number of novel effects and report an experiment suggesting that the generic-viewpoint assumption strongly influences illusory-contour perception.

Completing visual contours: the relationship between relatability and minimizing inflections.

Visual completion is a ubiquitous phenomenon: Human vision often constructs contours and surfaces in regions that have no sharp gradients in any image property. When does human vision interpolate a contour between a given pair of luminance-defined edges? Two different answers have been proposed: relatability and minimizing inflections. We state and prove a proposition that links these two proposals by showing that, under appropriate conditions, relatability is mathematically equivalent to the existence of a smooth curve with no inflection points that interpolates between the two edges. The proposition thus provides a set of necessary and sufficient conditions for two edges to be relatable. On the basis of these conditions, we suggest a way to extend the definition of relatability (1) to include the role of genericity, and (2) to extend the current all-or-none character of relatability to a graded measure that can track the gradedness in psychophysical data.

The interpretation of biological motion.

The term biological motion has been coined by Johansson (1973) to refer to the ambulatory patterns of terrestrial bipeds and quadripeds. In this paper a computational theory of the visual perception of biological motion is proposed. The specific problem addressed is how the three-dimensional structure and motions of animal limbs may be computed from the two dimensional motions of their projected images. It is noted that the limbs of animals typically do not move arbitrarily during ambulation. Rather, for anatomical reasons, they typically move in single planes for extended periods of time. This simple anatomical constraint is exploited as the basis for utilizing a "planarity assumption" in the interpretation of biological motion. The analysis proposed is: (1) divide the image into groups of two or three elements each; (2) test each group for pairwise-rigid planar motion; (3) combine the results from (2). Fundamental to the analysis are two "structure from planar motion" propositions. The first states that the structure and motion of two points rigidly linked and rotating in a plane is recoverable from three orthographic projections. The second states that the structure and motion of three points forming two hinged rods constrained to move in a plane is recoverable from two orthographic projections. The psychological relevance of the analysis and possible interactions with top down recognition processes are discussed.

Color from motion: dichoptic activation and a possible role in breaking camouflage.

'Color from motion' describes the perception of a spread of subjective color over achromatic regions seen as moving. The effect can be produced in a display of multiple frames shown in quick succession, each frame consisting of a fixed, random placement of colored dots on a high-luminance white background with color assignments of some dots, but not dot locations, changing from frame to frame. Evidence is presented that the perception of apparent motion and the spread of subjective color can be activated by binocular combination of disjoint signals to each eye. The dichoptic presentation of every odd-numbered frame of the full stimulus sequence presented to one eye and, out of phase, every even-numbered frame to the other eye produces a compelling perception of color from motion equal to that seen with the full sequence presented to each eye alone. This is consistent with the idea that color from motion is regulated in sites at or beyond the convergence of monocular pathways. When the background field in the stimulus display is of low luminance, an amodally complete object, fully colored and matching the dots defining the moving region in hue and saturation, is seen to move behind a partially occluding screen. Observers do not perceive such an object in still view. Hence, color from motion can be used by the visual system to produce amodal completion, which suggests that it may play a role in enhancing the visibility of camouflaged objects.

Inferring the relative three-dimensional positions of two moving points.

We show that four orthographic projections of two rigidly linked points are compatible with at most four interpretations of the relative three-dimensional positions of the points if the points rotate about a fixed axis--even when the points as a system undergo arbitrary rigid translations. A fifth view (projection) yields a unique interpretation and makes zero the probability that randomly chosen image points will receive a three-dimensional interpretation. Assuming that the points rotate at a constant angular velocity, instead of adding a fifth view, also yields a unique interpretation and makes zero the probability that randomly chosen image points will receive a three-dimensional interpretation.

Detection of one versus two objects in structure from motion.

The ability of subjects to detect whether a structure-from-motion display depicts one or two rigid objects was examined in the presence or the absence of noise points. Each object was composed of a set of points chosen randomly within the volume of a sphere. The objects rotated rigidly about different axes passing through the center of the sphere. For displays without noise points, detection increased with larger angles between the rotation axes and with more points in each object. For displays in which noise points were present, detection was above chance but, in general, worse than that for displays without noise points. The implications of these results for image segmentation in complex motion patterns is discussed.

Interpolation across surface discontinuities in structure from motion.

Interpolation across orientation discontinuities in simulated three-dimensional (3-D) surfaces was studied in three experiments with the use of structure-from-motion (SFM) displays. The displays depicted dots on two slanted planes with a region devoid of dots (a gap) between them. If extended through the gap at constant slope, the planes would meet at a dihedral edge. Subjects were required to place an SFM probe dot, located within the gap, on the perceived surface. Probe dot placements indicated that subjects perceived a smooth surface connecting the planes rather than a surface with a discontinuity. Probe dot placements varied with slope of the planes, density of the dots, and gap size, but not with orientation (horizontal or vertical) of the dihedral edge or of the axis of rotation. Smoothing was consistent with models of 2-D interpolation proposed by Ullman (1976) and Kellman and Shipley (1991) and with a model of 3-D interpolation proposed by Grimson (1981).

Inferring structure from motion in two-view and multiview displays.

Five experiments were conducted to examine constraints used to interpret structure-from-motion displays. Theoretically, two orthographic views of four or more points in rigid motion yield a one-parameter family of rigid three-dimensional (3-D) interpretations. Additional views yield a unique rigid interpretation. Subjects viewed two-view and thirty-view displays of five-point objects in apparent motion. The subjects selected the best 3-D interpretation from a set of 89 compatible alternatives (experiments 1-3) or judged depth directly (experiment 4). In both cases the judged depth increased when relative image motion increased, even when the increased motion was due to increased simulation rotation. Subjects also judged rotation to be greater when either simulated depth or simulated rotation increased (experiment 4). The results are consistent with a heuristic analysis in which perceived depth is determined by relative motion.

Interpolation in structure from motion.

We investigated surface interpolation in displays of structure from motion (SFM). To do so, we introduced a new method for measuring surface perception in dynamic displays--the SFM probe. An SFM probe is a dot that moves rigidly with the dots on a simulated surface, and whose distance from that surface can be adjusted with a joystick or similar control. The displays we studied were random-dot cylinders containing a vertical strip devoid of feature points (the gap). Subjects adjusted an SFM probe, presented in the gap, until the probe dot appeared to be on the surface. Variability in probe-dot placement decreased with increasing texture density on the cylinder and increased with increasing gap width. Subjects showed a consistent bias to place the probe dot outside the cylinder. This bias increased with increasing texture density for the SFM displays. (The opposite bias was found in a static two-dimensional interpolation task with an arc whose curvature matched that of the cylinder: Subjects placed the probe dot inside the arc.) This outside bias is inconsistent with several theoretical approaches to surface interpolation.

Parts of visual objects: an experimental test of the minima rule.

Three experiments were conducted to test Hoffman and Richards's (1984) hypothesis that, for purposes of visual recognition, the human visual system divides three-dimensional shapes into parts at negative minima of curvature. In the first two experiments, subjects observed a simulated object (surface of revolution) rotating about a vertical axis, followed by a display of four alternative parts. They were asked to select a part that was from the object. Two of the four parts were divided at negative minima of curvature and two at positive maxima. When both a minima part and a maxima part from the object were presented on each trial (experiment 1), most of the correct responses were minima parts (101 versus 55). When only one part from the object--either a minima part or a maxima part--was shown on each trial (experiment 2), accuracy on trials with correct minima parts and correct maxima parts did not differ significantly. However, some subjects indicated that they reversed figure and ground, thereby changing maxima parts into minima parts. In experiment 3, subjects marked apparent part boundaries. 81% of these marks indicated minima parts, 10% of the marks indicated maxima parts, and 9% of the marks were at other positions. These results provide converging evidence, from two different methods, which supports Hoffman and Richard's minima rule.

Parsing silhouettes: the short-cut rule.

Many researchers have proposed that, for the purpose of recognition, human vision parses shapes into component parts. Precisely how is not yet known. The minima rule for silhouettes (Hoffman & Richards, 1984) defines boundary points at which to parse but does not tell how to use these points to cut silhouettes and, therefore, does not tell what the parts are. In this paper, we propose the short-cut rule, which states that, other things being equal, human vision prefers to use the shortest possible cuts to parse silhouettes. We motivate this rule, and the well-known Petter's rule for modal completion, by the principle of transversality. We present five psychophysical experiments that test the short-cut rule, show that it successfully predicts part cuts that connect boundary points given by the minima rule, and show that it can also create new boundary points.

Equation counting and the interpretation of sensory data.

Many problems in biological information processing require the solution to a complex system of equations in many unknown variables. An equation-counting procedure is described for determining whether such a system of equations will indeed have a unique solution, and under what conditions the solution should be interpreted as 'correct'. Three examples of the procedure are given for illustration, one from auditory signal processing and two from vision.