The copycat solution to the shadow correspondence problem

Cast shadows (henceforth simply 'shadows') depicted in artworks can fulfil some of their perceptual roles, such as helping the retrieval of 3-D structure and of relative positions of objects, without having to be geometrically or physically accurate. The visual system displays a wide tolerance for shadows that are mostly inaccurate, at times making use of the scarce accurate but relevant information that can still be retrieved from them. However, the extent of the tolerable inaccuracy is at present still unexplored. I propose that inaccuracy can be not only totally acceptable but in some cases is even likely to be preferable to accuracy if the main perceptual role of shadows is to help locate in a scene the objects that cast them. I examined a small but effective historical corpus of pictorial endeavours, from which it appears that in some cases painters have used a copycat strategy for drawing the terminator of a shadow, ie they have produced a replica of the visible profile of the caster, which in the norm yields an impossible shadow. The copycat strategy is perceptually effective for solving the correspondence problem of associating a shadow with its caster; copycatting can be more effective than other solutions, including the depiction of the geometrically correct shadow, and is complementary to coarser solutions to the correspondence problem. These phenomena provide insight into the computations effectively used by the brain to deal with space perception. In particular, the brain is not relying on some sort of simplified physical model of the world, for the shadows produced by the copycat effect would correspond to a more complicated physical situation than the one encountered in real life.     

Differential activation solution to the

The correspondence problem arises in motion perception when more than one motion path is possible for discontinuously presented visual elements. Ullman’s (1979) “minimal mapping” solution to the correspondence problem, for which costs are assigned to competing motion paths on the basis of element affinities (e.g., greater affinity for elements that are closer together), is distinguished from a solution based on the differential activation of directionally selective motion detectors. The differential activation account was supported by evidence that path length affects detector activation in a paradigm for which motion correspondence is not a factor. Effects on detector activation in this paradigm also were the basis for the successful prediction of path luminance effects on solutions to the motion correspondence problem. Finally, the differential activation account was distinguished from minimal mapping theory by an experiment showing that the perception of an element moving simultaneously in two directions does not depend on whether the two motions are matched in path-length determined affinity; it is sufficient that the activation of detectors responding to each of the two motion directions is above the threshold level required for the motions to be perceived. Implications of the differential activation solution are discussed for the stability of perceived motions once they are established, and the adaptation of perceived andunperceived motions.     

The integration of orientation information in the motion correspondence problem

We examine how differently oriented components contribute to the discrimination of motion direction along a horizontal axis. Stimuli were two-frame random-dot kinematograms that were narrowband filtered in spatial frequency. On each trial, subjects had to state whether motion was to the left or the right. For each stimulus condition, Dmax (the largest displacement supporting 80% correct direction discrimination performance) was measured. In experiment 1, Dmax was measured for orientationally narrowband stimuli as a function of their mean orientation. Dmax was found to increase as the orientation of the stimuli became closer to the axis of motion. Experiment 2 used isotropic stimuli in which some orientation bands contained a coherent motion signal, and some contained only noise. When the noise band started at vertical orientations and increased until only horizontal orientations contained a coherent motion signal, Dmax increased slightly. This suggests that near-vertical orientations interfere with motion perception at large displacements when they contain a coherent motion signal. When the noise band started at horizontal and increased until only vertical orientations contained the motion signal, Dmax decreased steadily. This implies that Dmax depends at least partly on the most horizontal motion signal in the stimulus. These results were contrasted with two models. In the first, the visual system utilises the most informative orientations (nearest horizontal). In the second, all available orientations are used equally. Results supported an intermediate interpretation, in which all orientations are used but more informative ones are weighted more heavily.     

The how and why of what went where in apparent motion: modeling solutions to the motion correspondence problem

A model that is capable of maintaining the identities of individuated elements as they move is described. It solves a particular problem of underdetermination, the motion correspondence problem, by simultaneously applying 3 constraints: the nearest neighbor principle, the relative velocity principle, and the element integrity principle. The model generates the same correspondence solutions as does the human visual system for a variety of displays, and many of its properties are consistent with what is known about the physiological mechanisms underlying human motion perception. The model can also be viewed as a proposal of how the identities of attentional tags are maintained by visual cognition, and thus it can be differentiated from a system that serves merely to detect movement.     

Color correspondence in apparent motion

To maintain figural identity during motion perception, the visual system must match images over space and time. Correct matching requires a metric for identifying "corresponding" images, those representing the same physical object. To test whether matching is based on achromatic (black/white) polarity and chromatic (red/green) color, observers viewed an ambiguous motion display and judged the path of apparent motion. Matching preserved black/white identity regardless of whether frames were viewed binocularly or dichoptically. Red/green identity was also preserved, but coherence of motion depended in part on the number of frames in the motion sequence and on the background luminance. These results suggest that correspondence is computed by a weighted metric containing terms for image features coded early in visual processing.     

The influence of structure from motion on motion correspondence

The visual system has a remarkable ability to reconstruct 3-D structure from moving 2-D features. The processing of structure from motion is generally thought to consist of two stages. First, the direction and speed of features is measured (2-D velocity measurement) and, second, 3-D structure is reconstructed from the measured 2-D velocities (3-D structure recovery). Most models have assumed that these stages occur in a bottom-up fashion. Here, however, we present evidence that the 3-D structure-recovery stage influences the 2-D velocity-measurement stage. We developed a stimulus in which two perceptual modes of motion correspondence (one-way translation versus oscillation), and two perceptual modes of 3-D surface structure (flat surface versus cylinder) could be achieved. We found that the likelihood of perceiving both one-way motion and cylindrical structure increased in similar ways with increasing frame duration. In subsequent experiments we found, first, that a higher likelihood of perceiving one-way motion did not affect the likelihood of perceiving cylindrical structure; and, second, that a higher likelihood of perceiving cylindrical structure increased the likelihood of perceiving one-way motion. These results suggest that the higher, 3-D structure-recovery stage may influence the lower, 2-D motion-correspondence stage. This result is not in accordance with most computational models that assume that there is only one-way, feedforward information processing from the 2-D velocity (energy)-measurement stage to the 3-D structure-recovery stage. Perhaps, one of the roles of feedback processing is to seek consensus of the information processed in different stages.     

Impossible shadows and the shadow correspondence problem

Shadows cast by objects contain potentially useful information about the location of these objects in the scene as well as their surface reflectance. However, before the visual system can use this information, it has to solve the shadow correspondence problem, that is to match the objects with their respective shadows. In the first experiment, it is shown that the estimate of the light source position is affected by a gradual luminance ramp added to the image. In the second experiment, it is shown that observers process impossible shadow images as if they ignored the local features of the objects. All together, the results suggest that the visual system solves the shadow correspondence problem by relying on a coarse representation of the scene.     

Tooley's solution to the inference problem

Conclusion Tooley's speculative theory, I have tried to show, is beset with difficulties. I warned that this theory threatens to fail in its goal of illuminating the possible nature of a necessitation relation if it employs radical principles about parts and wholes and universals. Secondly, I argued that regardless of how we interpret the crucial phrase existing only as a part of, the speculative theory cannot solve the inference problem without appealing to such radical principles. Finally, I considered and rejected a version of Tooley's speculative theory that attempts to solve the inference problem using the Indiscernibility of Identicals.I conclude that the speculative theory fails. Tooley must fall back to the stipulative theory and live with the lack of an illuminating solution to the inference problem. But this is not to admit defeat. While it would be nice to have a more complete account of its workings, we may view the introduction of the necessitation relation as a theoretical posit, analogous to the positing of subatomic particles in physics to account for various data.I would like to thank Phillip Bricker for his persistent help with this paper. I would also like to thank David Lewis and an anonymous referee for Philosophical Studies for their comments.     

A solution to the many attitudes problem

Philosophical Studies - According to noncognitivism, normative beliefs are just desire-like attitudes. While noncognitivists have devoted great effort to explaining the nature of normative belief,...     

Illusory contours as the solution to a problem

The perception of certain figures with illusory contours entails a reversal of figure and ground. It is hypothesized that this process occurs in two stages. First, some factor must suggest or cue the reversal. Experiments are described that isolate three such factors, namely, alignment of physically present contours, recognized incompletion of parts of the stimulus array, and set. Once cued, however, other experiments indicate that in a further stage of processing the solution is examined with respect to its compatibility with the stimulus display or with other preceptual properties to which the display gives rise. Only if such compatibility is present will the perception of a figure with illusory contours be maintained.     

The elegant solution to the problem of impotence

Although most therapists are committed to debunking the dual myths that sex requires an erection and that sex equals intercourse, sex researchers continue to use successful intercourse as a primary dependent variable. It is here asserted that RET therapists would do well to approach the problem of erectile dysfunction from a more elegant philosophical perspective. The treatment approach outlined here is aimed at reducing client disturbance as well as increasing sexual satisfaction rather than at simply helping the client to regain his potency.     

Visible persistence and form correspondence in Ternus apparent motion

Visual stimuli remain visible for some time after their physical offset (visible persistence) Visible persistence has been hypothesized to play an important role in determining the pattern of correspondence matching in the Ternus apparent-motion display. In this display, one or more elements reappears in overlapping locations at different times, whereas another element appears alternately to the right or the left of these elements. Usually either the elements are perceived to move coherently as a group (group motion), or one element may be perceived to hop over one or more other elements (element motion). According to the visible-persistence account of the perceptual organization of the Ternus display, element motion is seen when the temporal gap between elements in overlapping locations is small enough to be bridged by visible persistence; if it is not, group motion is seen. We conducted four experiments to test this visible-persistence account. In Experiments 1 and 2, a form correspondence cue (line length) was introduced to bias the visual system toward the element-motion interpretation, while visible persistence was either reduced or eliminated. The element-motion percept dominated despite the elimination of visible persistence. In Experiments 3 and 4, we found that Ternus elements presented without interruption, and thus presumably persisting over time, can be perceived in group motion. Together, the results indicate that visible persistence is neither necessary nor sufficient to account for the pattern of correspondence matches in the Ternus display.     

Moorean pluralism as a solution to the incommensurability problem

Several prominent ethical philosophers have attempted to demonstrate that there exist instances or types of value that are of crucial moral significance but which cannot legitimately be compared with one another. Bernard Williams and Michael Stocker, for example, argue that it can sometimes be rational to regret having chosen the all-things-considered better of two alternatives, and that this sense of regret entails that the goodness of the worse option is not made up for by and is therefore incommensurable with that of the better. Joseph Raz and others have made similar points. In this paper, I propose a theory of value that is monistic in that it countenances just one sort of morally crucial value, but pluralistic in that several distinct properties bearer this value. I then explain how this view avoids incommensurable values without doing violence to the core intuitions that seemed to necessitate them, and how it fits into a larger conception of morality, right conduct, and moral psychology.     

A modest solution to the problem of religious disagreement

Many assume that the best, and perhaps only, way to address the so-called Problem of Evil (PoE) is to claim that God does not do evil, but that God merely allows evil. This assumption depends on two claims: (i) the doing-allowing distinction exists and (ii) the doing-allowing distinction is morally significant. In this paper I try to undermine both of these claims. Against (i) I argue that some of the most influential analyses of the doing-allowing distinction face grave difficulties and that these difficulties are only exacerbated when applied to God. Against (ii) I argue that broadly Kantian considerations give a better explanation of the moral differences in paradigm cases than the doing-allowing distinction and, when applied to God, effectively dissolve the moral significance of the doing-allowing distinction. The upshot of this is that those who claim God does evil are no worse off than those who claim God allows evil regarding the PoE.