Distortion in Art: the Eye and the Mind by J. B. Deregowski (review)

more to the point. ;I computeriied robot’s eye, given three separate LSiew\or frames o f a movie sequence of the flying Superman, can be absolutely sure that the figure is of a certain shape and flying in a certain direction. even if Superman is flying at night with just four lights attached to his body giving the visual cues to the idealized observer. For most of us who are blessed with the gift of sight, all this seems superfluous and rather tedious, since we already instinctively know it to be true. Ullman. however. has the well-defined aim of studying the tasks accomplished by a visual system in order to investigate the computations it performs. It almost seems that the author was searching for an ideal visual system and chose the human visual system because it is efficient, but not quite so efficient as certain mathematical algorithms (p. 155). This approach is fully justified, since the research is the product of MIT’s Artificial Intelligence Laboratory. The thrust of the work is to analyze those aspects of human vision of motion that can be useful in teaching a machine how to see. This aim is not clearly stated, but the discussion is colored by the computational approach to vision research. The results of the meticulous experiments are expressed mathematically and used to refute older, more intuitive results by Gibson (p. 140) and others. One cannot help but think there are many other aspects of the subject than those treated in this book. For example, what effect does body acceleration have on our experience of motion? When a 3-dimensional object is seen in motion, is it being seen with one eye or with two? What can we learn from such effects as the waterfall illusion or the Pulfrich pendulum illusion about the way we perceive motion? More basically, what is the physiological and neurological basis of the perception of motion’? All these matters are untreated in this very specialized and poorly illustrated book. Is it fair for a layman to criticize a work in this way’? I believe so: scientific truth is relative. To Ullnian a baby looks at a milk bottle from different viewpoints, “attaching them to the new superordinate ‘node”’. But does a baby have to learn all the formulas in the Appendix entitled “Structure from Perspective Projections”, as a robot must? There is a constant temptation for people working on artificial intelligence t o carry the notion. “this is the best way to design a robot vision”, all the way to “human vision is almost like a robot’s vision”. Most of the experiments discussed involve two pictures of dots or lines that were presented rapidly one after another to an observer, who saw apparent motion if there was displacement ofthestimuli. Ullmanshows that very few points or visual cues are sufficient to define an object’\ motion in two- or threedimensional space. The correspondence between the objects in the two frames is analyzed using a “minimal mapping theory”essentially a mathematical approach t o matching the two views topologically. The last two chapters of the book are entitled “The Interpretation of Structure from Motion” and “The Perception of Motion from Structure”. These relate to the perception of the shape of an unknown object known from the moving two-dimensional views the observer sees, and the perception of the motion of a known object, such as a cube. Although quite abst act. The Inrrrprrrarion of Vrrual Motion is not abstract enough. i n the sense that it only deals with the “real” visual world. There is n o mention of the contortions ot the pseudoscopically viewed scene. l’he mathematical treatment is lim~ted to generally rigid objects moving in our familiar perceptual world following the i-ules of perspective. But what about the perception of motion in artificial reality? In computer graphics. object, not only can be transformed magically from a cube to a n angel to a field of stars, but thevery space in which these objects move can he given new properties-for example, a spherical coordinate space where the perceived motion increases the more the object approaches the center. All this makes one...