Depth Perception in Frogs and Toads: A Study in Neural Computing PDF
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Kimura B. Kosko S. Levin (Managing Editor) R. May J. Murray G. F. Oster A. S. Perelson T. Poggio L. A. Segel Author Donald House Department of Computer Science Williams College Williamstown, MA01267, USA Mathematics Subject Classification (1980): 68 T XX, 92 A 18 CR Subject Classifications {1982}: J.3; 1.2.m ISBN-13: 978-0-387-97157-5 e-ISBN-13: 978-1-4684-6391-0 001: 10.1007/978-1-4684-6391-0 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich. © Springer-Verlag New York, Inc., 1989 2849/3140-543210 - Printed on acid-free paper Depth Perception in Frogs and Toads -- A Study in Neural Computing provides a comprehensive exploration of the phenomenon of depth perception in frogs and toads, as seen from a neuro-computational point of view. Perhaps the most important feature of the book is the development and presentation of two neurally realizable depth perception algorithms that utilize both monocular and binocular depth cues in a cooperative fashion. One of these algorithms is specialized for computation of depth maps for navigation, and the other for the selection and localization of a single prey for prey catching. The book is also unique in that it thoroughly reviews the known neuroanatomical, neurophysiological and behavioral data, and then synthesizes, organizes and interprets that information to explain a complex sensory-motor task. The book should be of special interest to that segment of the neural computing community interested in understanding natural neurocomputational structures, and will be of particular interest to those working in perception and sensory-motor coordination. It will also be of interest to neuroscientists interested in exploring the complex interactions between the neural substrates that underly perception and behavior. Donald H. House Williamstown July 14, 1989 Contents 1 Introduction 1 2 Modeling Depth Perception in Frogs and Toads 5 2.1 Previous Models of Depth Perception. . . . . . . . 5 2.2 Depth Perception in Frogs and Toads. . . . . . . . 7 2.2.1 The role of depth perception in detour behavior. 8 2.2.2 Monocular and binocular depth cues 10 2.3 Anatomy and Physiology ..... 14 2.3.1 The eyes. . . . . . . . . . . . . . . . 14 2.3.2 Optic nerve projection sites . . . . . 14 2.3.3 Nucleus isthmi - a source of binocular input to tectum 16 2.3.4 Binocular units in tectum and thalamus . . . . 18 2.3.5 Efferent pathways from tectum and thalamus . 20 2.4 Functional Analysis of the Major Visuomotor Centers 20 2.4.1 Retina..................... 20 2.4.2 Functions of thalamus and tectum . . . . . 22 2.4.3 Evidence for depth perception in thalamus 23 2.4.4 Motor pathways from tectum and thalamus 23 2.4.5 Depth perception dissociated from orientation. 24 2.4.6 Depth Maps, Motor activity and tectal retinotopy 25 2.4.7 Summary of the frog/toad visual system. 27 2.5 Modeling Assumptions . 27 2.6 Conclusions..................... 28 3 Monocular and Binocular Cooperation 31 3.1 Design of the Model 31 3.1.1 Structure ..... . 33 3.1.2 Constraints..... 34 3.1.3 Coordinate systems 35 3.1.4 Computational scheme. 37 3.2 Methods ........... . 40 3.2.1 Computer simulation. 40 3.2.2 Visual input. . . . . . 41 VI 3.3 Results................ .. . 44 3.3.1 Initial validation ........ . 44 3.3.2 Effect of lateral excitatory spread. 46 3.3.3 Depth segmentation .... 48 3.3.4 Effects of lenses and prisms 49 3.3.5 Barrier depth resolution 52 3.3.6 Monocular response 54 3.4 Discussion ........... . 55 4 Localization of Prey 57 4.0.1 Background. 57 4.0.2 Model overview . 59 4.1 Methods......... 60 4.1.1 Computer simulation. 60 4.1.2 Mathematical description for the simulation. 60 4.1.3 Graphical displays . . . . 66 4.1.4 Depth estimate categories 68 4.1.5 Visual input. . . . . . . . 69 4.2 Results............... 69 4.2.1 Experiments with single-prey stimuli. 69 4.2.2 Experiments with multiple-prey stimuli 71 4.2.3 The effect of lenses on two-prey experiments 78 4.3 Discussion........................ 78 4.3.1 A possible neural realization of the model 78 4.3.2 Suitability of the nucleus isthmi as a tecto-tectal re- lay for depth perception 83 4.3.3 Evaluation of the model . . . . . . . . . . . . . .. 84 5 Towards a Complete Model 87 5.1 The Cue Interaction and Prey Localization Models 87 5.1.1 Unities.. 87 5.1.2 Diversities.............. ... 88 5.1.3 A synthesis . . . . . . .. ........ 89 5.2 An Extended Model of Accommodation Control. 92 5.3 Experimental Verification of the Models' Depth Scale. 96 5.4 Discussion ...................... 98 6 Conclusions 101 6.1 The Models and their Contributions 102 6.2 Suggestions for Animal Experiments 103 6.3 Suggestions for Robotic Algorithms . 106 VII A Modeling and Simulation Details 109 A.1 Representation of a Neural Unit. 109 A.2 Representation of a Neural Layer 110 A.3 Numerical Methods ..... . 112 A.4 The Cue Interaction Model . 113 A.5 The Prey Localization Model 117 B Simulation Optics 123 B.1 Optical Geometry 123 B.2 Representation of Prisms 125 B.3 Retinal Projections . . .. 125 B.4 Disparity Input Planes . . 126 B.5 Accommodation Input Planes 126 B.6 Representation of Lenses . . . 127 B.7 Conversion from Internal to External Coordinates 127 B.8 Nominal Parameter Settings ............ . 128 Bibliography 129 1 Introduction In this study, w~ present a sequence of models exploring neural mechanisms by which frogs and toads may extract depth information from visual data. Although the models are constructed to be true, as far as possible, to what is known regarding depth perception in frogs and toads, they are also of more general interest. In particular, when they were developed they were the first depth models to exploit both binocular and monocular depth cues in a cooperative fashion. Our work differs from most current work in depth perception in several ways. Of course, the first of these is that we use frogs and toads, rather than mammals, as our study system. Second, we are particularly concerned with the ways in which depth information from multiple cue sources can be inte grated. Finally, our point of view is that perception is action-oriented. This has required us to pay careful attention to behavioral as well as anatomical and physiological data in our search for plausible neural algorithms. Our analysis suggests that frogs and toads do not use a single means for determining depth from visual input but, instead, use at least two different processes, one specialized for navigation and the other for prey catching. We present models of these two processes and outline features of an accommo dation control system that will support them both. Our model supporting navigation consists of two cooperative depth mapping processes, with one process receiving accommodation cues and the other receiving binocular disparity cues. By sharing information, the two processes are able to build a single depth map, whose accuracy is governed by binocularity. Our second model is of a process best suited for prey catching. Instead of building a depth map, it determines the spatial location of a single object by coupling prey-selection and lens-accommodation processes within a feedback loop. Information derived from prey selection supplies a setpoint for accommo dation. In turn, lens accommodation modifies the visual input and affects the prey selection process. This scheme automatically corrects spurious binocular matches. Our purpose in creating these models is twofold and involves two dis parate disciplines. First, the models are constrained to conform to existing knowledge of the visuomotor system of frogs and toads and are aimed at improving our understanding of visuomotor coordination in these animals. Second, by constructing and experimenting with computer simulations of the models, we have taken a first step in the development and testing of sensory-motor control algorithms for artificial systems. Experiments done with the computer simulations allowed us to go be- 2 1. Introduction yond mere plausibility arguments by providing concrete demonstrations of the efficacy of the models. They allowed us to analyze the sensitivity of the models to variations in parameter settings and in environmental con figurations. This analysis, in turn, led to many concrete predictions about animal behavior that are now open for verification by experimentalists. Further, the computer simulations represent operating algorithms that can be implemented in robotic systems. Experiments with these simulations provide important data concerning the tuning and expected performance characteristics of these algorithms. We approached this study of depth perception with the view that, when addressing the problems of sensory-motor coordination, there are no bound aries between artificial and natural sensory-motor systems. The study of natural systems, which are so successful at performing sensory-motor tasks that are difficult to implement in machines, holds promise of providing ele gant solutions to practical problems in robotics. Conversely, when a solution to a sensory-motor problem has proven successful in an artificial system, it becomes a rich source of analogy in the study of natural systems. Sensory processes and motor processes cannot and should not be put into separate categories. The purpose of sensation is to adjust action. Action in turn affects perception. Action and perception are two inseparable parts of a closed cycle [Neisser, 1976; Arbib, 1981]. If depth discrimination is embedded within a cycle of action and perception, then it cannot be viewed simply as an information-organizing process separate from action. If, for instance, a toad exhibits size-constancy in its preference for prey (Le. it appears to make judgements about visually presented objects that reflect the object's real size rather than subsumed visual angle) then do we assume that the toad estimates the distance of the prey and then determines its size, or do we assume that a side effect of the toad's prey acquistion strategy is that prey of a certain size are preferred? Our point of view does not allow us to treat depth perception as a passive process, concerned only with assigning a depth value to each point in visual space. Instead, it must be viewed as part of a dynamic process by which an animal (or machine or human) achieves a particular goal. If the goal is navigation through the environment, then what is required is quite different from what is required if the goal is to catch a passing fly. Depth perception, to the extent that it is an identifiable function of the visual system, may take as many different forms as there are distinctly different functions that require its use. Frogs and toads were chosen for this study for several reasons. First, they exhibit ballistic behavior. Their prey-catching sequence consists of periods of apparent inactivity followed by a series of movements that seem to be preplanned. Changes in the environment after initiation of overt activity do not seem to affect the way in which that sequence is carried out. Once a toad begins to stalk and strike at a prey object, it will not stop even if the prey target is artifically removed; the sequence, including swallowing and 1. Introduction 3 wiping the mouth after the strike, is uninterrupted [Ewert, 1980]. Ballistic behavior is remarkably akin to the actions of preprogrammed robots. A second reason for choosing frogs and toads is that they are vertebrates, but have relatively simple brains. Therefore, it may be possible to draw parallels to visual functioning in higher vertebrates without having to confront their greater complexity [Scalia and Fite, 1974]. Finally, frogs and toads exhibit highly developed depth vision but also appear to utilize fairly simple rules when using depth information to coordinate their behavior [Collett, 1982]. These rules employ only readily available visual cues, and thus they are of the sort which could conceivably be implemented in a robotic system. We have carefully examined data from experimentalists and hope that, in turn, our models will be the subject of experimental testing. We also hope that our models will prove useful in the design of control systems for robots, even if results of experients with frogs and toads prove to refute some of our speculations. Acknowledgements: The research reported in this book was initially sup ported by NIH grant NS14971 03-05, M. A. Arbib principle investigator. Later work and preparation of the manuscript were partially supported by Williams College. The author would like to extend special thanks to Michael Arbib for his guidance throughout this project, to Andrew Barto and Thomas Collett for their scientific guidance, and to Ann Ferguson Nauman for her expert and insightful editing.
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