Direct Computation of 3D Shape Invariants and the Focus of Expansion

Structure from motion often refers to the computation of 3D structure from a matched sequence of images. However, a depth map of a surface is difficult to compute and may not be a good representation for storage and recognition. Given matched images, I will first show that the sign of the normal curvature in a given direction at a given point in the image can be computed from a simple difference of slopes of line-segments in one image. Using this result, local surface patches can be classified as convex, concave, parabolic (cylindrical), hyperbolic (saddle point) or planar. At the same time the translational component of the optical flow is obtained, from which the focus of expansion can be computed.

Sequence-Seeking and Counter Streams: A Model for Information Processing in the Cortex

This paper presents a model for the general flow in the neocortex. The basic process, called "sequence-seeking," is a search for a sequence of mappings or transformations, linking source and target representations. The search is bi-directional, "bottom-up" as well as "top-down," and it explores in parallel a large numbe rof alternative sequences. This operation is implemented in a structure termed "counter streams," in which multiple sequences are explored along two separate, complementary pathways which seeking to meet. The first part of the paper discusses the general sequence-seeking scheme and a number of related processes, such as the learning of successful sequences, context effects, and the use of "express lines" and partial matches. The second part discusses biological implications of the model in terms of connections within and between cortical areas. The model is compared with existing data, and a number of new predictions are proposed.

Explanation of Big "P" as of March 20, 1959

ERROR is a routine to provide a common location for all routines. Its celling sequence is: SXD SERROR,4 TSX SERROR+1,4 The above is normally followed immediately by up to 20 registers of BCD remarks terminated by a word of 1's. This may be left out, however. ERROR prints out the remark, if any, the location of the TSX that entered error, restores the console except for the AC overflow, and transfers to the user's error routine specified by the calling sequence of SETUP.

Specialization of Perceptual Processes

In this report, I discuss the use of vision to support concrete, everyday activity. I will argue that a variety of interesting tasks can be solved using simple and inexpensive vision systems. I will provide a number of working examples in the form of a state-of-the-art mobile robot, Polly, which uses vision to give primitive tours of the seventh floor of the MIT AI Laboratory. By current standards, the robot has a broad behavioral repertoire and is both simple and inexpensive (the complete robot was built for less than $20,000 using commercial board-level components). The approach I will use will be to treat the structure of the agent's activity---its task and environment---as positive resources for the vision system designer. By performing a careful analysis of task and environment, the designer can determine a broad space of mechanisms which can perform the desired activity. My principal thesis is that for a broad range of activities, the space of applicable mechanisms will be broad enough to include a number mechanisms which are simple and economical. The simplest mechanisms that solve a given problem will typically be quite specialized to that problem. One thus worries that building simple vision systems will be require a great deal of {it ad-hoc} engineering that cannot be transferred to other problems. My second thesis is that specialized systems can be analyzed and understood in a principled manner, one that allows general lessons to be extracted from specialized systems. I will present a general approach to analyzing specialization through the use of transformations that provably improve performance. By demonstrating a sequence of transformations that derive a specialized system from a more general one, we can summarize the specialization of the former in a compact form that makes explicit the additional assumptions that it makes about its environment. The summary can be used to predict the performance of the system in novel environments. Individual transformations can be recycled in the design of future systems.

Recognition of Topological Invariants by Iterative Arrays

A study is made of the recognition and transformation of figures by iterative arrays of finite state automata. A figure is a finite rectangular two-dimensional array of symbols. The iterative arrays considered are also finite, rectangular, and two-dimensional. The automata comprising any given array are called cells and are assumed to be isomorphic and to operate synchronously with the state of a cell at time t+1 being a function of the states of it and its four nearest neighbors at time t. At time t=0 each cell is placed in one of a fixed number of initial states. The pattern of initial states thus introduced represents the figure to be processed. The resulting sequence of array states represents a computation based on the input figure. If one waits for a specially designated cell to indicate acceptance or rejection of the figure, the array is said to be working on a recognition problem. If one waits for the array to come to a stable configuration representing an output figure, the array is said to be working on a transformation problem.

Computational Structure of Human Language

The central thesis of this report is that human language is NP-complete. That is, the process of comprehending and producing utterances is bounded above by the class NP, and below by NP-hardness. This constructive complexity thesis has two empirical consequences. The first is to predict that a linguistic theory outside NP is unnaturally powerful. The second is to predict that a linguistic theory easier than NP-hard is descriptively inadequate. To prove the lower bound, I show that the following three subproblems of language comprehension are all NP-hard: decide whether a given sound is possible sound of a given language; disambiguate a sequence of words; and compute the antecedents of pronouns. The proofs are based directly on the empirical facts of the language user's knowledge, under an appropriate idealization. Therefore, they are invariant across linguistic theories. (For this reason, no knowledge of linguistic theory is needed to understand the proofs, only knowledge of English.) To illustrate the usefulness of the upper bound, I show that two widely-accepted analyses of the language user's knowledge (of syntactic ellipsis and phonological dependencies) lead to complexity outside of NP (PSPACE-hard and Undecidable, respectively). Next, guided by the complexity proofs, I construct alternate linguisitic analyses that are strictly superior on descriptive grounds, as well as being less complex computationally (in NP). The report also presents a new framework for linguistic theorizing, that resolves important puzzles in generative linguistics, and guides the mathematical investigation of human language.

Passive Dynamics in the Control of Gymnastic Maneuvers

The control of aerial gymnastic maneuvers is challenging because these maneuvers frequently involve complex rotational motion and because the performer has limited control of the maneuver during flight. A performer can influence a maneuver using a sequence of limb movements during flight. However, the same sequence may not produce reliable performances in the presence of off-nominal conditions. How do people compensate for variations in performance to reliably produce aerial maneuvers? In this report I explore the role that passive dynamic stability may play in making the performance of aerial maneuvers simple and reliable. I present a control strategy comprised of active and passive components for performing robot front somersaults in the laboratory. I show that passive dynamics can neutrally stabilize the layout somersault which involves an "inherently unstable" rotation about the intermediate principal axis. And I show that a strategy that uses open loop joint torques plus passive dynamics leads to more reliable 1 1/2 twisting front somersaults in simulation than a strategy that uses prescribed limb motion. Results are presented from laboratory experiments on gymnastic robots, from dynamic simulation of humans and robots, and from linear stability analyses of these systems.