Intelligence in Scientific Computing

Combining numerical techniques with ideas from symbolic computation and with methods incorporating knowledge of science and mathematics leads to a new category of intelligent computational tools for scientists and engineers. These tools autonomously prepare simulation experiments from high-level specifications of physical models. For computationally intensive experiments, they automatically design special-purpose numerical engines optimized to perform the necessary computations. They actively monitor numerical and physical experiments. They interpret experimental data and formulate numerical results in qualitative terms. They enable their human users to control computational experiments in terms of high-level behavioral descriptions.

Using English For Indexing and Retrieving

This paper describes a natural language system START. The system analyzes English text and automatically transforms it into an appropriate representation, the knowledge base, which incorporates the information found in the text. The user gains access to information stored in the knowledge base by querying it in English. The system analyzes the query and decides through a matching process what information in the knowledge base is relevant to the question. Then it retrieves this information and formulates its response also in English.

XP. A Common Lisp Pretty Printing System

XP provides efficient and flexible support for pretty printing in Common Lisp. Its single greatest advantage is that it allows the full benefits of pretty printing to be obtained when printing data structures, as well as when printing program code. XP is efficient, because it is based on a linear time algorithm that uses only a small fixed amount of storage. XP is flexible, because users can control the exact form of the output via a set of special format directives. XP can operate on arbitrary data structures, because facilities are provided for specifying pretty printing methods for any type of object. XP also modifies the way abbreviation based on length, nesting depth, and circularity is supported so that they automatically apply to user-defined functions that perform output ??g., print functions for structures. In addition, a new abbreviation mechanism is introduced that can be used to limit the total numbers of lines printed.

XP. A Common Lisp Pretty Printing System

XP provides efficient and flexible support for pretty printing in Common Lisp. Its single greatest advantage is that it allows the full benefits of pretty printing to be obtained when printing data structures, as well as when printing program code. XP is efficient, because it is based on a linear time algorithm that uses a small fixed amount of storage. XP is flexible, because users can control the exact form of the output via a set of special format directives. XP can operate on arbitrary data structures, because facilities are provided for specifying pretty printing methods for any type of object.

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.

Feature Matching for Object Localization in the Presence of Uncertainty

We consider the problem of matching model and sensory data features in the presence of geometric uncertainty, for the purpose of object localization and identification. The problem is to construct sets of model feature and sensory data feature pairs that are geometrically consistent given that there is uncertainty in the geometry of the sensory data features. If there is no geometric uncertainty, polynomial-time algorithms are possible for feature matching, yet these approaches can fail when there is uncertainty in the geometry of data features. Existing matching and recognition techniques which account for the geometric uncertainty in features either cannot guarantee finding a correct solution, or can construct geometrically consistent sets of feature pairs yet have worst case exponential complexity in terms of the number of features. The major new contribution of this work is to demonstrate a polynomial-time algorithm for constructing sets of geometrically consistent feature pairs given uncertainty in the geometry of the data features. We show that under a certain model of geometric uncertainty the feature matching problem in the presence of uncertainty is of polynomial complexity. This has important theoretical implications by demonstrating an upper bound on the complexity of the matching problem, an by offering insight into the nature of the matching problem itself. These insights prove useful in the solution to the matching problem in higher dimensional cases as well, such as matching three-dimensional models to either two or three-dimensional sensory data. The approach is based on an analysis of the space of feasible transformation parameters. This paper outlines the mathematical basis for the method, and describes the implementation of an algorithm for the procedure. Experiments demonstrating the method are reported.

Taxonomic Syntax for First-Order Inference

Most knowledge representation languages are based on classes and taxonomic relationships between classes. Taxonomic hierarchies without defaults or exceptions are semantically equivalent to a collection of formulas in first order predicate calculus. Although designers of knowledge representation languages often express an intuitive feeling that there must be some advantage to representing facts as taxonomic relationships rather than first order formulas, there are few, if any, technical results supporting this intuition. We attempt to remedy this situation by presenting a taxonomic syntax for first order predicate calculus and a series of theorems that support the claim that taxonomic syntax is superior to classical syntax.

Computer Perception of Three-Dimensional Objects

We first pose the following problem: to develop a program which takes line-drawings as input and constructs three-dimensional objects as output, such that the output objects are the same as the ones we see when we look at the input line-drawing. We then introduce the principle of minimum standard-deviation of angles (MSDA) and discuss a program based on MSDA. We present the results of testing this program with a variety of line- drawings and show that the program constitutes a solution to the stated problem over the range of line-drawings tested. Finally, we relate this work to its historical antecedents in the psychological and computer-vision literature.

Curved Inertia Frames: Visual Attention and Perceptual Organization Using Convexity and Symmetry

In this paper we present an approach to perceptual organization and attention based on Curved Inertia Frames (C.I.F.), a novel definition of "curved axis of inertia'' tolerant to noisy and spurious data. The definition is useful because it can find frames that correspond to large, smooth, convex, symmetric and central parts. It is novel because it is global and can detect curved axes. We discuss briefly the relation to human perception, the recognition of non-rigid objects, shape description, and extensions to finding "features", inside/outside relations, and long- smooth ridges in arbitrary surfaces.

Stimulus Familiarity Determines Recognition Strategy for Novel 3-D Objects

We describe a psychophysical investigation of the effects of object complexity and familiarity on the variation of recognition time and recognition accuracy over different views of novel 3D objects. Our findings indicate that with practice the response times for different views become more uniform and the initially orderly dependency of the response time on the distance to a "good" view disappears. One possible interpretation of our results is in terms of a tradeoff between memory needed for storing specific-view representations of objects and time spent in recognizing the objects.

A Theory of Networks for Appxoimation and Learning

Learning an input-output mapping from a set of examples, of the type that many neural networks have been constructed to perform, can be regarded as synthesizing an approximation of a multi-dimensional function, that is solving the problem of hypersurface reconstruction. From this point of view, this form of learning is closely related to classical approximation techniques, such as generalized splines and regularization theory. This paper considers the problems of an exact representation and, in more detail, of the approximation of linear and nolinear mappings in terms of simpler functions of fewer variables. Kolmogorov's theorem concerning the representation of functions of several variables in terms of functions of one variable turns out to be almost irrelevant in the context of networks for learning. We develop a theoretical framework for approximation based on regularization techniques that leads to a class of three-layer networks that we call Generalized Radial Basis Functions (GRBF), since they are mathematically related to the well-known Radial Basis Functions, mainly used for strict interpolation tasks. GRBF networks are not only equivalent to generalized splines, but are also closely related to pattern recognition methods such as Parzen windows and potential functions and to several neural network algorithms, such as Kanerva's associative memory, backpropagation and Kohonen's topology preserving map. They also have an interesting interpretation in terms of prototypes that are synthesized and optimally combined during the learning stage. The paper introduces several extensions and applications of the technique and discusses intriguing analogies with neurobiological data.

The Perceptual Buildup of Three-Dimensional Structure from Motion

We present psychophysical experiments that measure the accuracy of perceived 3D structure derived from relative image motion. The experiments are motivated by Ullman's incremental rigidity scheme, which builds up 3D structure incrementally over an extended time. Our main conclusions are: first, the human system derives an accurate model of the relative depths of moving points, even in the presence of noise; second, the accuracy of 3D structure improves with time, eventually reaching a plateau; and third, the 3D structure currently perceived depends on previous 3D models. Through computer simulations, we relate the psychophysical observations to the behavior of Ullman's model.

Compiling Scientific Code Using Partial Evaluation

Scientists are faced with a dilemma: either they can write abstract programs that express their understanding of a problem, but which do not execute efficiently; or they can write programs that computers can execute efficiently, but which are difficult to write and difficult to understand. We have developed a compiler that uses partial evaluation and scheduling techniques to provide a solution to this dilemma.

A Self-Organizing Multiple-View Representation of 3D Objects

We explore representation of 3D objects in which several distinct 2D views are stored for each object. We demonstrate the ability of a two-layer network of thresholded summation units to support such representations. Using unsupervised Hebbian relaxation, we trained the network to recognise ten objects from different viewpoints. The training process led to the emergence of compact representations of the specific input views. When tested on novel views of the same objects, the network exhibited a substantial generalisation capability. In simulated psychophysical experiments, the network's behavior was qualitatively similar to that of human subjects.

Battling Reality

In the four years that the MIT Mobile Robot Project has benn in existence, we have built ten robots that focus research in various areas concerned with building intelligent systems. Towards this end, we have embarked on trying to build useful autonomous creatures that live and work in the real world. Many of the preconceived notions entertained before we started building our robots turned out to be misguided. Some issues we thought would be hard have worked successfully from day one and subsystems we imagined to be trivial have become tremendous time sinks. Oddly enough, one of our biggest failures has led to some of our favorite successes. This paper describes the changing paths our research has taken due to the lessons learned from the practical realities of building robots.