Syntax-Based Analytic Reading of Musical Scores

As part of a larger research project in musical structure, a program has been written which "reads" scores encoded in an input language isomorphic to music notation. The program is believed to be the first of its kind. From a small number of parsing rules the program derives complex configurations, each of which is associated with a set of reference points in a numerical representation of a time-continuum. The logical structure of the program is such that all and only the defined classes of events are represented in the output. Because the basis of the program is syntactic (in the sense that parsing operations are performed on formal structures in the input string), many extensions and refinements can be made without excessive difficulty. The program can be applied to any music which can be represented in the input language. At present, however, it constitutes the first stage in the development of a set of analytic tools for the study of so-called atonal music, the revolutionary and little understood music which has exerted a decisive influence upon contemporary practice of the art. The program and the approach to automatic data-structuring may be of interest to linguists and scholars in other fields concerned with basic studies of complex structures produced by human beings.

The Quadric Reference Surface: Theory and Applications

The conceptual component of this work is about "reference surfaces'' which are the dual of reference frames often used for shape representation purposes. The theoretical component of this work involves the question of whether one can find a unique (and simple) mapping that aligns two arbitrary perspective views of an opaque textured quadric surface in 3D, given (i) few corresponding points in the two views, or (ii) the outline conic of the surface in one view (only) and few corresponding points in the two views. The practical component of this work is concerned with applying the theoretical results as tools for the task of achieving full correspondence between views of arbitrary objects.

3D Pose from Three Corresponding Points Under Weak-Perspective Projection

Model-based object recognition commonly involves using a minimal set of matched model and image points to compute the pose of the model in image coordinates. Furthermore, recognition systems often rely on the "weak-perspective" imaging model in place of the perspective imaging model. This paper discusses computing the pose of a model from three corresponding points under weak-perspective projection. A new solution to the problem is proposed which, like previous solutins, involves solving a biquadratic equation. Here the biquadratic is motivate geometrically and its solutions, comprised of an actual and a false solution, are interpreted graphically. The final equations take a new form, which lead to a simple expression for the image position of any unmatched model point.

Spatial Reference Frames for Object Recognition: Tuning for Rotations in Depth

The inferior temporal cortex (IT) of monkeys is thought to play an essential role in visual object recognition. Inferotemporal neurons are known to respond to complex visual stimuli, including patterns like faces, hands, or other body parts. What is the role of such neurons in object recognition? The present study examines this question in combined psychophysical and electrophysiological experiments, in which monkeys learned to classify and recognize novel visual 3D objects. A population of neurons in IT were found to respond selectively to such objects that the monkeys had recently learned to recognize. A large majority of these cells discharged maximally for one view of the object, while their response fell off gradually as the object was rotated away from the neuron"s preferred view. Most neurons exhibited orientation-dependent responses also during view-plane rotations. Some neurons were found tuned around two views of the same object, while a very small number of cells responded in a view- invariant manner. For five different objects that were extensively used during the training of the animals, and for which behavioral performance became view-independent, multiple cells were found that were tuned around different views of the same object. No selective responses were ever encountered for views that the animal systematically failed to recognize. The results of our experiments suggest that neurons in this area can develop a complex receptive field organization as a consequence of extensive training in the discrimination and recognition of objects. Simple geometric features did not appear to account for the neurons" selective responses. These findings support the idea that a population of neurons -- each tuned to a different object aspect, and each showing a certain degree of invariance to image transformations -- may, as an assembly, encode complex 3D objects. In such a system, several neurons may be active for any given vantage point, with a single unit acting like a blurred template for a limited neighborhood of a single view.

MIT Scheme Reference Manual

MIT Scheme is an implementation of the Scheme programming language that runs on many popular workstations. The MIT Scheme Reference Manual describes the special forms, procedures, and datatypes provided by the implementation for use by application programmers.

Control of Vibration in Mechanical Systems Using Shaped Reference Inputs

Dynamic systems which undergo rapid motion can excite natural frequencies that lead to residual vibration at the end of motion. This work presents a method to shape force profiles that reduce excitation energy at the natural frequencies in order to reduce residual vibration for fast moves. Such profiles are developed using a ramped sinusoid function and its harmonics, choosing coefficients to reduce spectral energy at the natural frequencies of the system. To improve robustness with respect to parameter uncertainty, spectral energy is reduced for a range of frequencies surrounding the nominal natural frequency. An additional set of versine profiles are also constructed to permit motion at constant speed for velocity-limited systems. These shaped force profiles are incorporated into a simple closed-loop system with position and velocity feedback. The force input is doubly integrated to generate a shaped position reference for the controller to follow. This control scheme is evaluated on the MIT Cartesian Robot. The shaped inputs generate motions with minimum residual vibration when actuator saturation is avoided. Feedback control compensates for the effect of friction Using only a knowledge of the natural frequencies of the system to shape the force inputs, vibration can also be attenuated in modes which vibrate in directions other than the motion direction. When moving several axes, the use of shaped inputs allows minimum residual vibration even when the natural frequencies are dynamically changing by a limited amount.