A General Theory of Semi-Unification

Various restrictions on the terms allowed for substitution give rise to different cases of semi-unification. Semi-unification on finite and regular terms has already been considered in the literature. We introduce a general case of semi-unification where substitutions are allowed on non-regular terms, and we prove the equivalence of this general case to a well-known undecidable data base dependency problem, thus establishing the undecidability of general semi-unification. We present a unified way of looking at the various problems of semi-unification. We give some properties that are common to all the cases of semi-unification. We also the principality property and the solution set for those problems. We prove that semi-unification on general terms has the principality property. Finally, we present a recursive inseparability result between semi-unification on regular terms and semi-unification on general terms.

Robust Tracking of Human Motion

This technical report presents a combined solution for two problems, one: tracking objects in 3D space and estimating their trajectories and second: computing the similarity between previously estimated trajectories and clustering them using the similarities that we just computed. For the first part, trajectories are estimated using an EKF formulation that will provide the 3D trajectory up to a constant. To improve accuracy, when occlusions appear, multiple hypotheses are followed. For the second problem we compute the distances between trajectories using a similarity based on LCSS formulation. Similarities are computed between projections of trajectories on coordinate axes. Finally we group trajectories together based on previously computed distances, using a clustering algorithm. To check the validity of our approach, several experiments using real data were performed.

Recognition of Human Action Using Moment-Based Feature

The performance of different classification approaches is evaluated using a view-based approach for motion representation. The view-based approach uses computer vision and image processing techniques to register and process the video sequence. Two motion representations called Motion Energy Images and Motion History Image are then constructed. These representations collapse the temporal component in a way that no explicit temporal analysis or sequence matching is needed. Statistical descriptions are then computed using moment-based features and dimensionality reduction techniques. For these tests, we used 7 Hu moments, which are invariant to scale and translation. Principal Components Analysis is used to reduce the dimensionality of this representation. The system is trained using different subjects performing a set of examples of every action to be recognized. Given these samples, K-nearest neighbor, Gaussian, and Gaussian mixture classifiers are used to recognize new actions. Experiments are conducted using instances of eight human actions (i.e., eight classes) performed by seven different subjects. Comparisons in the performance among these classifiers under different conditions are analyzed and reported. Our main goals are to test this dimensionality-reduced representation of actions, and more importantly to use this representation to compare the advantages of different classification approaches in this recognition task.

Intersubject Regularity in the Intrinsic Shape of Human V1

Previous studies have reported considerable intersubject variability in the three-dimensional geometry of the human primary visual cortex (V1). Here we demonstrate that much of this variability is due to extrinsic geometric features of the cortical folds, and that the intrinsic shape of V1 is similar across individuals. V1 was imaged in ten ex vivo human hemispheres using high-resolution (200 μm) structural magnetic resonance imaging at high field strength (7 T). Manual tracings of the stria of Gennari were used to construct a surface representation, which was computationally flattened into the plane with minimal metric distortion. The instrinsic shape of V1 was determined from the boundary of the planar representation of the stria. An ellipse provided a simple parametric shape model that was a good approximation to the boundary of flattened V1. The aspect ration of the best-fitting ellipse was found to be consistent across subject, with a mean of 1.85 and standard deviation of 0.12. Optimal rigid alignment of size-normalized V1 produced greater overlap than that achieved by previous studies using different registration methods. A shape analysis of published macaque data indicated that the intrinsic shape of macaque V1 is also stereotyped, and similar to the human V1 shape. Previoud measurements of the functional boundary of V1 in human and macaque are in close agreement with these results.

Frequency-Dependent Phase Transitions in the Coordination of Human Bimanual Tasks

The 2-channel Ellias-Grossberg neural pattern generator of Cohen, Grossberg, and Pribe [1] is shown to simulate data from human bimanual coordination tasks in which anti-phase oscillations at low frequencies spontaneously switch to in-phase oscillations at high frequencies, in-phase oscillations can be performed at both low and high frequencies, phase fluctuations occur at the anti-phase to in-phase transition, and a "seagull effect" of larger errors occurs at intermediate phases.

A Neural Theory of Visual Search: Recursive Attention to Segmentations and Surfaces

A neural theory is proposed in which visual search is accomplished by perceptual grouping and segregation, which occurs simultaneous across the visual field, and object recognition, which is restricted to a selected region of the field. The theory offers an alternative hypothesis to recently developed variations on Feature Integration Theory (Treisman, and Sato, 1991) and Guided Search Model (Wolfe, Cave, and Franzel, 1989). A neural architecture and search algorithm is specified that quantitatively explains a wide range of psychophysical search data (Wolfe, Cave, and Franzel, 1989; Cohen, and lvry, 1991; Mordkoff, Yantis, and Egeth, 1990; Treisman, and Sato, 1991).

A Neural Theory of Attentive Visual Search: Interactions of Boundary, Surface, Spatial, and Object Representations

Visual search data are given a unified quantitative explanation by a model of how spatial maps in the parietal cortex and object recognition categories in the inferotemporal cortex deploy attentional resources as they reciprocally interact with visual representations in the prestriate cortex. The model visual representations arc organized into multiple boundary and surface representations. Visual search in the model is initiated by organizing multiple items that lie within a given boundary or surface representation into a candidate search grouping. These items arc compared with object recognition categories to test for matches or mismatches. Mismatches can trigger deeper searches and recursive selection of new groupings until a target object io identified. This search model is algorithmically specified to quantitatively simulate search data using a single set of parameters, as well as to qualitatively explain a still larger data base, including data of Aks and Enns (1992), Bravo and Blake (1990), Chellazzi, Miller, Duncan, and Desimone (1993), Egeth, Viri, and Garbart (1984), Cohen and Ivry (1991), Enno and Rensink (1990), He and Nakayarna (1992), Humphreys, Quinlan, and Riddoch (1989), Mordkoff, Yantis, and Egeth (1990), Nakayama and Silverman (1986), Treisman and Gelade (1980), Treisman and Sato (1990), Wolfe, Cave, and Franzel (1989), and Wolfe and Friedman-Hill (1992). The model hereby provides an alternative to recent variations on the Feature Integration and Guided Search models, and grounds the analysis of visual search in neural models of preattentive vision, attentive object learning and categorization, and attentive spatial localization and orientation.

A Biomechanical Model of Human Oculomotor Plant Kinematics Based Upon Geometric Algebra

A biomechanical model of the human oculomotor plant kinematics in 3-D as a function of muscle length changes is presented. It can represent a range of alternative interpretations of the data as a function of one parameter. The model is free from such deficits as singularities and the nesting of axes found in alternative formulations such as the spherical wrist (Paul, l98l). The equations of motion are defined on a quaternion based representation of eye rotations and are compact atnd computationally efficient.

Laminar Cortical Dynamics of Cognitive and Motor Working Memory, Sequence Learning and Performance: Toward a Unified Theory of How the Cerebral Cortex Works

How do the layered circuits of prefrontal and motor cortex carry out working memory storage, sequence learning, and voluntary sequential item selection and performance? A neural model called LIST PARSE is presented to explain and quantitatively simulate cognitive data about both immediate serial recall and free recall, including bowing of the serial position performance curves, error-type distributions, temporal limitations upon recall, and list length effects. The model also qualitatively explains cognitive effects related to attentional modulation, temporal grouping, variable presentation rates, phonemic similarity, presentation of non-words, word frequency/item familiarity and list strength, distracters and modality effects. In addition, the model quantitatively simulates neurophysiological data from the macaque prefrontal cortex obtained during sequential sensory-motor imitation and planned performance. The article further develops a theory concerning how the cerebral cortex works by showing how variations of the laminar circuits that have previously clarified how the visual cortex sees can also support cognitive processing of sequentially organized behaviors.

Towards a Unified Theory of Neocortex: Laminar Cortical Circuits for Vision and Cognition

A key goal of computational neuroscience is to link brain mechanisms to behavioral functions. The present article describes recent progress towards explaining how laminar neocortical circuits give rise to biological intelligence. These circuits embody two new and revolutionary computational paradigms: Complementary Computing and Laminar Computing. Circuit properties include a novel synthesis of feedforward and feedback processing, of digital and analog processing, and of pre-attentive and attentive processing. This synthesis clarifies the appeal of Bayesian approaches but has a far greater predictive range that naturally extends to self-organizing processes. Examples from vision and cognition are summarized. A LAMINART architecture unifies properties of visual development, learning, perceptual grouping, attention, and 3D vision. A key modeling theme is that the mechanisms which enable development and learning to occur in a stable way imply properties of adult behavior. It is noted how higher-order attentional constraints can influence multiple cortical regions, and how spatial and object attention work together to learn view-invariant object categories. In particular, a form-fitting spatial attentional shroud can allow an emerging view-invariant object category to remain active while multiple view categories are associated with it during sequences of saccadic eye movements. Finally, the chapter summarizes recent work on the LIST PARSE model of cognitive information processing by the laminar circuits of prefrontal cortex. LIST PARSE models the short-term storage of event sequences in working memory, their unitization through learning into sequence, or list, chunks, and their read-out in planned sequential performance that is under volitional control. LIST PARSE provides a laminar embodiment of Item and Order working memories, also called Competitive Queuing models, that have been supported by both psychophysical and neurobiological data. These examples show how variations of a common laminar cortical design can embody properties of visual and cognitive intelligence that seem, at least on the surface, to be mechanistically unrelated.