The complex representation of algebraic curves and its simpleexploitation for pose estimation and invariant recognition

Representations are introduced for handling 2D algebraic curves (implicit polynomial curves) of arbitrary degree in the scope of computer vision applications. These representations permit fast, accurate pose-independent shape recognition under Euclidean transformations with a complete set of invariants, and fast accurate pose-estimation based on all the polynomial coefficients. The latter is accomplished by a centering of a polynomial based on its coefficients, followed by rotation estimation by decomposing polynomial coefficient space into a union of orthogonal subspaces for which rotations within two-dimensional subspaces or identity transformations within one-dimensional subspaces result from rotations in x, y measured-data space. Angles of these rotations in the two-dimensional coefficient subspaces are proportional to each other and are integer multiples of the rotation angle in the x, y data space. By recasting this approach in terms of a complex variable, i.e., x+iy=z, and complex polynomial-coefficients, further conceptual and computational simplification results. Application to shape-based indexing into databases is presented to illustrate the usefulness and the robustness of the complex representation of algebraic curves     

Reconstruction of cellular biological structures from optical microscopy data

Developments in optical microscopy imaging have generated large high-resolution data sets that have spurred medical researchers to conduct investigations into mechanisms of disease, including cancer at cellular and subcellular levels. The work reported here demonstrates that a suitable methodology can be conceived that isolates modality-dependent effects from the larger segmentation task and that 3D reconstructions can be cognizant of shapes as evident in the available 2D planar images. In the current realization, a method based on active geodesic contours is first deployed to counter the ambiguity that exists in separating overlapping cells on the image plane. Later, another segmentation effort based on a variant of Voronoi tessellations improves the delineation of the cell boundaries using a Bayesian formulation. In the next stage, the cells are interpolated across the third dimension thereby mitigating the poor structural correlation that exists in that dimension. We deploy our methods on three separate data sets obtained from light, confocal, and phase-contrast microscopy and validate the results appropriately.     

Interruptibility as a constraint on hybrid systems

It is widely mooted that a plausible computational cognitive model should involve both symbolic and connectionist components. However, sound principles for combining these components within a hybrid system are currently lacking; the design of such systems is oftenad hoc. In an attempt to ameliorate this we provide a framework of types of hybrid systems and constraints therein, within which to explore the issues. In particular, we suggest the use of system independent constraints, whose source lies in general considerations about cognitive systems, rather than in particular technological or task-based considerations. We illustrate this through a detailed examination of an interruptibility constraint: handling interruptions is a fundamental facet of cognition in a dynamic world. Aspects of interruptions are delineated, as are their precise expression in symbolic and connectionist systems. We illustrate the interaction of the various constraints from interruptibility in the different types of hybrid systems. The picture that emerges of the relationship between the connectionist and the symbolic within a hybrid system provides for sufficient flexibility and complexity to suggest interesting general implications for cognition, thus vindicating the utility of the framework.     

Use of Graduate Study in Psychology as a data source.

Comments on an article by C. M. Stoup and L. T. Benjamin, Jr. (see record 1983-24200-001), in which they used various editions of Graduate Study in Psychology, published by the American Psychological Association (APA), to report the GPAs and Graduate Record Examination scores of master's and doctoral students across various areas of psychology. It is cautioned that the use of Graduate Study in Psychology as a data source calls for skepticism, as there is sufficient reason to question some of the data that are submitted to the APA by psychology departments. (3 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Bayesian recognition of local 3-d shape by approximating image intensity functions with quadric polynomials

The recognition in image data of viewed patches of spheres, cylinders, and planes in the 3-D world is discussed as a first step to complex object recognition or complex object location and orientation estimation. Accordingly, an image is partitioned into small square windows, each of which is a view of a piece of a sphere, or of a cylinder, or of a plane. Windows are processed in parallel for recognition of content. New concepts and techniques include approximations of the image within a window by 2-D quadric polynomials where each approximation is constrained by one of the hypotheses that the 3-D surface shape seen is either planar, cylindrical, or spherical; a recognizer based upon these approximations to determine whether the object patch viewed is a piece of a sphere, or a piece of a cylinder, or a piece of a plane; lowpass filtering of the image by the approximation. The shape recognition is computationally simple, and for large windows is approximately Bayesian minimum-probability-of-error recognition. These classifications are useful for many purposes. One such purpose is to enable a following processor to use an appropriate estimator to estimate shape, and orientation and location parameters for the 3-D surface seen within a window.     

Aromatic Hydrogenation Catalysis: A Review

High aromatic content in diesel fuel has been recognized both to lower the fuel quality and to contribute significantly to the formation of undesired emissions in exhaust gases [1, 2]. Because of the health hazards associated with these emissions, environmental regulations governing the composition of diesel fuels are being tightened in both Europe and the United States, leading to limitations on aromatics [3, 4].     

Complexity and computability of solutions to linear programming systems

Through key examples and constructs, exact and approximate, complexity, computability, and solution of linear programming systems are reexamined in the light of Khachian's new notion of (approximate) solution. Algorithms, basic theorems, and alternate representations are reviewed. It is shown that the Klee-Minty example hasnever been exponential for (exact) adjacent extreme point algorithms and that the Balinski-Gomory (exact) algorithm continues to be polynomial in cases where (approximate) ellipsoidal centered-cutoff algorithms (Levin, Shor, Khachian, Gacs-Lovasz) are exponential. By model approximation, both the Klee-Minty and the new J. Clausen examples are shown to be trivial (explicitly solvable) interval programming problems. A new notion of computable (approximate) solution is proposed together with ana priori regularization for linear programming systems. New polyhedral constraint contraction algorithms are proposed for approximate solution and the relevance of interval programming for good starts or exact solution is brought forth. It is concluded from all this that the imposed problem ignorance of past complexity research is deleterious to research progress on computability or efficiency of computation.This research was partly supported by Project NR047-071, ONR Contract N00014-80-C-0242, and Project NR047-021, ONR Contract N00014-75-C-0569, with the Center for Cybernetic Studies, The University of Texas at Austin.