José R. A. Torreão

Linear gate assignment: a fast statistical mechanics approach

This paper deals with the problem of linear gate assignment in two layout styles: one-dimensional logic array and gate matrix layout. The goal is to find the optimal sequencing of gates in order to minimize the required number of tracks, and thus to reduce the overall circuit layout area. This is known to be an NP-hard optimization problem, for which no absolute approximation algorithm exists. Here we report the use of a new optimization heuristic derived from statistical mechanics-the microcanonical optimization algorithm, /spl mu/0-to solve the linear gate assignment problem. Our numerical results show that /spl mu/0 compares favorably with at least five previously employed heuristics: simulated annealing, the unidirectional and the bidirectional Hong construction methods, and the artificial intelligence heuristics GM Plan and GM Learn. We also show how the algorithm is able to outperform microcanonical annealing. Moreover, in a massive set of experiments with circuits whose optimal layout is not known, our algorithm has been able to match and even to improve, by as much as seven tracks, the best solutions known so far.

A Green's function approach to shape from shading

We present a new algorithm for shape from shading, inspired on the recently introduced disparity-based approach to photometric stereo (DBPS). Assuming that the single input image will be matched to a second image through a uniform disparity field, we construct an irradiance conservation equation and solve it for the matching image, via Greens function. When a linear expansion of the reflectance map is considered, this leads to a closed-form approximate expression for the surface function, whose parameters can be estimated via a structure-from-motion approach already used for DBPS.

Signal differentiation through a Green's function approach

We introduce a new approach for the design of differential operators, based on the Greens function solution to a signal matching equation. Its use is illustrated by the construction of step-edge enhancement filters whose performance figures are comparable, and even superior, to those reported in the literature.

Efficient, recursively implemented differential operator, with application to edge detection

The estimation of derivatives is an important and sensitive task in digital image processing and analysis, both accuracy and computational efficiency being expected of a differential operator. Here we propose a new filter-designed through a strategy based on the Greens function of a signal matching equation-that responds to such demands. When used for edge detection, it yields theoretical performance indices that rival, and even top, the best reported marks. It is also computationally efficient, allowing very simple recursive implementation. The results of extensive edge-detection experimentation are reported here. Being explicitly designed as a first-derivative operator, our filter should also find application in other signal processing domains.

A new approach to photometric stereo

Abstract We introduce a new approach to shape estimation from photometric stereo images. The input images are matched through an optical flow algorithm, with the matching direction iteratively refined. The resulting disparity field is then used in a structure-from-motion reconstruction which does not require reflectance map information.

Single-Image Shape from Defocus

The limited depth of field causes scene points at various distances from a camera to be imaged with different amounts of defocus. If images captured under different aperture settings are available, the defocus measure can be estimated and used for 3D scene reconstruction. Usually, defocusing is modeled by gaussian convolution over local image patches, but the estimation of a defocus measure based on that is hampered by the spurious high-frequencies introduced by windowing. Here we show that this can be ameliorated by the use of unnormalized gaussians, which allow defocus estimation from the zero-frequency Fourier component of the image patches, thus avoiding spurious high frequencies. As our main contribution, we also show that the modified shape from defocus approach can be extended to shape estimation from single shading inputs. This is done by simulating an aperture change, via gaussian convolution, in order to generate the second image required for defocus estimation. As proven here, the gaussian-blurred image carries an explicit depth-dependent blur component - which is missing from an ideal shading input -, and thus allows depth estimation as in the multi-image case.

Microcanonical Optimization Applied to the Traveling Salesman Problem

Optimization strategies based on simulated annealing and its variants have been extensively applied to the traveling salesman problem (TSP). Recently, there has appeared a new physics-based metaheuristic, called the microcanonical optimization algorithm (μO), which does not resort to annealing, and which has proven a superior alternative to the annealing procedures in various applications. Here we present the first performance evaluation of μO as applied to the TSP. When compared to three annealing strategies (simulated annealing, microcanonical annealing and Tsallis annealing), and to a tabu search algorithm, the microcanonical optimization has yielded the best overall results for several instances of the euclidean TSP. This confirms μO as a competitive approach for the solution of general combinatorial optimization problems.

Matching photometric-stereo images

We introduce a new process of shape estimation through the matching of photometric-stereo images, which are monocular images obtained under different illuminations. If the illumination directions are not far apart, and if the imaged surface is smooth, so that a linear approximation to the reflectance map is applicable, the disparities produced by the matching process can be related to the depth function of the imaged surface through a differential equation whose approximate solution is easily found. We thus obtain a closed-form expression for surface depth, depending only on the coefficients of the linear-reflectance-map function. If those coefficients are not available, a simple iterative scheme still allows the recovery of depth, up to an overall scale factor.

A SIGNAL-TUNED GABOR TRANSFORM WITH APPLICATION TO EEG ANALYSIS

We introduce a time-frequency transform based on Gabor functions whose parameters are given by the Fourier transform of the analyzed signal. At any given frequency, the width and the phase of the Gabor function are obtained, respectively, from the magnitude and the phase of the signals corresponding Fourier component, yielding an analyzing kernel which is a representation of the signals content at that particular frequency. The resulting Gabor transform tunes itself to the input signal, allowing the accurate detection of time and frequency events, even in situations where the traditional Gabor and S-transform approaches tend to fail. This is the case, for instance, when considering the time-frequency representation of electroencephalogram traces (EEG) of epileptic subjects, as illustrated by the experimental study presented here.

Disparity estimation through Green’s functions of matching equations

Binocular disparities arise from positional differences of scene features projected in the two retinae, and constitute the primary sensory cue for stereo vision. Here we introduce a new computational model for disparity estimation, based on the Green’s function of an image matching equation. When filtering a Gabor-function-modulated signal, the considered Green’s function yields a similarly modulated but shifted version of the original signal. Since a Gabor function models the receptive field of a cortical simple cell, the Green’s kernel thus allows the simulation of relative shifts between the cell’s left and right binocular inputs. A measure of the local degree of matching of such shifted inputs can then be introduced which affords disparity estimation in a similar manner to the energy model of the complex cortical cells. We have therefore effectively reformulated, in physiologically plausible terms, an image matching approach to disparity estimation. Our experiments show that the Green’s function method allows the detection of disparities both from random-dot and real-world stereograms.