Results

**11 - 17**of**17**### Modified Whittle Estimation of Multilateral Spatial Models

, 2003

"... We consider the estimation of parametric models for stationary spatial or spatio-temporal data on a d-dimensional lattice, for d ≥ 2. The achievement of asymptotic efficiency under Gaussianity, and asymptotic normality more generally, with standard convergence rate, faces two obstacles. One is the & ..."

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We consider the estimation of parametric models for stationary spatial or spatio-temporal data on a d-dimensional lattice, for d ≥ 2. The achievement of asymptotic efficiency under Gaussianity, and asymptotic normality more generally, with standard convergence rate, faces two obstacles. One is the "edge effect", which worsens with increasing d. The other is the difficulty of computing a continuous-frequency form of Whittle estimate or a time domain Gaussian maximum likelihood estimate, especially in case of multilateral models, due mainly to the Jacobian term. An extension of the discrete-frequency Whittle estimate from the time series literature deals conveniently with the latter problem, but when subjected to a standard device for avoiding the edge effect has disastrous asymptotic performance, along with finite sample numerical drawbacks, the objective function lacking a minimum-distance interpretation and losing any global convexity properties. We overcome these problems by first optimizing a standard, guaranteed non-negative, discrete-frequency, Whittle function, without edge-effect correction, providing an estimate with a slow convergence rate, then improving this by a sequence of computationally conve-nient approximate Newton iterations using a modified, almost-unbiased periodogram, the desired asymptotic properties being achieved after finitely many steps. A Monte Carlo study of finite sample behaviour is included. The asymptotic regime allows increase in both directions, unlike the usual random fields formulation, with the central limit theorem established after re-ordering as a triangular array. When the data are non-Gaussian, the asymptotic variances of all parameter estimates are likely to be affected, and we provide a consistent, non-negative definite, estimate of the asymptotic variance matrix.

### Texture-Independent Vision-Based Closed-Loop Fuzzy Controllers for Navigation Tasks *

"... This paper deals with vision-based closed-loop control schemes for collision avoidance as well as maintenance of clearance in a-priori unknown textured environments. These control schemes are based on fuzzy logic and employ a visual motion cue, we call the Visual Threat Cue (VTC) that provides some ..."

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This paper deals with vision-based closed-loop control schemes for collision avoidance as well as maintenance of clearance in a-priori unknown textured environments. These control schemes are based on fuzzy logic and employ a visual motion cue, we call the Visual Threat Cue (VTC) that provides some measure for a relative change in range as well as clearance between 3D surface and a fixated observer in motion. It is a collective measure obtained directly from the raw data of gray level images, is independent of the 3D surface texture and needs no optical flow information, 3D reconstruction, segmentation, feature tracking or preprocessing. This motion cue is scale-independent, rotation independent and is measured in [time-1] units. Design of a closed-loop conventional controller for vision based navigation tasks pose a problem as the system is complex and ill-defined. On the other hand fuzzy control which is closer in spirit to human thinking and can implement linguistically expressed heuristic control policies directly without any knowledge about the dynamics of the complex process. The fuzzy controllers were tested in real time using a 486-based Personal Computer and a camera capable of undergoing 6-DOF motion. Results are highly encouraging.

### Reflectance and Texture of Real-World Surfaces to appear ACM TOGS

"... In this work, we investigate the visual appearance of real-world surfaces and the dependence of appearance on the geometry of imaging conditions. We discuss a new texture representation called the BTF (bidirectional texture function) which captures the variation in texture with illumination and view ..."

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In this work, we investigate the visual appearance of real-world surfaces and the dependence of appearance on the geometry of imaging conditions. We discuss a new texture representation called the BTF (bidirectional texture function) which captures the variation in texture with illumination and viewing direction. We present a BTF database with image textures from over 60 different samples, each observed with over 200 different combinations of viewing and illumination directions. We describe the methods involved in collecting the database as well as the importance and uniqueness of this database for computer graphics. A related quantity to the BTF is the familiar BRDF (bidirectional reflectance distribution function). The measurement methods involved in the BTF database are conducive to a simultaneous measurement of the BRDF. Accordingly, we also present a BRDF database with reflectance measurements for over 60 different samples, each observed with over 200 different combinations of viewing and illumination directions. Both of these unique databases are publicly available and have important implications for computer graphics. 1.

### Robust RA Estimators in AR-2D Models for Images

, 1999

"... Usually it is adopted for processing and analysis of images SAR, the multiplicative model ( ) ( ) ( ) n m n m n m Y X Z , , , = , where Z are the observations, X is the backscatter process and Y the noise speckle. In Frost et al (1982) (mentioned by Sant'Anna (1995)) a model AR-2D is suggested ..."

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Usually it is adopted for processing and analysis of images SAR, the multiplicative model ( ) ( ) ( ) n m n m n m Y X Z , , , = , where Z are the observations, X is the backscatter process and Y the noise speckle. In Frost et al (1982) (mentioned by Sant'Anna (1995)) a model AR-2D is suggested for the process X . Because the noise speckle is not cleaned totally, the robust methods are the most appropriate alternative to estimate this model's parameters. The purpose of this paper is to present a proposal of robust estimation in the AR-2D contaminated model: The RA estimators. They conform the bidimensional version of the estimators based on the residual covariances for the ARMA unidimensional models, introduced by Bustos and Yohai (1986).