**Publications**(164)

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Automated analysis of multivariate nonlinear gene relations based on cDNA microarray expression data

_{t}depending on the vector parameter t equals (t

_{1}..., t

_{n}). The present paper generalizes the concept of a parameterized reconstructive (tau) -opening to the multivariate setting, where the reconstructive filter (Lambda)

_{t}fully passes any connected component not fully eliminated by (Psi)

_{t}. The problem of minimizing the MAE between the filtered and ideal image processes becomes one of vector optimization in an n- dimensional search space. Unlike the univariate case, the MAE achieved by the optimum filter (Lambda)

_{t}is global in the sense that it is independent of the relative sizes of structuring elements in the filter basis. As a consequence, multivariate granulometries provide a natural environment to study optimality of the choice of structuring elements. If the shapes of the structuring elements are themselves parameterized, the expected error is a deterministic function of the shape and size parameters and its minimization yields the optimal MAE filter.

_{r}to be opening by reconstruction. Adaptation of (Lambda)

_{r}(transition of r) is in accordance to whether or not (Lambda)

_{r}correctly or incorrectly passes signal and noise grains sampled from the image. Signal and noise are modeled as unions of randomly parameterized and randomly translated primary grains. Transition probabilities are discussed for two adaptation protocols and the state- probability increment equations are deduced from the appropriate Chapman-Kolmogorov equations. Adaptation convergence is characterized by the steady-state distributions of the Markov chains and these are computed numerically.

^{N}yields M, where L and M are complete lattices. Representations are grounded on the Riemann zeta function and provide lattice-valued extensions of the classical disjunctive- normal-form, reduced, and positive logical representations. Both direct and dual representations are given. Representations are morphological because they involve elemental forms of erosion, dilation, or the hit-or-miss transform.

_{t}). A rather general result for the k

^{th}pattern spectrum moment is derived. For polynomial choice of h

^{-1}(t), the asymptotic expressions for the mean and variance of the pattern spectrum moments can be obtained and the asymptotic distribution can be shown to be normal. For other choices, the asymptotic expressions for the mean and variance are shown to provide excellent agreement with simulated pattern spectra, but the asymptotic distribution is not known.

*expert*approach involves prior sublibrary formation based on knowledge of important filter bases and the

*first-order*approach employs single-erosion statistical information to limit the basis search to likely useful candidates.

*granulometries*. Granulometries filter the image by structuring elements of ever-increasing size, the result being a distribution whose statistics carry information regarding the shape and size of particles within the image. A granulometric approach to the analysis of the microstructure of electrophotographic images is discussed. The method is applied to both simulated and real images, the former being generated in a manner consistent with existing magnetic brush development and optical density transform models. Size distribution statistics are analyzed in terms of feedback control and copier quality control.

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**Proceedings Volume Editor**(29)

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This course introduces the basics of real-time image processing. It discusses efficient implementation of image processing algorithms. Standard image algorithm approaches do not yield real-time solutions. These algorithms must be rewritten to include real-time approaches connected to the hardware. The goal of this course is to show how software and hardware are used to achieve real-time image processing tasks.

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