Josef Heers

Fast Parallel Algorithms for a Broad Class of Nonlinear Variational Diffusion Approaches

Variational segmentation and nonlinear diffusion approaches have been very active research areas in the fields of image processing and computer vision during recent years. In the present paper, we review recent advances in the development of efficient numerical algorithms for these approaches. The performance of parallel implementations of these algorithms on general-purpose hardware is assessed. A mathematically clear connection between variational models and nonlinear diffusion filters is presented that allows to interpret one approach as an approximation of the other, and vice versa. Extending this continuous connection to the fully discrete setting enables us to derive many structural similarities between efficient numerical algorithms for both frameworks. These results provide a perspective for uniform implementations of nonlinear variational models and diffusion filters on parallel architectures.

Globally convergent iterative numerical schemes for nonlinear variational image smoothing and segmentation on a multiprocessor machine

We investigate several iterative numerical schemes for nonlinear variational image smoothing and segmentation implemented in parallel. A general iterative framework subsuming these schemes is suggested for which global convergence irrespective of the starting point can be shown. We characterize various edge-preserving regularization methods from the image processing literature involving auxiliary variables as special cases of this general framework. As a by-product, global convergence can be proven under conditions slightly weaker than these stated in the literature. Efficient Krylov subspace solvers for the linear parts of these schemes have been implemented on a multiprocessor machine. The performance of these parallel implementations has been assessed and empirical results concerning convergence rates and speed-up factors are reported.

Investigation of parallel and globally convergent iterative schemes for nonlinear variational image smoothing and segmentation

We consider a nonquadratic convex variational segmentation approach and investigate numerical schemes to allow for an efficient computation of the global minimum on a parallel architecture. We focus on iterative schemes for which we can show global convergence to the unique solution irrespective of the starting point. In the context of (semi-)automated image processing tasks, such a feature is of utmost importance. We characterize various approaches that have been proposed in the literature as special cases of a general iterative scheme. Among these approaches are the linearization technique introduced by Geman and Reynolds (1992) and the half-quadratic regularization scheme proposed by Geman and Yang (see IEEE Trans. Image Proc., no.4, p.932-45, 1995). As a result, we can show global convergence to the unique solution under weaker conditions. Efficient Krylov subspace solvers for the resulting linear systems have been implemented on a parallel architecture to assess the performance of these numerical schemes. Experimental results concerning convergence rates and speed-up are reported. Due to the similarity of the segmentation approach considered here with total variation based image restoration methods, our results are relevant for this latter class of methods as well.

Dynamic circular cellular networks for adaptive smoothing of multi-dimensional signals

In Schnorr et al. (1996) a theoretical framework for locally-adaptive smoothing of multi-dimensional data was presented. Based on this framework we introduce a hardware efficient architecture suitable for mixed-mode VLSI implementation. Substantial shortcomings of analogue implementations are overcome by connecting all cells in a circular structure: (i) influence of process parameter deviation, (ii) limited number of cells, (iii) input/output bottleneck. The connections between the analogue cells and the cells themselves are dynamically reconfigured. This results in a non-linear adaptive filter kernel which is shifted virtually over the signal vector of infinite length. A 1D prototype with 32 cells has been fabricated using 0.8 /spl mu/m CMOS-technology. The chip is fully functional with an overall error less than 1%; experimental results are presented in the paper.

A One-Dimensional Analog VLSI Implementation for Nonlinear Real-Time Signal Preprocessing

Reconstruction of given noisy data is an ill-posed problem and a computationally intensive task. Nonlinear regularization techniques are used to find a unique solution under certain constraints. In our contribution we present a parallel mixed-signal architecture which solves this nonlinear problem with in microseconds. By connecting all parallel cells in a circular manner it is possible to process noisy data vectors of infinite length. This is achieved by virtually shifting the nonlinear adaptive filter kernel over the noisy data vector. Additionally, we focus on the interaction between theory, discretization, numerical simulations, macro-modeling, and analog VLSI implementation for a theoretically well understood class of computer vision in an exemplary and paradigmatic way. A one-dimensional (1D) experimental chip has been fabricated using 0.8 ?m CMOS technology. On-chip measurements are shown to agree with results from numerical simulations. Results from applying the 1D chip to nonlinear smoothing of two-dimensional image data will also be given correspondence.

Real-Time Adaptive Smoothing with a 1-D Nonlinear Relaxation Network in Analogue VLSI Technology

Reconstruction of given noisy data is an ill-posed problem and a computationally intensive task. Non-linear regularisation techniques are used to find a unique solution under certain constraints. In our contribution we present a parallel mixed-signal architecture which solves this non-linear problem within microseconds. By connecting all parallel cells in a circular manner it is possible to process noisy data vectors of infinite length. This is achieved by virtually shifting the non-linear adaptive filter kernel over the noisy data vector. A 1-D experimental chip has been fabricated using 0.8μxm CMOS technology. On-chip measurements are shown to agree with results from numerical simulations. Results from applying the 1-D chip to nonlinear smoothing of image data will also be given correspondence.

A Class of Parallel Algorithms for Nonlinear Variational Segmentation: A preprocess for robust feature-based image coding

Compact feature-based image coding as well as view-based object representations require a preprocessing step that abstracts from image details while preserving essential signal structures. Variational segmentation and nonlinear diffusion approaches provide powerful methods for the design of such a preprocessing stage. This motivates two investigate parallel numerical schemes to enable preprocessing of large image databases in a reasonable amount of time.

Parallele und global konvergente iterative Minimierung nichtlinearer Variationsansätze zur adaptiven Glättung und Segmentation von Bildern

Wir betrachten nicht-quadratische, konvexe Variationsansatze zur Bildsegmentation und untersuchen numerische Verfahren, die eine effiziente Berechnung globaler Minima auf parallelen Architekturen erlauben. Unser Augenmerk gilt dabei Verfahren mit globaler Konvergenz, d.h. Konvergenz gegen die eindeutige Losung bei beliebigen Startwerten. Im Kontext der (semi-)automatischen Bildverarbeitung ist eine solche Eigenschaft sehr wichtig.