Parallel Genetic Algorithms for Optimizing Morphological Filters

RESUME
Ce papier presente une modi cation d'un algorithme genetique standard utilisant des techniques paralleles. Cet algorithme permet de trouver les solutions optimales de ltres morphologiques pour une application au traitement d'images. La structure de cet algorithme genetique general developpee cidessous est basee sur un nouveau modele de souspopulation qui balance et reequilibre integralement le poids de chaque t^che et apporte de la soupa lesse au mechanisme de synchronisation. Cela accro^t l'e cacite des t^ches paralleles m^me distribuees sur a e un ensemble de stations de travail, avec plusieurs utilisateurs sous di erents environements. Cet avantage apporte aux utilisateurs qui n'ont pas acces aux echanges paralleles, l'opportunite d'ameliorer la rapidite d'execution de leurs algorithmes. Di erentes simulations presentent les resultats obtenus en utilisant une station avec plusieurs processeurs et plusieurs stations de travail. 9] or highly complicated. Common design tools such as Fourier and Laplace transformations are of no use due to the violation of the superposition assumptions by the non-linear operations. GAs can be employed to o er a non-deterministic tool for designing MFs. This leads to simple methods for designing MFs and gives the opportunity to test new approaches in MFs such as Rank-Order MFs 5] which have shown a signi cant improvement in performance.
A PARALLEL GENETIC ALGORITHM FOR OPTIMIZING MORPHOLOGICAL FILTERS ON INHOMOGENEOUS WORKSTATION CLUSTERS
P Kraft, M Nolle , G Schreiber , S Marshall, H Burkhardt University of Strathclyde, Glasgow, Scotland Technische Universitat Hamburg-Harburg, Hamburg, Germany
create an initial random population REPEAT generation select pairings for all individuals and perform genetic operations evaluate tness values for all individuals select copies of best individuals for the next generation UNTIL termination condition is true Applied to the problem of lter optimization, the tness value of an individual of the population (a chromosome representing a SE and a sequence of morphological operations) is calculated based on the performance of the associated lter in a given task, such as noise suppression. Therefore, a lter operation has to be computed for each chromosome of the population, in every generation. The arithmetic complexity O for the calculation of a single tness value results in: O = (n n) (m m) M . Here n refers to the dimension of the ltered image, m refers to the dimension of the lter mask and M is the number of performed morphological operations (erosion and dilation). This leads for average problems (image size 512x512 pixel, mask size 7x7 values and 4 morphologicaloperations) to a calculation time of more than 30 seconds (on a T805 transputer or a Sun SPARCstation 1), giving a total run-time for a normal sequential GA (one population with 100 individuals and 200 generations) of about 7 hours. To achieve more acceptable computation times, which are required for real-time image analysis, it is necessary to speed up the algorithm using the power of parallel computers.
ABSTRACT
In this paper a modi cation of a standard parallel genetic algorithm (SPGA) is introduced which can be run e ciently on di erent types of parallel computers. The purpose of the algorithm is to nd optimal morphological lters for grey scale image processing tasks. The structure of the developed General Parallel Genetic Algorithm (GPGA) is based on a new subpopulation model which uses an integral load balancing and soft synchronization mechanism. It is designed to lead to good parallelization e ciencies even on distributed workstation clusters with multi-user operating systems. This is especially important for user groups which have no access to massively parallel computers to speed up their algorithms. Run time results from tests on a massively parallel computer and a workstation cluster are shown.
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Morphological Filters (MFs)
MFs are non-linear digital signal processing operators which consist of a structuring element (SE) and morphological operations. They have various applications in tasks such as texture analysis, biomedical image processing, noise reduction (especially if it is di cult to characterize the type of noise) and object recognition. The SE can have any shape, which makes it possible to adjust it to the special features of the problem (for example to the type of noise or to characteristics of objects). However, deterministic design methods which exist for these morphological lters tend to be computationally intractable 4] 3]
The Model of Genetic Algorithms
The standard GA model is based on the evolutionary process found in nature, applied to arti cial optimization problems 7]. A set of chromosomes (individuals) decodes all possible solutions for a given problem, while an evaluation function assigns a tness value to a given individual which is a measurement for the quality of the solution given by an individual. Genetic operations such as crossover and mutation are used to modify individuals to progressively achieve a higher maximal and average tness in the given set of individuals (population). The basic GA can be described as follows:
INTRODUCTION AND PROBLEM BACKGROUND
Genetic algorithms (GAs) provide a class of robust stochastic search algorithms for various optimization problems. The application of GAs to the design of morphological lters for grey scale image processing is a promising attempt and has recently become an important area of research 6] 4] 2].