Morphological transformations of binary images with arbitrary structuring elements

doi:10.1016/0165-1684(91)90025-E

Signal Processing

Volume 22, Issue 1, January 1991, Pages 3-23

https://doi.org/10.1016/0165-1684(91)90025-E Get rights and content

Abstract

This paper proposes a versatile algorithm for computing dilations and erosions of digital binary pictures with structuring elements of arbitrary size and shape. The first step consists in a tracking of the contours of the image under study and their encoding as loops. In a second step, the structuring element is efficiently propagated along the different loops thanks to its encoding in a customized data structure. The algorithm turns out to be extremely fast whatever the utilized elements. Moreover, even when simple shapes like squares or hexagons are considered, it is faster than most existing implementations. Finally, the present paper provides some examples of application, which highlight the practical interest of arbitrary structuring elements in the field of mathematical morphology.

Zusammenfassung

Dieser Aufsatz stellt einen anpassungsfähigen Algorithmus für die Bestimmung von Dilatationen und Erosionen binärer Bilder mit Hilfe beliebiger Structurierender Elemente vor. Der erste Schritt besteht darin, die Umrisse des betrachteten Bildes zu erfassen und sie als Schleifen zu Kodieren. In einem zweiten Schritt wird das strukturierende Element, das mittels einer geigneten Datenstruktur dargestellt ist, entlang den Schleifen verbreitet. Der Algorithmus arbeitet schnell und wirksam mit allen möglichen strukturierenden Elementen. Des weiteren, selbst wenn das Element eine einfache Form hat, wie ein Viereck oder ein Sechseck, sind die Rechenzeiten kürzer als bei den meisten existierenden Implementierungen. Am Ende des Aufsatzes werden Anwendungsbeispiele erläutert, die zeigen daβ die Verwendung beliebiger strukturierender Elemente für die mathematische Morphologie von groβem Interesse ist.

Résumé

Cet article propose un algorithme souple et performant pour déterminer des dilatations et érosions d'images binaires avec des éléments structurants quelconques. La premiére étape consiste en un suivi des contours de l'image considérée et en leur codage sous forme de boucles. Dans un deuxième temps, l'élément structurant, représénté sous la forme d'une structure de donnée appropriée, est efficacement propagé le long de ces boucles. L'algorithme s'avère extrêmement rapide quel que soit l'élément structurant employé. En outre, même lorsque cet élément est une forme simple, comme un carré ou un hexagone, les temps de calculs sont inférieurs à ceux de la plupart des implémentations existantes. La fin de l'article est consacrée à des exemples d'application, qui prouvent que l'utilisation d'élément structurants quelconques présente un grand intérêt pratique en morphologie mathématique.

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^∗: Present address: Division of Applied Sciences, Harvard University, Pierce Hall, Cambridge MA 02138, USA.

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Image processingMorphological transformations of binary images with arbitrary structuring elements

Abstract

Zusammenfassung

Résumé

Comput. Graph. Image Process.

Comput. Graph. Image Process.

Signal Processing

Placement automatique de formes: une approche géométrique

Morphologie mathématique et représentation d'images par arbres

Distance transformations in digital images

Comput. Vision Graph. Image Process.

The polygon containment problem

On the encoding of arbitrary geometric configurations

IEEE Trans. Comput.

Hexagonal pattern transforms