Grey-level hit-or-miss transforms—part I : unified theory

Naegel, Benoît (School of Engineering, Architecture and Landscape (hepia), HES-SO // University of Applied Sciences Western Switzerland) ; Passat, Nicolas (LSIIT, UMR 7005 CNRS-ULP (Laboratoire des Sciences de l’Image, de l’Informatique et de la Télédétection), Illkirch Cedex, France ; Institut Gaspard Monge, Laboratoire A2SI (Algorithmique et Architecture des Systèmes Informatiques), Groupe ESIEE, Cité Descartes, Noisy-le-Grand Cedex, France) ; Ronse, Christian (LSIIT, UMR 7005 CNRS-ULP (Laboratoire des Sciences de l’Image, de l’Informatique et de la Télédétection), Illkirch Cedex, France)

The hit-or-miss transform (HMT) is a fundamental operation on binary images, widely used since 40 years. As it is not increasing, its extension to grey-level images is not straightforward, and very few authors have considered it. Moreover, despite its potential usefulness, very few applications of the grey-level HMT have been proposed until now. Part I of this paper, developed hereafter, is devoted to the description of a theory leading to a unification of the main definitions of the grey-level HMT, mainly proposed by Ronse and Soille, respectively (part II will deal with the applicative potential of the grey-level HMT, which will be illustrated by its use for vessel segmentation from 3D angiographic data). In this first part, we review the previous approaches to the grey-level HMT, especially the supremal one of Ronse, and the integral one of Soille; the latter was defined only for flat structuring elements (SEs), but it can be generalized to non-flat ones. We present a unified theory of the grey-level HMT, which is decomposed into two steps. First a fitting associates to each point the set of grey-levels for which the SEs can be fitted to the image; as in Soille's approach, this fitting step can be constrained. Next, a valuation associates a final grey-level value to each point; we propose three valuations: supremal (as in Ronse), integral (as in Soille) and binary.

Article Type:
Ingénierie et Architecture
HEPIA - Genève
inSTI - Institut des Sciences et Technologies industrielles
13 p.
Published in:
Pattern Recognition
Numeration (vol. no.):
2007, vol. 40, no. 2, pp. 635-647
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