The algebraic basis of mathematical morphology. I. dilations and erosions
Computer Vision, Graphics, and Image Processing
Why mathematical morphology needs complete lattices
Signal Processing
Minimal representations for translation-invariant set mappings by mathematical morphology
SIAM Journal on Applied Mathematics
Advances in the Analysis of Topographic Features on Discrete Images
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Morphological Image Analysis: Principles and Applications
Morphological Image Analysis: Principles and Applications
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Convergence, continuity, and iteration in mathematical morphology
Journal of Visual Communication and Image Representation
Flat morphological operators on arbitrary power lattices
Proceedings of the 11th international conference on Theoretical foundations of computer vision
Template matching based on a grayscale hit-or-miss transform
IEEE Transactions on Image Processing
A Multivariate Hit-or-Miss Transform for Conjoint Spatial and Spectral Template Matching
ICISP '08 Proceedings of the 3rd international conference on Image and Signal Processing
A hit-or-miss transform for multivariate images
Pattern Recognition Letters
Spatial and spectral morphological template matching
Image and Vision Computing
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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.