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2014 | OriginalPaper | Chapter

Vector Ordering and Multispectral Morphological Image Processing

Authors : Santiago Velasco-Forero, Jesus Angulo

Published in: Advances in Low-Level Color Image Processing

Publisher: Springer Netherlands

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Abstract

This chapter illustrates the suitability of recent multivariate ordering approaches to morphological analysis of colour and multispectral images working on their vector representation. On the one hand, supervised ordering renders machine learning notions and image processing techniques, through a learning stage to provide a total ordering in the colour/multispectral vector space. On the other hand, anomaly-based ordering, automatically detects spectral diversity over a majority background, allowing an adaptive processing of salient parts of a colour/multispectral image. These two multivariate ordering paradigms allow the definition of morphological operators for multivariate images, from algebraic dilation and erosion to more advanced techniques as morphological simplification, decomposition and segmentation. A number of applications are reviewed and implementation issues are discussed in detail.

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previous chapter Spatially Adaptive Color Image Processing

next chapter Morphological Template Matching in Color Images

Theoretically, a partial ordering is enough but to make easier the presentation we analyse the case of total ordering.

Adaptive in the sense that the mapping depend on the information contained in a multivariate image \({\mathbf {I}}\). The correct notation should be \(h(\cdot ;{\mathbf {I}})\). However, in order to make easier the understanding of the section we use \(h\) for adaptive mapping.

In this case the sense of the inequality change, i.e., \({\mathbf {x}}_1 \le _{h_\mathtt{REF}} {\mathbf {x}}_2 \iff ||{\mathbf {x}}_1-{\mathbf {t}}||^2 \ge ||{\mathbf {x}}_2-{\mathbf {t}}||^2\).

It is important to note that any adjunction based morphological transformations as openings, closings, levelings and so on, can be implemented in similar way, i.e., by changing the function \(\mathtt {Erode}\) by another grey scale morphological transformation.

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Title: Vector Ordering and Multispectral Morphological Image Processing
Authors: Santiago Velasco-Forero
Jesus Angulo
Publisher: Springer Netherlands
Book: Advances in Low-Level Color Image Processing
Print ISBN: 978-94-007-7583-1

Electronic ISBN: 978-94-007-7584-8

Copyright Year: 2014
DOI: https://doi.org/10.1007/978-94-007-7584-8_7

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