Abstract
Abstract Connected operators based on hierarchical image models have been increasingly considered for the design of efficient image segmentation and filtering tools in various application fields. Among hierarchical image models, component-trees represent the structure of grey-level images by considering their nested binary level-sets obtained from successive thresholds. Recently, a new notion of component-graph was introduced to extend the component-tree to any grey-level or multivalued images. The notion of shaping was also introduced as a way to improve the anti-extensive filtering by considering a two-layer component-tree for grey-level image processing. In this article, we study how component-graphs (that extend the component-tree from a spectral point of view) and shapings (that extend the component-tree from a conceptual point of view) can be associated for the effective processing of multivalued images. We provide structural and algorithmic developments. Although the contributions of this article are theoretical and methodological, we also provide two illustration examples that qualitatively emphasize the potential use and usefulness of the proposed paradigms for image analysis purposes.
Highlights
Mathematical morphology is a well known non-linear theory of image processing [1, 2]
We study how component-graphs and shapings can be associated for the effective processing of multivalued images
In [17], we proposed to associate both notions of component-graphs and shaping for the effective processing of multivalued images, opening the way to new paradigms for connected filtering based on hierarchical representations
Summary
Mathematical morphology is a well known non-linear theory of image processing [1, 2]. Two main ways were explored: splitting the value space into several totally ordered ones (marginal processing), or defining ad hoc total order relations [7], often guided by semantic considerations (vectorial processing) This is considered for handling colour images [12,13,14] and less frequently multi- / hyperspectral images [15]: marginal ordering, conditional ordering (C-ordering, widely studied in the framework of colour morphology [7], including lexicographic ordering [14, 16]), reduced ordering (R-ordering) [4], partial ordering (P-ordering), and more recently a combination of several of these orderings [12].
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