Abstract
The theory of hierarchical image representations has been well-established in Mathematical Morphology, and provides a suitable framework to handle images through objects or regions taking into account their scale. Such approaches have increased in popularity and been favourably compared to treating individual image elements in various domains and applications. This survey paper presents the development of hierarchical image representations over the last 20 years using the framework of component trees. We introduce two classes of component trees, partitioning and inclusion trees, and describe their general characteristics and differences. Examples of hierarchies for each of the classes are compared, with the resulting study aiming to serve as a guideline when choosing a hierarchical image representation for any application and image domain.
Highlights
Properties such as accuracy, size and relation between elements are considered for an image representation in accordance with the application domain
In contrast to these and other theoretical works from Mathematical Morphology presented in a more general framework (e.g., [48]) and appropriated for different domains, we examine the component trees built directly from monochannel images represented by vertex-valued graphs and equipped with a 4-connectivity
We present a unifying survey of hierarchies of partitions and partial partitions used in practice, and propose a framework which decouples the structural shape information from the scale information added by indexing
Summary
Properties such as accuracy, size and relation between elements are considered for an image representation in accordance with the application domain. The reduced number of regions based on interpreting image information keeps the representational accuracy [2], but further unions of regions need to be considered to detect semantic structures [25] Hierarchical representations propose those most likely unions of regions on different scales of the image, from fine to coarse [25]. The “building blocks” of hierarchical image representations were thoroughly investigated by Serra [26] and Ronse [27], who study the (partial) segmentations and partitions, and further the lattices of those (partial) partitions forming hierarchies [45,46,47] In contrast to these and other theoretical works from Mathematical Morphology presented in a more general framework (e.g., [48]) and appropriated for different domains, we examine the component trees built directly from monochannel images represented by vertex-valued graphs and equipped with a 4-connectivity.
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