Incremental attribute computation and image manipulation using morphological trees

• Ano de defesa: 2025
• Autor(a) principal: Silva, Dênnis José da
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Árvore de formas; Árvores de componentes; Árvores morfológicas; Attribute computation; Component trees; Computação de atributos; Image manipulation; Manipulação de imagens; Morphological trees; Tree of shapes
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/45/45134/tde-02082025-161749/

Morphological trees are image representations that can be used in a wide range of applications from medical imaging to digital photography. Morphological trees are interesting representations because they hierarchically encode the connected components (with and without their holes filled) according to their subset relationship. In this way, we can analyse and process connected regions of the images based on the hierarchy represented by the tree. A common morphological tree application pipeline consists of building the tree, computing attributes, processing the tree based on the tree structure and attributes of each node, and outputting results. Consequently, efficient attribute computation is a recurrent demand for unlocking new morphological tree applications. In this thesis, we describe our research on how to efficiently compute bit-quad counts, contours and distance transforms in morphological trees by exploiting the subset relationship encoded in trees for reuse of the attribute computation of the child nodes into their parent. First, we review how we can count bit-quads in component trees incrementally from the leaves to the root. Next, we design a novel incremental algorithm to count bit-quads in the tree of shapes. Then, we design a novel incremental method that can extract the contour of the nodes of component trees by counting the number of background neighbours of the pixels. Finally, we use our incremental contour method and Differential Image Foresting Transform to differentially compute the distance transform of component trees. We experimentally show that our differential and incremental methods are faster than non-incremental node-reconstruction approaches. We also explore the usage of morphological trees for image manipulation. In particular, we propose a novel morphological tree visualisation using icicle plots for node selection. In this visualisation, the nodes are coloured by an iso-illuminant colour map according to an attribute which aids the user in selecting the nodes. Then, the selected nodes can be manipulated using a spline-based dense medial descriptor. In summary, the thesis shows that we can compute bit-quad counts, contours, and distance transforms in morphological trees quickly by reusing the computation on the child nodes into their parent. It also discusses a software application of morphological trees for image manipulation.