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Hierarchical Graph Encodings
Published in Olivier Lézoray, Leo Grady, Image Processing and Analysis with Graphs, 2012
One of the most common graph data structure, within the segmentation, framework is the region adjacency graph. A RAG is defined from a partition by associating one vertex to each region and by creating an edge between two vertices if the associated regions share a common boundary segment (Figure 11.13(c)). A RAG thus encodes the meet_exists relationship. It corresponds to a simple graph without any double edge between vertices nor self-loop. The simplification of a RAG is based on the following graph transformations: Edge removal: The removal of an edge from a graph G=(V,ℰ) consists to remove it from ℰ. In order to avoid to disconnect the graph, removed edges should not define a bridge.Edge contraction: The contraction of an edge consists to collapse the two vertices incident to the edge into a single vertex and to remove the edge. Self-loops are excluded from edge contraction since both end points correspond to a same point which cannot collapse with itself.
Optimised CNN based Brain Tumour Detection and 3D Reconstruction
Published in Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 2023
Sushitha Susan Joseph, Aju Dennisan
(2) Contract edge for minimising the triangular patches count: Moreover, the grid scheme is simplified into four methods like vertex merging, decimation, adaptive subdivision and sampling. The edge contraction method is chosen by merging the simplicity and robustness of the vertex. The three constraint conditions are satisfied only, the edge including the two contract vertices into a point and two vertices merged into one. In addition, the triangle will be kept only when the conditions are not met.