Abstract EN:

The inclusion and adjacency relationship between image regions usually carry contextual information. The later is widely used since it tells how regions are arranged in images. The former is usually not taken into account although it parallels the object-background relationship. The mathematical morphology framework provides several hierarchical image representations. They include the Tree of Shapes (ToS), which encodes the inclusion of level-line, and the hierarchies of segmentation (e.g., alpha-tree, BPT), which is useful in the analysis of the adjacency relationship. In this work, we take advantage of both inclusion and adjacency information in these representations for computer vision applications. We introduce the spatial alignment graph w.r.t inclusion that is constructed by adding a new adjacency relationship to nodes of the ToS. In a simple ToS such as our Tree of Shapes of Laplacian sign, which encodes the inclusion of Morphological Laplacian 0-crossings, the graph is reduced to a disconnected graph where each connected component is a semantic group. In other cases, e.g., classic ToS, the spatial alignment graph is more complex. To address this issue, we expand the shape-spaces morphology. Our expansion has two primary results: 1)It allows the manipulation of any graph of shapes. 2)It allows any tree filtering strategy proposed by the connected operators frameworks. With this expansion, the spatial graph could be analyzed with the help of an alpha-tree. We demonstrated the application aspect of our method in the application of text detection. The experiment results show the efficiency and effectiveness of our methods, which is appealing to mobile applications.