Image analysis methods based on hierarchies of graphs and multi-scale mathematical morphology

This thesis is about image analysis methods based on hierarchical graph represen-tations. A hierarchical graph representation of an image is an ordered set of graphs that represent the image on different levels of abstraction. The vertices of the graph represent image structures (lines, areas). Its edges represent the relations between those structures (adjacency, collinearity). Graphs on higher levels of the hierarchy give a more global and abstract representa-ti-on of the image. A number of image analysis methods based on hierarchical graph repre-senta-tions were developed. These methods were applied to image segmentation, detection of linear structures and edge detection. It is found that a hierarchical graph is an attractive framework for image analysis, because it can easily encode and handle different structures, and because structures and there relations are encoded in the same repre-sentation. The only restriction of the method is its 'bottom-up' character. However it is suggested how this can be remedied by a 'top-down' analysis in a later stage of the proces. The second part of this study is about multiresolution morphology. Discs defined by weighted metrics were used as structuring elements. Weighted metrics can approximate the Euclidian metric to within a few percent. Algorithms were developed to perform the elementary morphological operations (erosion, dilation, opening, closing), and some advanced operations as the medial axis transform, the opening transform, and the patttern spec-trum-transform. The computational costs of these methods is comparable to the cost of conventional morphological methods using square structuring elements