Abstract
The classical framework of connected filters relies on the removal of some connected components of a graph. To apply those filters, it is often useful to transform an image into a component tree, and to prune the tree to simplify the original image. Those trees have some remarkable properties for computer vision. A first illustration of their usefulness is the proposition of a local feature detector, truly invariant to change of contrast. which allows us to obtain the state-of-the-art results in image registration and in multi-view 3D reconstruction. Going further in the use of those trees, we propose to expand the classical framework of connected filters. For this, we introduce the notion of tree-based shape spaces: instead of filtering the connected components of the graph corresponding to the image, we propose to filter the connected components of the graph given by the component tree of the image. This general framework, which we call shape-based morphology can be used for object detection and segmentation, hierarchical segmentation, and image filtering. Many applications and illustrations show the usefulness of the proposed framework.