A Root-to-Leaf Algorithm Computing the Tree of Shapes of an Image

Abstract

We propose an algorithm computing the tree of shapes of an image, a unified variation of the component trees, proceeding from the root to the leaf shapes in a recursive fashion. It proceeds differently from existing algorithms that start from leaves, which are regional extrema of intensity, and build the intermediate shapes up to the root, which is the whole image. The advantage of the proposed method is a simpler, clearer, and more concise implementation, together with a more favorable running time on natural images. For integer-valued images, the complexity is proportional to the total variation, which is the memory size of the output tree, which makes the algorithm optimal.