Meaningful disjoint level lines selection

Abstract

Many methods based on the morphological notion of shapes (i.e., connected components of level sets) have been proved to be very efficient in shape recognition and shape analysis. The inclusion relationship of the level lines (boundaries of level sets) forms the tree of shapes, a tree-based image representation with a high potential. Numerous applications using this tree representation have been proposed. In this article, we propose an efficient algorithm that extracts a set of disjoint level lines in the image. These selected level lines yield a simplified image with clean contours, which provides an intuitive idea about the main structure of the tree of shapes. Besides, we obtain a saliency map without transition problems around the contours by weighting level lines with their significance. Experimental results demonstrate the efficiency and usefulness of our method.

Region-based classification of remote sensing images with the morphological tree of shapes

“…The Tree of Shapes (ToS) [1,2] is a morphological tree that represents images in a self-dual and contrast invariant way. Due to the versatility of its structure, the ToS has proven to be a suitable representation for addressing many applications, such as visualization [3], filtering [4],object detection [5], segmentation [6] and image simplification [7].…”

Morphological object picking based on the color tree of shapes

“…. The versatility of the structure is no more to demonstrate since it has been applied for visualization [6], filtering [7], object detection [8], image registration [9], and image simplification [10,11]. It is not such a surprise if the Tree of Shapes achieves such good results but it is rather due to the mathematical properties held by the representation [12].…”