Max-tree

Abstract

The max-tree is a mathematical morphology tool that represents all connected components resulting of every possible upper threshold of an image. This work focus on advancing further the max-tree theory, algorithms and applications. In the theory domain, extinction filters (EFs) for increasing attributes are defined and a procedure for computing EFs for nonincreasing attributes, based on the space of shapes approach, is presented. In the algorithms domain, an array-based node-oriented data structure to store the max-tree and algorithms to process it are proposed. This structure gives direct access to the max-tree nodes, is more memory efficient and allows faster processing than other structures described in the literature. Using this proposed structure, EFs can be implemented efficiently as our experiments and complexity analysis indicate. EFs are experimentally compared to attribute filters and the results show that EFs are better in terms of simplification for recognition. We provide an open-source toolbox entitled iamxt that implements the data structure and the algorithms proposed using an array-based programming style. In the applications domain, we investigate two problems: classification of satellite images and magnetic resonance (MR) images brain segmentation. These applications are built upon EFs and the efficient max-tree algorithms. The satellite image classification approach we propose is called Extinction Profiles. It is currently the state-of-the-art for the classification of this kind of image. We validate this comparing to another state-of-the-art approach called Attribute Profile using two different datasets. For the brain segmentation application, we propose a public multi-vendor multi-field strength T 1-weighted brain MR dataset with 359 volumes and brain segmentation "silver standards" generated using supervised classification. We validate our method using this dataset and two other public datasets. The results show that our method has the highest sensitivity among the methods compared, i.e. preserves the brain, and it is robust to parameter initialization.