Ultimate levelings

摘要

This work presents a new class of residual operators called ultimate levelings which are powerful image operators based on numerical residues. Within a multi-scale framework, these operators analyze a given image under a series of levelings. Thus, contrasted objects can be detected if a relevant residue is generated when they are filtered out by one of these levelings. Our approach consists of, firstly, (i) representing the input image as a morphological tree; then, (ii) showing that a certain operation on this tree results in a leveling operator; and finally (iii) demonstrating that a sequential application of this operation on the tree is able to produce a family of levelings that satisfies scale-space properties. Besides, other contributions of this paper include: (i) the statement of properties of ultimate levelings, (ii) the presentation of an efficient algorithm for their computation, (iii) the provision of strategies for choosing families of primitives, (iv) the presentation of strategies for filtering undesirable residues, and (v) the provision of some illustrative examples of application of ultimate levelings. Furthermore, ultimate levelings are computationally efficient and their performance evaluations are comparable to the state of art methods for filtering and image segmentation.