Robust and flexible multi-scale medial axis computation

Abstract

The principle of the multi-scale medial axis (MMA) is important in that any object is detected at a blurring scale proportional to the size of the object. Thus it provides a sound balance between noise removal and preserving detail. The robustness of the MMA has been reflected in many existing applications in object segmentation, recognition, description and registration. This thesis aims to improve the computational aspects of the MMA. The MMA is obtained by computing ridges in a “medialness” scale-space derived from an image. In computing the medialness scale-space, we propose an edge-free medialness algorithm, the Concordance-based Medial Axis Transform (CMAT). It not only depends on the symmetry of the positions of boundaries, but also is related to the symmetry of the intensity contrasts at boundaries. Therefore it excludes spurious MMA branches arising from isolated boundaries. In addition, the localisation accuracy for the position and width of an object, as well as the robustness under noisy conditions, is preserved in the CMAT. In computing ridges in the medialness space, we propose the sliding window algorithm for extracting locally optimal scale ridges. It is simple and efficient in that it can readily separate the scale dimension from the search space but avoids the difficult task of constructing surfaces of connected maxima. It can extract a complete set of MMA for interfering objects in scale-space, e.g. embedded or adjacent objects. These algorithms are evaluated using a quantitative study of their performance for 1-D signals and qualitative testing on 2-D images