Topology Preserving Warping of Binary Images: Application to Atlas-Based Skull Segmentation

Abstract

Abstract. Lots of works have been recently carried out in the field of non-rigid registration to ensure the estimation of one-to-one mappings. However, warping a binary image with such transformations may alter its discrete topological properties if common resampling strategies are considered. This paper proposes an original method for warping a binary image according to some continuous and bijective mapping, while preserving its discrete topological properties. Results obtained in the context of atlas-based segmentation highlight the interest of the approach. Indeed, the method has been successfully applied to the segmentation of skull structures from a database of 15 CT-scans, providing both geometrically and topologically satisfactory results.

Topological Properties of Thinning in 2-D Pseudomanifolds

“…In this context, numerous methods have been developed to process discrete 2-D and 3-D binary images, essentially to perform skeletonisation, homotopic transforms or segmentation (see e.g. [1][2][3]).…”

3D Angiographic Image Segmentation

“…The readers who are interested in other works related to mathematical morphologybased segmentation methods of 3D angiographic data can also refer to the following articles [21,2,20,1]. More generally, besides the use of morphological and geometric knowledge [9,13], other solutions dealing with the integration of topological knowledge [6,5,7], relational knowledge [3,8], or even the use of temporal information [4] (see also the previous chapter of this book) for the segmentation of medical images, have been investigated during the last years, and have already led to quite interesting results.…”

Topology Preserving Warping of 3-D Binary Images According to Continuous One-to-One Mappings

“…This article presents a new strategy to tackle this problem, whose preliminary results have been published in [21]. We propose here to formulate the problem of warping a binary image according to a continuous deformation field in an optimization framework.…”