Topologically Correct Image Segmentation using Alpha Shapes

Existing theories on shape digitization are not very realistic: they impose strong constraints on feasible shapes, and require measurements to be free of error. In this paper, we propose a new approach based on Delaunay triangulation and α-shapes which significantly weakens these restrictions. It assumes that sampling points (edgels) represent true object edges with a certain bounded error. We are able to prove under which conditions a topologically correct segmentation can be reconstructed from the edgels. Experiments on real and generated images demonstrate the good performance of the new method and confirm the predictions of our theory

H.: Topologically Correct Image Segmentation using Alpha Shapes

Abstract. Existing theories on shape digitization impose strong constraints on feasible shapes and require error-free measurements. We use Delaunay triangulation and ff-shapes to prove that topologically correct segmentations can be obtained under much more realistic conditions. Our key assumption is that sampling points represent object boundaries with a certain maximum error. Experiments on real and generated images demonstrate the good performance and correctness of the new method. 1 Introduction A fundamental question of image analysis is how closely a computed imagesegmentation corresponds to the underlying real-world partitioning. Existing geometric sampling theorems are limited to binary partitionings, where the planeis split into (not necessarily connected) fore- and background components. In this case, the topology of the partition is preserved under various discretizationschemes when the original regions ar