Multi-Label Simple Points Definition for 3D Images Digital Deformable Model

Abstract

Abstract. The main contribution of this paper is the definition of multilabel simple points that ensures that the partition topology remains invariant during a deformable partition process. The definition is based on simple intervoxel properties and is easy to implement. A deformation process is carried out with a greedy energy minimization algorithm. A discrete area estimator is used to approach at best standard regularizers classically used in continuous energy minimizing methods. The effectiveness of our approach is shown on several 3D image segmentations.

Fully deformable 3D digital partition model with topological control

“…This paper is an extension of the work [16], where a first notion of simple point in a partition was proposed. This first definition was enough to simulate movements of boundaries between two regions, but it forbade movements of boundaries between three or more regions (1-dimensional boundaries).…”

“…It aims at combining the advantages of the continuous and the discrete energy-minimizing techniques. This paper is an extension of the work of [16]. It shares with it the following features: discrete model : it is a purely digital formulation of energy minimization, which can be solved by combinatorial algorithms.…”

“…Furthermore, compared with [16], this paper describes a new method to guarantee that the topology of the whole partition is preserved during the deformation process, which allows a larger class of partition deformation at each step while guaranteeing that the partition topology remains unchanged.…”

“…In [16], we give a first definition of multi-label simple points allowing to preserve both the topology of regions and the surface relations, recalled in Definition 2. In this paper, we refer to this previous definition as restricted multi-label simple points (rML-simple points).…”

“…The definition is based on intervoxel properties, and uses the notion of collapse on cubical complexes. This work is an extension of a former restricted definition [16] that prohibits the move of intersections of boundary surfaces. A deformation process is carried out with a greedy energy minimization algorithm.…”