Prior-Based Piecewise-Smooth Segmentation by Template Competitive Deformation Using Partitions of Unity

Abstract

Abstract. We propose a new algorithm for two-phase, piecewise-smooth segmentation with shape prior. The image is segmented by a binary template that is deformed by a regular geometric transformation. The choice of the template together with the constraint on the transformation introduce the shape prior. In particular, the topology of the shape is preserved if the transformation is diffeomorphic. The deformation is guided by the maximization of the likelihood of foreground and background intensity models, so that we can refer to this approach as Competitive Deformation. In each region, the intensity is modelled as a smooth approximation of the original image. We represent the transformation using a Partition of Unity Finite Element Method, which consists in representing each component with polynomial approximations within local patches. A conformity constraint between the patches provides a way to control the globality of the deformation. We show several results on synthetic images, as well as on medical data from different modalities.

Minimally Interactive MRI Segmentation for Subject-Specific Modelling of the Tongue

“…Saddi et al used a template matching procedure as the complementary step to their liver segmentation process, in order to compensate for the limitations of their learning set [24]. Somphone et al transformed their binary template, subject to conformity constraints between local patches [25]. In a different approach, Gilles et al used explicit shape representation of the template to segment the musculoskeletal structures out of MR images [26].…”

Kidney Detection and Segmentation in Contrast-Enhanced Ultrasound 3D Images

“…We follow the template deformation framework described in [13,14] and extended in [15], as it a very efficient modelbased algorithm and it has already been applied successfully to kidney segmentation in CT images [16] . …”

Real-Time 3D Image Segmentation by User-Constrained Template Deformation

“…To cope with these problems, alternative approaches have been proposed [10][11][12] to define Φ as the deformation of a given implicit template Φ 0 , defined in a referential Ω 0 , with a geometric transformation ψ (see Fig. 1):…”

“…Compliance with the shape prior is determined by both the deformation model ψ and its associated constraint R(ψ). In the non-rigid case, Saddi et al represented the deformation with a diffeomorphic fluid model [10], Somphone et al proposed deformations based on finite elements [11], and Huang and Metaxas adopted Free Form Deformations in their Metamorphs [12].…”

“…Template-to-image registration is a possible alternative, recently applied to medical applications such as liver segmentation in CT [10], in which segmentation is performed by geometrically deforming a binary template towards the image [10][11][12]. The prior is the template itself and the shape constraint consists in a regularization of the deformation.…”