Implicit planar and in-plane deformable mapping in medical images through high order graphs

Abstract

In this paper we propose a novel method based on discrete optimization of high order graphs, to perform deformable sliceto-volume registration of 2D images and 3D volumes. To this end, a 2D grid superimposed to the image is considered with control points deforming in 3D and their deformations corresponding to the label space. Geometrical consistency (unique plane selection) and deformation smoothness (in-plane deformations) as well as image similarity (visual matching) are encoded in different third order cliques. The proposed formulation is optimized through its mapping to a factor graph using conventional graph optimization methods. A dataset composed of 2D slices and 3D MRI volumes of the heart was used to evaluate its accuracy leading to very promising results.

Graph-Based Slice-to-Volume Deformable Registration

“…In this paper we extend our previous work presented in [10,9,8] through the introduction of a single, mathematically rigorous and theoretically sound framework derived as a discrete labeling problem on a graphical model. Graphical models and discrete optimization are powerful formalisms that have been successfully used during the past years in the field of computer vision [45].…”

“…In [10], the overparameterized approach was optimized using the FastPD algorithm [23] while for the decoupled [9] and the higher order models [8], we consider loopy belief propagation networks. For the sake of fairness, in order to improve the confidence of the comparison among the three Figure 7 Factor graph derivation and labels spaces corresponding to the overparameterized, decoupled and highorder approaches.…”

“…It allows us to reduce the dimensionality of the label space by increasing the number of edges and vertices, while keeping a pairwise graph. Finally, in the high-order approach [8], we achieve this dimensionality reduction by augmenting the order of the graphical model, using third-order cliques which exploits the expression power of this type of variable interactions. Such a model provides better satisfaction of the global deformation constraints at the expense of quite challenging inference.…”

“…In that way we explore a wider range of parameters which result in more accurate sampling when composed after several iterations. A similar approach has been successfully used in previous graph-based registration papers ( [10,8,9,15,16]). …”

Rigid Slice-To-Volume Medical Image Registration Through Markov Random Fields

“…In case of projective 2D/3D image registration, only linear transformations were estimated using discrete methods by [3,4]. More recently, several graph-based approaches to perform deformable slice-tovolume registration were introduced in [14][15][16]. In these works, rigid transformations were computed as a by-product of the deformable parameters, leading to unnecessary computational burden (since rigid transformations are by far lower dimensional than deformable ones).…”