Efficient MRF deformation model for non-rigid image matching

Abstract

We propose a novel MRF-based model for deformable image matching. Given two images, the task is to estimate a mapping from one image to the other maximizing the quality of the match. We consider mappings defined by a discrete deformation field constrained to preserve 2D continuity. We pose the task as finding MAP configurations of a pairwise MRF. We propose a more compact MRF representation of the problem which leads to a weaker, though computationally more tractable, linear programming relaxation -the approximation technique we choose to apply. The number of dual LP variables grows linearly with the search window side, rather than quadratically as in previous approaches. To solve the relaxed problem (suboptimally), we apply TRW-S (Sequential Tree-Reweighted Message passing) algorithm [13,5]. Using our representation and the chosen optimization scheme, we are able to match much wider deformations than was considered previously in global optimization framework. We further elaborate on continuity and data terms to achieve more appropriate description of smooth deformations. The performance of our technique is demonstrated on both synthetic and real-world experiments.

Integrated 3d flow-based multi-atlas brain structure segmentation

“…To avoid passing messages inefficiently in a six-neighbor system while still pursuing a good approximation for energy minimization, an appropriate message update schedule is required by exploring the special structure of a 3D image grid. As suggested by Liu et al [ 49 ] and Shekhovtsov et al [ 79 ], the smoothness term in the energy function in Eq (3) is decoupled in L1 norm form for three dimensions, which makes the MRF model decomposable in belief propagation. Hence, the message of a flow vector about the smoothness penalty can be divided into three individual parts for its three-dimensional components.…”

“…We use the term, layer, for the isomorphic volume when referring to inter-layer and intra-layer messages, which follows from the 2D dual-layer expression. With this setup and the help of Shekhovtsov et al [ 79 ], an efficient 3D message passing scheme is designed as follows. During propagation, at the beginning of one iteration, we update inter-layer messages by passing them from the two counterpart volumes to the current volume.…”

Slice-to-volume medical image registration: A survey

“…FastPD was adopted as the optimization algorithm given the properties of the energy function (pairwise terms and non-submodularity). Motivated by the work of Shekhovtsov et al (2008), in an effort to reduce the dimensionality of the label space, the work by presents a different model (the socalled decoupled model) where linear and deformable parameters are now separated into two interconnected subgraphs which refer to lower dimensional label spaces. It reduces the dimensionality of the label space by increasing the number of edges and vertices, while keeping a pairwise graph.…”

Slice-to-volume deformable registration: efficient one-shot consensus between plane selection and in-plane deformation

“…In that way, the complexity of the model reduces to the square of the cardinality of the biggest label space (instead of being quadratic in the product of the cardinalities of the two spaces), with a slight increase of the graphical model connectivity. This technique has been previously applied in 2D-2D registration [24]. The main advantage is related to the fact that, while the number of nodes augment linearly, the number of labels is decreased in a quadratic order.…”