Nonrigid Image and Volume Registration Using Higher-Order Markov Random Fields

Abstract

In this dissertation, we propose nonrigid registration methods using a continuous energy model with a sparse local descriptor and a discrete energy model with or without a dense local descriptor. First, we propose a nonrigid registration method using a continuous energy model with a sparse local descriptor. This method is targeted for aligning two input volumes efficiently and resulting deformation fields can be used as initial data for more complex registration methods such as intensity-based registrations. For input volumes, we extract 3D features with their descriptors and estimate correspondences by finding nearest neighbor in descriptor space. An energy function is constructed using the correspondence information and the smoothness measure of free-form deformation model based on B-splines. We integrate an approximated smoothness energy function and a robust correspondence energy estimator controlled by the confidence radius of the matching distance in this energy model. The energy function is optimized by sequentially reducing the confidence radius, and outlier correspondences are discarded systematically during convergence. We propose a highly efficient optimization procedure using the preconditioned nonlinear conjugate gradient method. The multi-phase liver CT volumes are used for building and evaluating the proposed method. In the experiments, quantitative and qualitative results on synthetic and clinical data sets are provided. Secondly, we propose a nonrigid registration method using a discrete energy model built on the Markov Random Field (MRF) with a higher-order smoothness prior. The registration is designed as finding a set of discrete displacement vectors on a deformable mesh, using the energy model defined by label sets relating to these vectors. In this method, a new energy model which adopts a higher-order spatial prior for the smoothness cost is introduced. This model improves limitations of pairwise spatial priors which cannot fully incorporate the natural smoothness of deformations. Also, a dynamic energy model to generate optimal displacements is introduced. This model works iteratively with optimal data cost while the spatial prior preserve the smoothness cost of previous iteration. For optimization, we convert the proposed model to pairwise MRF model to apply the tree-reweighted message passing (TRW). Concerning the complexity, we apply the decomposed scheme to reduce the label dimension of the proposed model and incorporate the linear constrained node (LCN) technique for efficient message passings. In the experiments, the competitive performance of the proposed model compared with previous models, presenting both quantitative and qualitative analysis using synthetically deformed data and real photo data for 2D images and uni- and multi-modal brain MRI data and inter-subject data for 3D volumes are provided. Thirdly, we propose a nonrigid registration method using a MRF energy model with higher-order smoothness priors and a dense local descriptor. The registration is designed as finding an optimal labeling of the MRF energy model where the label corresponds to a discrete displacement vector. The proposed MRF energy model uses matching scores of dense local descriptors between images as a data cost. In this model, spatial relationships are constructed between nodes using higher-order smoothness priors. As the local descriptor is invariant to scale and rotation and also robust to changing appearances, this method can handle multi-modal images involving scale and rotation transformations. The higher-order smoothness priors can generate desired smoother displacement vector fields and do not suffer from fronto-parallel effects commonly occurred in first-order priors. The usage of higher-order priors in the energy model enables this method to produce more accurate registration results. In the experiments, registration results using multi-modal brain MRI Images and facial images with expression and light changes are provided. Finally, we propose a new method for solving the MRF energies with higher-order smoothness priors. The main idea of the proposed method is a graph conversion which decomposes higher-order cliques as hierarchical auxiliary nodes. For a special class of smoothness priors which can be formulated as gradient-based potentials, we introduce an efficient representation of an auxiliary node called a gradient node. We denote a graph converted using gradient nodes as a hierarchical gradient node (HGN) graph. Given a label set L, the computational complexity of message passings of HGN graphs are reduced to O(

L

^2) from exponential complexity of a conventional factor graph representation. Moreover, as the HGN graph can integrate multiple orders of the smoothness priors inside its hierarchical structure, this method provides a way to combine different smoothness orders naturally in MRF frameworks. For optimizing HGN graphs, we apply the TRW message passing which outperforms the belief propagation. In experiments, the efficiency of the proposed method on the 1D signal reconstructions and demonstrate the performance of the proposed method in three applications: image denoising, sub-pixel stereo matching and nonrigid image registration are provided.