Nonrigid Medical Image Registration Using an Information Theoretic Measure Based on Arimoto Entropy with Gradient Distributions

Abstract

This paper introduces a new nonrigid registration approach for medical images applying an information theoretic measure based on Arimoto entropy with gradient distributions. A normalized dissimilarity measure based on Arimoto entropy is presented, which is employed to measure the independence between two images. In addition, a regularization term is integrated into the cost function to obtain the smooth elastic deformation. To take the spatial information between voxels into account, the distance of gradient distributions is constructed. The goal of nonrigid alignment is to find the optimal solution of a cost function including a dissimilarity measure, a regularization term, and a distance term between the gradient distributions of two images to be registered, which would achieve a minimum value when two misaligned images are perfectly registered using limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimization scheme. To evaluate the test results of our presented algorithm in non-rigid medical image registration, experiments on simulated three-dimension (3D) brain magnetic resonance imaging (MR) images, real 3D thoracic computed tomography (CT) volumes and 3D cardiac CT volumes were carried out on elastix package. Comparison studies including mutual information (MI) and the approach without considering spatial information were conducted. These results demonstrate a slight improvement in accuracy of non-rigid registration.

Keywords: Arimoto entropy; free-form deformations; gradient distributions; non-rigid registration; nonextensive entropy; normalized divergence measure.

Figure 1

Block diagram of our registration algorithm.

Figure 2

(a) MR T1 image; (b) MR T2 image; (c) deformation field; (d) deformation vector.

Figure 3

The axis slice of 10 3D cardiac CT images in one 4D sequence. (a–j) represent the 10 frames acquired from one whole cardiac cycle of one patient.

Figure 4

The registration results of the simulated 3D brain MR T1 & MR T2, MR T1 & MR PD, and MR T2 & MR PD volumes using three algorithms. The red color crosses for each box represents these outliers.

Figure 5

The TREs obtained when employing NJAD-GD algorithm, the registration method based on JAD without gradient distribution.

Figure 6

Statistics of TREs before registration and after alignment exploiting the NJAD-GD, JAD methods.

Figure 7

HDMs obtained when employing NJAD-GD algorithm, the registration method based on JAD without gradient distribution.

Figure 8

Registration results of 12 groups of 3D cardiac images. (a–l) display the test results of patient 1 to 12, respectively. In each group, left image represents the checkboard before registration, and the right accounts for the result after registration.