Evaluation of Optimization Methods for Nonrigid Medical Image Registration Using Mutual Information and B-Splines

Abstract

A popular technique for nonrigid registration of medical images is based on the maximization of their mutual information, in combination with a deformation field parameterized by cubic B-splines. The coordinate mapping that relates the two images is found using an iterative optimization procedure. This work compares the performance of eight optimization methods: gradient descent (with two different step size selection algorithms), quasi-Newton, nonlinear conjugate gradient, Kiefer-Wolfowitz, simultaneous perturbation, Robbins-Monro, and evolution strategy. Special attention is paid to computation time reduction by using fewer voxels to calculate the cost function and its derivatives. The optimization methods are tested on manually deformed CT images of the heart, on follow-up CT chest scans, and on MR scans of the prostate acquired using a BFFE, T1, and T2 protocol. Registration accuracy is assessed by computing the overlap of segmented edges. Precision and convergence properties are studied by comparing deformation fields. The results show that the Robbins-Monro method is the best choice in most applications. With this approach, the computation time per iteration can be lowered approximately 500 times without affecting the rate of convergence by using a small subset of the image, randomly selected in every iteration, to compute the derivative of the mutual information. From the other methods the quasi-Newton and the nonlinear conjugate gradient method achieve a slightly higher precision, at the price of larger computation times.

Evaluation of 4D-CT Lung Registration

“…[7] After extracting lung surface and vessel tree a method of deformable surface models is applied on the generated [8] B-splines SSD -no elastix [9] B-splines NCC -yes DROP [10] B-splines SAD grid vector distances yes POPI-nonpar [5] non-par. SSD Gaussian + linear elastic no FEIR [11] non-par.…”

“…Volumetric Registrations [5,8,9,10,11]. An overview of the employed volumetric schemes is given in Tab.…”

Self-similarity Weighted Mutual Information: A New Nonrigid Image Registration Metric

“…We adopt an iterative stochastic gradient descent optimization method [20] for solving Eq. 1, which is fast and is less likely to get trapped in local minima.…”

“…1) wrt μ. The step size is a decaying function of the iteration number: a t = a/(A + t) τ , with a > 0, A ≥ 0 and 0 < τ ≤ 1 user-defined constants [20]. From Eq.…”

A CNN Based Hybrid Approach Towards Automatic Image Registration

“…Soft computing techniques such as neural networks, genetic algorithms, and fuzzy logic followed by probabilistic concepts such as random field variations, have been extensively applied in this context (Liu, Wu 2012;Gouveia et al 2012;jack, Roux 1995;Chow et al 2004;jankó et al 2006). Literature has also revealed many mutual information as well as intensity-based approaches (Klein et al 2007;Viola, Wells 1997;Cvejic et al 2006;Mohanalin et al 2009). N-dimensional classifiers as well as random field concepts and different transformation techniques (SIFT, Wavelet etc.)…”