Deformable Medical Image Registration: A Survey <s> C. Miscellaneous <s> A new approach is presented for elastic registration of medical images, and is applied to magnetic resonance images of the brain. Experimental results demonstrate remarkably high accuracy in superposition of images from different subjects, thus enabling very precise localization of morphological characteristics in population studies. There are two major novelties in the proposed algorithm. First, it uses an attribute vector, i.e. a set of geometric moment invariants that is defined on each voxel in an image, to reflect the underlying anatomy at different scales. The attribute vector, if rich enough, can distinguish between different parts of an image, which helps establish anatomical correspondences in the deformation procedure. This is a fundamental deviation of our method, referred to as HAMMER, from other volumetric deformation methods, which are typically based on maximizing image similarity. Second, in order to avoid being trapped by local minima, i.e. suboptimal poor matches, HAMMER uses a successive approximation of the energy function being optimized by lower dimensional energy functions, which are constructed to have significantly fewer local minima. This is achieved by hierarchically selecting features that have distinct attribute vectors, thus drastically reducing ambiguity in finding correspondence. A number of experiments in this paper have demonstrated excellent performance. <s> BIB001 </s> Deformable Medical Image Registration: A Survey <s> C. Miscellaneous <s> This paper puts forward two useful methods for self-adaptation of the mutation distribution - the concepts of derandomization and cumulation. Principle shortcomings of the concept of mutative strategy parameter control and two levels of derandomization are reviewed. Basic demands on the self-adaptation of arbitrary (normal) mutation distributions are developed. Applying arbitrary, normal mutation distributions is equivalent to applying a general, linear problem encoding. The underlying objective of mutative strategy parameter control is roughly to favor previously selected mutation steps in the future. If this objective is pursued rigorously, a completely derandomized self-adaptation scheme results, which adapts arbitrary normal mutation distributions. This scheme, called covariance matrix adaptation (CMA), meets the previously stated demands. It can still be considerably improved by cumulation - utilizing an evolution path rather than single search steps. Simulations on various test functions reveal local and global search properties of the evolution strategy with and without covariance matrix adaptation. Their performances are comparable only on perfectly scaled functions. On badly scaled, non-separable functions usually a speed up factor of several orders of magnitude is observed. On moderately mis-scaled functions a speed up factor of three to ten can be expected. <s> BIB002 </s> Deformable Medical Image Registration: A Survey <s> C. Miscellaneous <s> This paper presents a method of deformable registration of cortical structures across individuals, using hybrid volumetric and surface warping. The proposed method uses two steps. In the first step, a HAMMER-based volumetric registration algorithm warps the model surface to the individual’s space. In the second step, an attribute-based surface registration method further refines the results of the volumetric warping. An attribute vector is defined for each vertex on the cortical surface, and used to capture the local and global geometric features of the surface patch. The attribute vector is designed to be as distinctive as possible, so that each vertex on the model surface can find its correspondence on the individual surface. Experimental results on synthesized and real brain data are provided to demonstrate the performance of the proposed method in registering cortical structures across individuals. <s> BIB003 </s> Deformable Medical Image Registration: A Survey <s> C. Miscellaneous <s> Finding point correspondence in anatomical images is a key step in shape analysis and deformable registration. This paper proposes an automatic correspondence detection algorithm for intramodality MR brain images of different subjects using wavelet-based attribute vectors (WAVs) defined on every image voxel. The attribute vector (AV) is extracted from the wavelet subimages and reflects the image structure in a large neighborhood around the respective voxel in a multiscale fashion. It plays the role of a morphological signature for each voxel, and our goal is, therefore, to make it distinctive of the respective voxel. Correspondence is then determined from similarities of AVs. By incorporating the prior knowledge of the spatial relationship among voxels, the ability of the proposed algorithm to find anatomical correspondence is further improved. Experiments with MR images of human brains show that the algorithm performs similarly to experts, even for complex cortical structures. <s> BIB004 </s> Deformable Medical Image Registration: A Survey <s> C. Miscellaneous <s> This paper presents a learning-based method for deformable registration of magnetic resonance (MR) brain images. There are two novelties in the proposed registration method. First, a set of best-scale geometric features are selected for each point in the brain, in order to facilitate correspondence detection during the registration procedure. This is achieved by optimizing an energy function that requires each point to have its best-scale geometric features consistent over the corresponding points in the training samples, and at the same time distinctive from those of nearby points in the neighborhood. Second, the active points used to drive the brain registration are hierarchically selected during the registration procedure, based on their saliency and consistency measures. That is, the image points with salient and consistent features (across different individuals) are considered for the initial registration of two images, while other less salient and consistent points join the registration procedure later. By incorporating these two novel strategies into the framework of the HAMMER registration algorithm, the registration accuracy has been improved according to the results on simulated brain data, and also visible improvement is observed particularly in the cortical regions of real brain data <s> BIB005 </s> Deformable Medical Image Registration: A Survey <s> C. Miscellaneous <s> 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. <s> BIB006 </s> Deformable Medical Image Registration: A Survey <s> C. Miscellaneous <s> Abstract Image registration (IR) aims to find a transformation between two or more images acquired under different conditions. This problem has been established as a very active research field in computer vision during the last few decades. IR has been applied to a high number of real-world problems ranging from remote sensing to medical imaging, artificial vision, and computer-aided design. Recently, there is an increasing interest on the application of the evolutionary computation paradigm to this field in order to solve the ever recurrent drawbacks of traditional image registration methods as the iterated closest point algorithm. Specially, evolutionary image registration methods have demonstrated their ability as robust approaches to the problem. Unlike classical IR methods, they show the advantage of not requiring a good initial estimation of the image alignment to proceed. In this contribution, we aim to review the state-of-the-art image registration methods that lay their foundations on evolutionary computation. Moreover, we aim to analyze the performance of some of the latter approaches when tackle a challenging real-world application in forensic anthropology, the 3D modeling of forensic objects. <s> BIB007
The continuous and discrete methods are limited regarding what objective functions and structures they can optimize. Heuristic and metaheuristic methods, on the contrary, can handle a wide range of problems and explore large solution spaces. Nevertheless, they are not able to provide any guarantee with respect to the optimality of the solution. 1) Greedy Approaches: Making at each step the locally optimal choice is an approach that has been used in image registration. This greedy strategy requires the definition of a set of plausible solutions and a score function. Being gradient free and intuitive, it was applied to tackle the problem of featuredriven image registration. The candidate sets were constructed in a multi-resolution fashion while a standard similarity measure was used. More information about the practical implementation of this strategy can be found in BIB001 , BIB003 , BIB004 - BIB005 . 2) Evolutionary Algorithms: Evolutionary algorithms have been used in medical image registration to mainly tackle linear registration BIB007 . These algorithms derive from the theory of evolution and natural selection. They start from an initial set of solutions that are ranked according to a fitness measure and a subset of them is chosen in a stochastic fashion to generate a new set of solutions. The new set of solutions is generated by adapting the current set following a nature-motivated strategy such as mutation. In BIB006 , the covariance matrix adaptation method was investigated BIB002 and found to converge slowly. For a more elaborated presentation and comparison of state-ofthe-art evolutionary methods for image registration the interested reader is referred to the work of Santamaria et al. BIB007 .