A probabilistic framework is presented that enables image registration, tissue classification, and bias correction to be combined within the same generative model. A derivation of a log-likelihood objective function for the unified model is provided. The model is based on a mixture of Gaussians and is extended to incorporate a smooth intensity variation and nonlinear registration with tissue probability maps. A strategy for optimising the model parameters is described, along with the requisite partial derivatives of the objective function.

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Deformable image registration is a fundamental task in medical image processing. Among its most important applications, one may cite: i) multi-modality fusion, where information acquired by different imaging devices or protocols is fused to facilitate diagnosis and treatment planning; ii) longitudinal studies, where temporal structural or anatomical changes are investigated; and iii) population modeling and statistical atlases used to study normal anatomical variability. In this paper, we attempt to give an overview of deformable registration methods, putting emphasis on the most recent advances in the domain. Additional emphasis has been given to techniques applied to medical images. In order to study image registration methods in depth, their main components are identified and studied independently. The most recent techniques are presented in a systematic fashion. The contribution of this paper is to provide an extensive account of registration techniques in a systematic manner.

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. Index Terms—B-splines, mutual information, nonrigid image registration, optimization, subsampling. I.

Abstract—In the field of image segmentation, most level-setbased active-contour approaches take advantage of a discrete representation of the associated implicit function. We present in this paper a different formulation where the implicit function is modeled as a continuous parametric function expressed on a B-spline basis. Starting from the active-contour energy functional, we show that this formulation allows us to compute the solution as a restriction of the variational problem on the space spanned by the B-splines. As a consequence, the minimization of the functional is directly obtained in terms of the B-spline coefficients. We also show that each step of this minimization may be expressed through a convolution operation. Because the B-spline functions are separable, this convolution may in turn be performed as a sequence of simple 1-D convolutions, which yields an efficient algorithm. As a further consequence, each step of the level-set evolution may be interpreted as a filtering operation with a B-spline kernel. Such filtering induces an intrinsic smoothing in the algorithm, which can be controlled explicitly via the degree and the scale of the chosen B-spline kernel. We illustrate the behavior of this approach on simulated as well as experimental images from various fields. Index Terms—Active contours, B-spline, level-sets, segmentation, variational method.

Regularized nonrigid medical image registration algorithms usually estimate the deformation by minimizing a cost function, consisting of a similarity measure and a penalty term that discourages “unreasonable ” deformations. Conventional regularization methods enforce homogeneous smoothness properties of the deformation field; less work has been done to incorporate tissue-type-specific elasticity information. Yet ignoring the elasticity differences between tissue types can result in non-physical results, such as bone warping. Bone structures should move rigidly (locally), unlike the more elastic deformation of soft issues. Existing solutions for this problem either treat different regions of an image independently, which requires precise segmentation and incurs boundary issues; or use an empirical spatial varying “filter ” to “correct” the deformation field, which requires the knowledge of a stiffness map and departs from the cost-function formulation. We propose a new approach to incorporate tissue rigidity information into the nonrigid registration problem, by developing a space variant regularization function that encourages the local Jacobian of the deformation to be a nearly orthogonal matrix in rigid image regions, while allowing more elastic deformations elsewhere. For the case of X-ray CT data, we use a simple monotonic increasing function of the CT numbers (in HU) as a “rigidity index ” since bones typically have the highest CT numbers. Unlike segmentation-based methods, this approach is flexible enough to account for partial volume effects. Results using a B-spline deformation parameterization illustrate that the proposed approach improves registration accuracy in inhale-exhale CT scans with minimal computational penalty. Keywords: X-ray computed tomography (CT), regularization, homomorphism, orthogonal matrix, Frobenius norm 1.

Remote-Sensing Images (ARRSI); an automatic registration system built to register satellite and aerial remotely sensed images. The system is designed specifically to address the problems associated with the registration of remotely sensed images obtained at different times and/or from different sensors. The ARRSI system is capable of handling remotely sensed images geometrically distorted by various transformations such as translation, rotation, and shear. Global and local contrast issues associated with remotely sensed images are addressed in ARRSI using control-point detection and matching processes based on a phasecongruency model. Intensity-difference issues associated with multimodal registration of remotely sensed images are addressed in ARRSI through the use of features that are invariant to intensity mappings during the control-point matching process. An adaptive control-point matching scheme is employed in ARRSI to reduce the performance issues associated with the registration of large remotely sensed images. Finally, a variation on the Random Sample and Consensus algorithm called Maximum Distance Sample Consensus is introduced in ARRSI to improve the accuracy of the transformation model between two remotely sensed images while minimizing computational overhead. The ARRSI system has been tested using various satellite and aerial remotely sensed images and evaluated based on its accuracy and computational performance. The results indicate that the registration accuracy of ARRSI is comparable to that produced by a human expert and improvement over the baseline and multimodal sum of squared differences registration techniques tested. Index Terms—Image registration, intersensor, intrasensor, invariant descriptor, remote sensing.

This dissertation investigated how three-dimensional (3D) tissue models can be used to improve ultrasonic tissue characterization (UTC) techniques. Anatomic sites in tissue responsible for ultrasonic scattering are unknown, which limits the potential applications of ultrasound for tumor diagnosis. Accurate 3D models of tumor tissues may help identify the scattering sites. Three mammary tumors were investigated: a rat fibroadenoma, a mouse carcinoma, and a mouse sarcoma. A 3D acoustic tissue model, termed 3D impedance map (3DZM), was carefully constructed from consecutive histologic sections for each tumor. Spectral estimates (scatterer size and acoustic concentration) were obtained from the 3DZMs and compared to the same estimates obtained with ultrasound. Scatterer size estimates for three tumors were found to be similar (within 10%). The 3DZMs were also used to extract tissue-specific scattering models. The scattering models were found to allow clear distinction between the three tumors. This distinction demonstrated that UTC techniques may be helpful for noninvasive clinical tumor diagnosis.