Global optimization algorithms for image registration and clustering

Global optimization is a classical problem of finding the minimum or maximum value of an objective function. It has applications in many areas, such as biological image analysis, chemistry, mechanical engineering, financial analysis, deep learning and image processing. For practical applications, it is important to understand the efficiency of global optimization algorithms. This dissertation develops and analyzes some new global optimization algorithms and applies them to practical problems, mainly for image registration and data clustering. First, the dissertation presents a new global optimization algorithm which approximates the optimum using only function values. The basic idea is to use the points at which the function has been evaluated to decompose the domain into a collection of hyper-rectangles. At each step of the algorithm, it chooses a hyper-rectangle according to a certain criterion and the next function evaluation is at the center of the hyper-rectangle. The dissertation includes a proof that the algorithm converges to the global optimum as the number of function evaluations goes to infinity, and also establishes the convergence rate. Standard test functions are used to experimentally evaluate the algorithm. The second part focuses on applying algorithms from the first part to solve some practical problems. Image processing tasks often require optimizing over some set of parameters. In the image registration problem, one attempts to determine the best transformation for aligning similar images. Such problems typically require minimizing a dissimilarity measure with multiple local minima. The dissertation describes a global optimization algorithm and applies it to the problem of identifying the best transformation for aligning two images. Global optimization algorithms can also be applied to the data clustering problem. The basic purpose of clustering is to categorize data into different groups by their similarity. The objective cost functions for clustering usually are non-convex. $k$-means is a popular algorithm which can find local optima quickly but may not obtain global optima. The different starting points for $k$-means can output different local optima. This dissertation describes a global optimization algorithm for approximating the global minimum of the clustering problem. The third part of the dissertation presents variations of the proposed algorithm that work with different assumptions on the available information, including a version that uses derivatives

Adaptive Stochastic Conjugate Gradient optimization for temporal medical image registration

We propose an Adaptive Stochastic Conjugate Gradient (ASCG) optimization algorithm for temporal medical image registration. This method combines the advantages of Conjugate Gradient (CG) method and Adaptive Stochastic Gradient Descent (ASGD) method. The main idea is that the search direction of ASGD is replaced by stochastic approximations of the conjugate gradient of the cost function. In addition, the step size of ASCG is based on the approximation of the Lipschitz constant of the stochastic gradient function. Thus, this algorithm could maintain the good properties of the conjugate gradient method, meanwhile it uses less gradient computation time per iteration and adjusts the step size adaptively as the ASGD method. As a result, this algorithm takes less CPU time than the previous ASGD method. We demonstrate the efficiency of our algorithm on the public available 4D Lung CT data and our clinical Lung/Tumor CT data using the general 4D image registration model. We compare the ASCG with several existing iterative optimization strategies: steepest gradient descent method, conjugate gradient method, Quasi-Newton method (LBFGS) and adaptive stochastic gradient descent method. Our preliminary results indicate that our ASCG algorithm achieves 22% higher accuracy on the POPI dataset and it also performs better than existing methods on other datasets(DIR-Lab dataset and our clinical dataset). Furthermore, we demonstrate that compared with other methods, our ASCG algorithm is more robust to image noises

Retrospective study on phantom for the application of medical image registration in the operating room scenario

This paper presents a phantom study to asses the feasibility of the medical image registration algorithms in the operating room (OR) scenario. The main issues of the registration algorithms in an OR application are, on one hand, the lack of the initial guess of the registration transformation - the images to be registered may be completely independentand, on the other hand, the multimodality of the data. Other requirements to be addressed by the OR registration algorithms are: real-time execution and the necessity of the validation of the results. This work analyzes how, under these requirements, the current state of the art algorithms in medical image registration may be used and shows which direction should be taken when designing a OR navigation system that includes registration as a component

Interactive Medical Image Registration With Multigrid Methods and Bounded Biharmonic Functions

Interactive image registration is important in some medical applications since automatic image registration is often slow and sometimes error-prone. We consider interactive registration methods that incorporate user-specified local transforms around control handles. The deformation between handles is interpolated by some smooth functions, minimizing some variational energies. Besides smoothness, we expect the impact of a control handle to be local. Therefore we choose bounded biharmonic weight functions to blend local transforms, a cutting-edge technique in computer graphics. However, medical images are usually huge, and this technique takes a lot of time that makes itself impracticable for interactive image registration. To expedite this process, we use a multigrid active set method to solve bounded biharmonic functions (BBF). The multigrid approach is for two scenarios, refining the active set from coarse to fine resolutions, and solving the linear systems constrained by working active sets. We\u27ve implemented both weighted Jacobi method and successive over-relaxation (SOR) in the multigrid solver. Since the problem has box constraints, we cannot directly use regular updates in Jacobi and SOR methods. Instead, we choose a descent step size and clamp the update to satisfy the box constraints. We explore the ways to choose step sizes and discuss their relation to the spectral radii of the iteration matrices. The relaxation factors, which are closely related to step sizes, are estimated by analyzing the eigenvalues of the bilaplacian matrices. We give a proof about the termination of our algorithm and provide some theoretical error bounds. Another minor problem we address is to register big images on GPU with limited memory. We\u27ve implemented an image registration algorithm with virtual image slices on GPU. An image slice is treated similarly to a page in virtual memory. We execute a wavefront of subtasks together to reduce the number of data transfers. Our main contribution is a fast multigrid method for interactive medical image registration that uses bounded biharmonic functions to blend local transforms. We report a novel multigrid approach to refine active set quickly and use clamped updates based on weighted Jacobi and SOR. This multigrid method can be used to efficiently solve other quadratic programs that have active sets distributed over continuous regions

Development Of A High Performance Mosaicing And Super-Resolution Algorithm

In this dissertation, a high-performance mosaicing and super-resolution algorithm is described. The scale invariant feature transform (SIFT)-based mosaicing algorithm builds an initial mosaic which is iteratively updated by the robust super resolution algorithm to achieve the final high-resolution mosaic. Two different types of datasets are used for testing: high altitude balloon data and unmanned aerial vehicle data. To evaluate our algorithm, five performance metrics are employed: mean square error, peak signal to noise ratio, singular value decomposition, slope of reciprocal singular value curve, and cumulative probability of blur detection. Extensive testing shows that the proposed algorithm is effective in improving the captured aerial data and the performance metrics are accurate in quantifying the evaluation of the algorithm

Multimodal Elastic Matching of Brain Images

This paper presents an original method for three-dimensional elastic registration of multimodal images. We propose to make use of a scheme that iterates between correcting for intensity di#erences between images and performing standard monomodal registration. The core of our contribution resides in providing a method that finds the transformation that maps the intensities of one image to those of another. It makes the assumption that there are at most two functional dependences between the intensities of structures present in the images to register, and relies on robust estimation techniques to evaluate these functions. We provide results showing successful registration between several imaging modalities involving segmentations, T1 magnetic resonance (MR), T2 MR, proton density (PD) MR and computed tomography (CT)

Investigation of Intensity Correction in the Context of Image Registration

An image registration algorithm with intensity correction was developed. A particular goal was to apply intensity correction instead of using multimodal similarity measures. The algorithm utilises common Levenberg-Marquardt optimisation. The author has chosen two dimensional affine and one dimensional B-Spline model as spatial transformation, as well as intensity correction models specific to CT images. They are global non-linear mapping and smooth local affine correction. The algorithm was tested experimentally using a wide class of simulated images and a limited class of medical images. Affine registration works properly even for deformations which exceed typical deformation encountered in medical practice. B-Spline registration works properly for small deformations and requires further development to increase capture range. The idea of separating intensity correction mapping from similarity measure is shown to have advantages. Choosing intensity correction model can make the registration algorithm specific to the image class of interest