Variational methods for shape and image registrations.

Abstract

Fahmi, Rachid 1971-, "Variational methods for shape and image registrations." (2008 Thank you for your endless love, support, and sacrifices.I love you more than anything else in this world.iii ACKNOWLEDGMENTS First of all, my deepest thanks are due to Almighty God, the merciful, the compassionate for all the blessings bestowed upon me. Estimating and analysis of deformation, either rigid or non-rigid, is an active area of research in various medical imaging and computer vision applications. Its importance stems from the inherent inter-and intra-variability in biological and biomedical object shapes and from the dynamic nature of the scenes usually dealt with in computer vision research. For instance, quantifying the growth of a tumor, recognizing a person's face, tracking a facial expression, or retrieving an object inside a data base require the estimation of some sort of motion or deformation undergone by the object of interest. To solve these problems, and other similar problems, registration comes into play. This is the process of bringing into correspondences two or more data sets. Depending on the application at hand, these data sets can be for instance gray scale/color images or objects' outlines. In the latter case, one talks about shape registration while in the former case, one talks about image/volume registration. In some situations, the combinations of different types of data can be used complementarily to establish point correspondences.One of most important image analysis tools that greatly benefits from the process of registration, and which will be addressed in this dissertation, is the image segmentation.This process consists of localizing objects in images. Several challenges are encountered in image segmentation, including noise, gray scale inhomogeneities, and occlusions. To cope with such issues, the shape information is often incorporated as a statistical model into the segmentation process. Building such statistical models requires a good and accurate v shape alignment approach. In addition, segmenting anatomical structures can be accurately solved through the registration of the input data set with a predefined anatomical atlas. Furthermore, it can deal with noisy, occluded and missing or corrupted data. The classical way of solving the shape-based segmentation problems within a level set framework is by directly solving the underlying Euler-Lagrange equations using a gradient descent scheme. This is very computationally expensive given the non-linear parabolic nature of the corresponding PDE's. To overcome these difficulties, a fast algorithm is designed and implemented to solve both the two-phase and the multi-phase shape-based segmentation problem. This algorithm exploits the fact that only the sign of the level set function, not its value, is needed to evolve the segmenting interface. The integration of multiple selective shape priors and the segmentation into multiple regions has never been addressed before.Third, a new image/volume non-rigid registration approach based on scale s...

Shape analysis of the corpus callosum of autistic and normal subjects in neuroimaging.

“…Contours (e.g., [38][39][40][41][51]). Figure 11 illustrates the Procrustes distance between two shapes a and b.…”