Correspondence For Statistical Analysis On Brain Structure With Skeletal Representation

Modeling, correspondence and statistical analysis for Anatomy of the human body and various parts of the brain structures have been one of the most researched areas in the medical domain. Representation of anatomic structures is the basis of successful and accurate statistical shape analysis. Nearly two decades of researches have brought various approaches for modeling such images, but each has different strengths and weaknesses. Today, there is not a well established methodology to model the shape of an organ. Meanwhile, segmentations of organ are complicated and rigid alignment are inapproate to describe local information and shape variations that specialists using to diagnose diseases. There is an increasing need for techniques to support volumetric information and to differentiate similar objects in a population. This requires computing statistics on shape.In this work, we analysed three widely used statistical shape models: Point Distribution Model(PDM), function model and skeletal model. We chose to use one of the popular skeletal model called Skeletal Representation(abbr. s-rep) that is able to model surface and internal features, and is suited to compute shape statistics. The s-rep is consisted by a Skeletal Sheet(SS) and a field of vectors point out from the SS to the boundary of an object. The main contribution and results of this thesis are as follows:① With respect to the tedious and frequent manual intervention, time consuming in the fitting process, the sensitivity to shape distrotion(e.g., bending or twisting) as well as the weaknesses in correspondence of the widely used Standard Method(abbr. STDM) to fitting s-rep for relatively simple objects, we proposed a novel unsupervised Thin Plate Spline based skeletal objects Modeling(TPSW) approach to produce stable s-rep. TPSW starts from a reference template() and a set of target objects’ described by SPherical HARMonics based Point Distribution Model(SPHARM-PDM). By Thin Plate Spline(TPS) warping of to each of the SPHARM-PDMs, a mapping function was calculated and applied to each spoke end of . Each group of deformed spokes was used to form the target s-rep for this object. Experimental results clearly show that the proposed automatic TPSW approach promises to make s-rep fitting robust for complicated objects, which allows s-rep based statistics to be available to all. The improvement in fitting and statistics is significant compared with the previous methods and in statistics compared with a state-of-the-art boundary based method.② In order to address the issues 1) depending on a mean s-rep which was very complicated to compute; 2) ignoring the spoke tips’ information; 3) needing iterative processes of translation, scaling and rotaion, a new s-rep alignment method named Skeletal Shape Alignment using Procrustes Analysis(SSAPA) was proposed. SSAPA based on a weighted spoke ends sampling algrithm and the singular value decomposition, which turns the alignment problem to be solving the motion parameters of a rigid body deformation. For each object, one one rotation is needed. Experimental results proved that the propsed SSAPA method can effectively align the s-reps of a given population. Meanwhile, please note that the SSAPA method can also be applied to align PDM-based shape models.③ In order to address the issue of the unsmooth, coarse and irregular object surface/boundary interpolated using medial-based interpolation method, a new skeletal-based interpolation method(SI) was proposed. The SI approach using the cubic Hermite spline basis functions and a quaternion-based interpolation to compute the spoke direction derivatives. Experimental results proved that the propsed SI approach gains improved continue surfaces than the medial-based method.④ Regarding to the reliability and accuracy of statistical shape analysis and related applications, a novel non-rigid alignment approach, named Skeletal Shape Correspondence via Entropy Optimization(SSCEO), for improving the shape statistics of medical image objects by generating correspondence of skeletal points. Each object’s interior is modeled by an s-rep, i.e., by a sampled, folded, 2-sided skeletal sheet with spoke vectors proceeding from the skeletal sheet to the boundary. The SSCEO approach optimizes an objective function consists of two parts of entropies: geometry entropy and regularity entropy, which were derived from Geometric Properties(GPs) and Regularity Properties(RPs) respectively. The goal of the optimization was to minimize the geometry entropy and to maximize the regularity entropy. This approach has the following four main contributions. Firstly, it borrowed the projection procedures from composite principal nested spheres technique to compute the GPs; and it calculated the RPs by a subdivision along each of the four edges that forms a quad and an interpolation to that place. Secondly, it defined the RPs to effictively measure the regularity entropy in a way without repeat and omission. The computation process was discussed and finally obtain three approximately statistically independent features: horizontal edge length, vertical edge length and normal swing. These features imply quad side lengths, areas, and inter-quad-pair volume. Thirdly, it invented a new form of s-rep in which the skeleton is divided into three parts: the up side, the down side and the fold curve. The spokes on each part are treated separately and, using spoke interpolation, are shifted along that skeleton in each training sample so as to tighten the probability distribution on those spokes’ geometric properties while sampling the object interior regularly. Finally, it proposed a new spoke sliding mechanism which allows the optimization shifting a original spoke to a new position accroding to a prior sliding criteria via an interpolation to that new position. To produce correspondence, the spoke shifting is optimized iteratively until convergence is achieved. Whereas the interpolation used in the shifting is always based on the original s-rep; the computations of GPs and RPs are always based on the shifted s-rep. Evaluation on synthetic and real world lateral ventricle and hippocampus datasets demonstrate improvement in the performance of statistics using the resulting probability distributions. This improvement is greater than that achieved by an entropy-based correspondence method on the boundary points.