B-spline Based Image Segmentation, Registration and Modeling Neuron Growth

In the field of image analysis, geometric modeling and simulation of real-world problems, spline-based methods are powerful tools to develop smooth and accurate representation of the solution. In this dissertation, we propose several methods to improve the efficiency and

accuracy of B-spline based methods for different applications such as image registration, image segmentation and modeling neuron growth. Image registration is the process of finding accurate spatial correspondence between two or more images. This field has several applications such as feature tracking and fusion of images taken at different perspectives, time frames or even modalities. Image segmentation is the process of detecting important

features from images. The image is partitioned into multiple labeled regions denoting each object of interest.

The development of a B-spline based image registration framework that can capture large scale deformations through local refinement is carried out in order to achieve higher accuracy in less computational time. We present an efficient approach for Finite Element Method (FEM)-based nonrigid image registration, in which the spatial transformation is constructed using truncated hierarchical B-splines (THB-splines). Instead of uniform subdivision, we propose an adaptive local refinement scheme to only refine the areas of large change in deformation of the image. By incorporating the key advantages of THB-spline

basis functions such as linear independence, partition of unity and reduced overlap into the FEM-based framework, we improve the matrix sparsity and computational efficiency.

The performance of the proposed method is demonstrated on 2D synthetic and medical images. We extend the algorithm to perform 3D nonrigid image registration suitable for large deformation and topology change. Control points are dynamically updated without constructing large matrices as in the finite element method. The proposed method is

demonstrated on 3D synthetic and medical images to show robustness with respect to topology change as compared to other image registration methods. In order to combine segmentation and registration in one framework, we present a novel approach for joint image segmentation and nonrigid registration using bidirectional composition to update the spatial transformation function. Unlike previous approaches,

the implicit level set function defining the segmentation contour and the spatial transformation

function are both represented using B-splines. This joint level set framework uses a variational form of an atlas-based segmentation together with large deformation based

nonrigid registration. The improvement in the description of the segmentation result using B-splines leads to better accuracy of both the image segmentation and registration process. We propose a novel automatic neuron segmentation framework using a B-spline based active

contour deformation model with hyperelastic regularization and automatic initialization. This boundary-extraction based algorithm utilizes cubic B-splines to deform active contours

to match the neuron cell surface accurately. Using adaptive local refinement, finer level deformation of the active contour is captured using THB-splines in a multiresolution manner.

By introducing hyperelastic regularization, we allow large nonlinear deformations of the active contours. Unlike other existing methods which represent neuron boundary as

piecewise constant function, we provide a more accurate and smooth representation of the neuron geometry.

Lastly, we have focused on developing realistic computational models for modeling different stages of neuron growth using phase field method. The multi-resolution phase field method utilizes THB-splines to evaluate the gradient of the phase field variable and

improve smoothness. The stages modeled include lamellipodia formation, initial neurite outgrowth, axon differentiation and dendritic branching. Neuron growth is driven by the extracellular culture medium and intracellular transport of tubulin. Through comparison with

experimental observations, we can demonstrate a good reproduction of neuron morphologies at different stages of growth and allow extension towards formation of neurite networks.