Line-to-Point Registration with Applications in Geometric Reconstruction of Coronary Stents Open Access

Abstract

Registration is a process of geometrically transforming one object to correspond to the other. It can utilized to align images, surfaces, or point clouds. The Iterative Closest Point algorithm is widely used in registration to achieve reconstruction of geometric shapes, but has drawbacks such as non-differentiability. This thesis introduces a line-to-point registration method, useful in imposing a skeletal structure, defined by nodes and edges, on a given set of points in 2D or 3D. This method computes the distance from a point cloud to a skeletal structure using projections, and uses rigid, affine, and nonparametric transformations for distance minimization, taking into account regularization on the nonparametric transformation. The proposed approach can be utilized in the registration of two geometric objects, where one has a known structural skeleton, and the other is a point set. In this thesis, this method is used to achieve correspondence between the undeformed and deformed configurations of a coronary prosthesis, called a bioresorbable stent. The undeformed configuration is represented by a skeleton of the prosthesis based on the manufacturer's design, and the deformed configuration is represented by a set of points obtained from medical images. Registration is used to automatize the geometric reconstruction of implanted coronary stents in patient-specific cases, to allow Computational Fluid Dynamics (CFD) analysis in the clinical trials at Emory University.

Table of Contents

1 Introduction. 1

1.1 Motivation. 2

1.2 Related Work. 3

1.3 Contribution. 4

1.4 Outline. 5

2 Iterative Closest Point. 6

2.1 The ICP Algorithm. 6

2.2 ICP vs. Line-to-Point, 7

3 Line-to-Point Registration. 10

3.1 Template. 10

3.2 Objective Function. 11

3.2.1 Projection. 12

3.2.2 Transformations. 14

3.2.3 Distance Measure. 17

3.2.4 Regularization. 18

3.3 Numerical Optimization. 21

4 Numerical Experiments. 22

4.1 3D Case Step-by-Step Demonstration. 22

4.2 Supplementary Procedures. 24

4.2.1 Data Selection and Denoising. 24

4.2.2 Correction of Rotation. 25

4.3 Semi-Automatic 3D Registration of a Coronary Stent. 27

5 Conclusions. 28

5.1 Current Work. 28

5.2 Future Directions. 28

References. 30

Symbols and Abbreviations. 32

About this Honors Thesis

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School	Emory College
Department	Mathematics and Computer Science
Degree	BS
Submission	Honors Thesis
Language	English
Research Field	Applied Mathematics
Keyword	Inverse Problems Registration Methods Geometric Reconstruction
Committee Chair / Thesis Advisor	Ruthotto, Lars , Emory University
Committee Members	Piccinelli, Marina , Emory University Veneziani, Alessandro, Emory University Nagy, James, Emory University

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