Convex Optimisation for Inverse Kinematics

We consider the problem of inverse kinematics (IK), where one wants to find the parameters of a given kinematic skeleton that best explain a set of observed 3D joint locations. The kinematic skeleton has a tree structure, where each node is a joint that has an associated geometric transformation that is propagated to all its child nodes. The IK problem has various applications in vision and graphics, for example for tracking or reconstructing articulated objects, such as human hands or bodies. Most commonly, the IK problem is tackled using local optimisation methods. A major downside of these approaches is that, due to the non-convex nature of the problem, such methods are prone to converge to unwanted local optima and therefore require a good initialisation. In this paper we propose a convex optimisation approach for the IK problem based on semidefinite programming, which admits a polynomial-time algorithm that globally solves (a relaxation of) the IK problem. Experimentally, we demonstrate that the proposed method significantly outperforms local optimisation methods using different real-world skeletons

간 조영술을 위한 혈관 모델 기반의 국부 적응 2D-3D 정합 알고리즘 기법 연구

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2017. 2. 신영길.Two-dimensional–three-dimensional (2D–3D) registration between intra-operative 2D digital subtraction angiography (DSA) and pre-operative 3D computed tomography angiography (CTA) can be used for roadmapping purposes. However, through the projection of 3D vessels, incorrect intersections and overlaps between vessels are produced because of the complex vascular structure, which make it difficult to obtain the correct solution of 2D–3D registration. To overcome these problems, we propose a registration method that selects a suitable part of a 3D vascular structure for a given DSA image and finds the optimized solution to the partial 3D structure. The proposed algorithm can reduce the registration errors because it restricts the range of the 3D vascular structure for the registration by using only the relevant 3D vessels with the given DSA. To search for the appropriate 3D partial structure, we first construct a tree model of the 3D vascular structure and divide it into several subtrees in accordance with the connectivity. Then, the best matched subtree with the given DSA image is selected using the results from the coarse registration between each subtree and the vessels in the DSA image. Finally, a fine registration is conducted to minimize the difference between the selected subtree and the vessels of the DSA image. In experimental results obtained using 10 clinical datasets, the average distance errors in the case of the proposed method were 2.34 ± 1.94 mm. The proposed algorithm converges faster and produces more correct results than the conventional method in evaluations on patient datasets.Chapter 1 Introduction 1 1.1 Background 1 1.2 Problem statement 6 1.3 Main contributions 8 1.4 Contents organization 10 Chapter 2 Related Works 12 2.1 Overview 12 2.1.1 Definitions 14 2.1.2 Intensity-based and feature-based registration 17 2.2 Neurovascular applications 19 2.3 Liver applications 22 2.4 Cardiac applications 27 2.4.1 Rigid registration 27 2.4.2 Non-rigid registration 31 Chapter 3 3D Vascular Structure Model 33 3.1 Vessel segmentation 34 3.1.1 Overview 34 3.1.2 Vesselness filter 36 3.1.3 Vessel segmentation 39 3.2 Skeleton extraction 40 3.2.1 Overview 40 3.2.2 Skeleton extraction based on fast marching method 41 3.3 Graph construction 45 3.4 Generation of subtree structures from 3D tree model 46 Chapter 4 Locally Adaptive Registration 52 4.1 2D centerline extraction 53 4.1.1 Extraction from a single DSA image 54 4.1.2 Extraction from angiographic image sequence 55 4.2 Coarse registration for the detection of the best matched subtree 58 4.3 Fine registration with selected 3D subtree 61 Chapter 5 Experimental Results 63 5.1 Materials 63 5.2 Phantom study 65 5.3 Performance evaluation 69 5.3.1 Evaluation for a single DSA image 69 5.3.2 Evaluation for angiographic image sequence 75 5.4 Comparison with other methods 77 5.5 Parameter study 87 Chapter 6 Conclusion 90 Bibliography 92 초록 109Docto