Flux-based Curvilinear Structure Analysis

The Hong Kong University of Science and Technology
Department of Computer Science and Engineering


PhD Thesis Defence


Title: "Flux-based Curvilinear Structure Analysis"

By

Mr. Jierong WANG


Abstract

The curvilinear structure is a vital clue in many vessel diseases. During 
curvilinear structure analysis, high-level information such as eccentricity, 
scale, structural orientation, and abnormality can be collected for disease 
diagnosis and pathology quantification. Among a wide range of techniques for 
curvilinear structure analysis, linear descriptors based on various assumptions 
and prior knowledge of the target structures have been drawing attention for 
decades.

In this thesis, we improve the flux-based curvilinear analysis in various 
aspects. The first two proposed methods focus on the higher-order extension. 
The typical derivative operators, including the oriented flux, are based on the 
eigen-analysis of order-2 tensors. We provide two distinct ideas to construct 
the higher-order tensor from the oriented flux. In the first method, we first 
define a novel variant of cross-sectional flux using an adaptive oriented 
cylinder model. With the help of the cylindrical model, the simulation of the 
HARDI diffusion signal under various directions can be more straightforward. A 
4D higher-order Cartesian tensor construction and decomposition framework are 
employed to evaluate the angular coherence of the vessels. On the contrary, we 
improve the efficiency of the higher-order analysis with the help of spherical 
harmonics transform. The diffusion signal is simulated with the oriented flux 
response, which is assisted by a gradient antisymmetry measurement, in a manual 
cylinder extension. Then, the higher-order tensor is implicitly constructed in 
the frequency domain by solving the spherical harmonics coefficients. The final 
vesselness is measured by the fiber orientation distribution function. In 
conclusion, in the first method we present a higher-order tensor framework in 
the spatial domain and simulate the diffusion signal with a novel cylindrical 
flux, while in our second proposal the higher-order tensor analysis is purely 
performed in the frequency domain and the signal simulation is carried out in a 
manual cylinder extension to include the projections.

The third method improves the oriented flux itself with respect to eccentricity 
and orientation. With the assumption of an elliptical cross-section of the 
curvilinear structure, the semi-minor axis is sought by projecting the 3D 
oriented flux onto a 2D sub-plane, resulting in lower computation load and 
higher accuracy compared to other elliptical models. We then accumulate the 
flux responses during the construction of the higher-order Markov tree based on 
the orientation coherence. While the first three proposed methods concentrate 
on the improvement of the low-level descriptors, the last presented method 
contributes to the graphical framework.  Concretely, in our fourth work, the 
random walks framework is improved by a modified Forman's curvature function, 
which is modeled in sub-pixel resolution and can capture details in a higher 
order.


Date:			Wednesday, 18 May 2022

Time:			2:00pm - 4:00pm

Zoom Meeting: 
https://hkust.zoom.us/j/98669697382?pwd=N3lmbmJQbnljVjhYbWQ5Vk1yU0xmdz09

Chairperson:		Prof. Anthony LEUNG (CIVL)

Committee Members:	Prof. Albert CHUNG (Supervisor)
 			Prof. Chi Keung TANG (Supervisor)
 			Prof. Huamin QU
 			Prof. Nevin ZHANG
 			Prof. Shing Yu LEUNG (MATH)
 			Prof. Lin SHI (CUHK)


**** ALL are Welcome ****