On Visualizing Branched Surface: an Angle/Area Preserving Approach

Algorithms;Area-preserving flattening;Conformal mapping;Image interpolation;Interpolation;Monge-Kantorovich problem;Surface flattening;Surfaces (Technology) Analysis

Zhu, Lei ; Biomedical Engineering

University:Georgia Institute of Technology

Department:Biomedical Engineering

关键词: Algorithms;    Area-preserving flattening;    Conformal mapping;    Image interpolation;    Interpolation;    Monge-Kantorovich problem;    Surface flattening;    Surfaces (Technology) Analysis;   

Others  :  https://smartech.gatech.edu/bitstream/1853/7783/1/zhu_lei_200412_phd.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

The techniques of surface deformation and mapping are useful tools for the visualization of medical surfaces, especially for highly undulated or branched surfaces. In this thesis, two algorithmsare presented for flattened visualizations of multi-branched medical surfaces, such as vessels. The first algorithm is an angle preserving approach, which is based on conformal analysis. The mapping function is obtained by minimizing two Dirichlet functionals. On a triangulated representation of vessel surfaces, this algorithm can be implemented efficiently using a finiteelement method. The second algorithm adjusts the result from conformal mapping to produce a flattened representation of the original surface while preserving areas. It employs the theory ofoptimal mass transport via a gradient descent approach.A new class of image morphing algorithms is also considered based on the theory of optimal mass transport. The mass moving energy functional is revised by adding an intensity penalizing term, inorder to reduce the undesired "fading" effects. It is a parameter free approach. This technique has been applied on several natural and medical images to generate in-between image sequences.