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The Global ETD Search service is a free service for researchers
to find electronic theses and dissertations. This service is
provided by the
Networked Digital Library of Theses and Dissertations.
Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
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On Visualizing Branched Surface: an Angle/Area Preserving ApproachZhu, Lei 12 September 2004 (has links)
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 algorithms
are 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 finite
element 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 of
optimal 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, in
order 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.
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