Date of Award

2013

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Applied Mathematics

First Advisor

James C. Gee

Abstract

Multi-scale representation and local scale extraction of images are important in computer vision research, as in general , structures within images are unknown. Traditionally, the multi-scale analysis is based on the linear diusion (i.e. heat diusion) with known limitation in edge distortions. In addition, the term scale which is used

widely in multi-scale and local scale analysis does not have a consistent denition and it can pose potential diculties in real image analysis, especially for the proper interpretation of scale as a geometric measure. In this study, in order to overcome

limitations of linear diusion, we focus on the multi-scale analysis based on total variation minimization model. This model has been used in image denoising with the power that it can preserve edge structures. Based on the total variation model, we construct the multi-scale space and propose a denition for image local scale. The

new denition of local scale incorporates both pixel-wise and orientation information.

This denition can be interpreted with a clear geometrical meaning and applied in general image analysis. The potential applications of total variation model in retinal fundus image analysis is explored. The existence of blood vessel and drusen structures within a single fundus image makes the image analysis a challenging problem.

A multi-scale model based on total variation is used, showing the capabilities in both drusen and blood vessel detections. The performance of vessel detection is compared with publicly available methods, showing the improvements both quantitatively and

qualitatively. This study provides a better insight into local scale study and shows the potentials of total variation model in medical image analysis.

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