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Active Contour Models:

Consistency, Stability, and Parameter Estimation

A Dissertation

Presented to the Faculty of the Graduate School


Yale University

in Candidacy for the Degree of

Doctor of Philosophy


Tianyun Ma

Dissertation Directors: Hemant Tagare and Drew McDermott

May 1998


Active contour models are a very appealing method in image segmentation. In the thesis, we will point out two significant problems of them and develop our solutions.

First, the external energy of an active contours is often formulated as Euclidean arc length integrals. In this thesis, we show that such formulations are biased. By this we mean that the minimum of the external energy does not occur at an image edge. In addition we also show that for certain forms of external energy the active contour is unstable -- when initialized at the location where the first variation of the energy is zero, the contour drifts away and becomes jagged. Both of these phenomena are due to the use of Euclidean arc length.

We propose a non-Euclidean arc length which eliminates this problem. This requires a reformulation of active contours where the the global external energy function is replaced by a sequence of local external energy functions and the contour evolves as an integral curve of the gradient of the local energies.

Second, all the active contour models require the user to set a smoothness parameter manually. This step has always been annoying to users. By exploiting image properties near an object boundary, we develop a principle to set the parameter to an appropriate value, and further, we develop an algorithm to set the parameter automatically and an energy functional needed by the algorithm.

With the two pieces of work, we build a system that finds the object boundary automatically given an initial position near the boundary. Finding a good initial position, or say finding a rough position of the boundary, is a tough problem by itself, which we do not get into in the thesis.

Experimental evidence is provided in support of the theoretical claims. Possible extensions of the work is also presented.

BibTeX Entry

author =  "Tianyun Ma",
title =   "Active Contour Models: Consistency, Stability, and Parameter Estimation"
school =  "Yale University",
month =   "May",
year =    "1998")

The complete text of the thesis is available as a .pdf file. (137 pages, 1.5 MB)

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