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# Geodesic Active Contours and Splines

Shai Tirosh

Communication Systems Department, EPFL

Doctoral School Project

July 2002

## Introduction

Segmentation is one of the most basic steps in a vision system. Unfortunately, although human beings can perform this step in a split of a second, researchers have been trying to teach computers to do that for many years, without satisfactory success until now. Therefore, it is still a very active research field.

Segmentation is needed for many kinds of applications, like biomedical applications, which are of specific interest to this group, and in addition to home entertainment industry, robotics, security and military etc.

The segmentation process is usually done by representing the contours as image edges, which are local image features most commonly extracted from the gradient of the image. However, in this way, the result is usually fragmented, and intelligent techniques have to be applied in order to obtain a non-fragmented segmentation.

A different approach was suggested which evolves a curve from an initial segmentation guess to the actual object boundary. This approach, known as Snakes or Active Contours, suffers from the fact that it cannot handle changes in topology and sharp corners very well.

Recently, Geodesic Active Contours has been proposed. This method is based on Snakes, but uses the Level Sets methods in order to automatically handle sharp corners and changes in topology.

Strangely, although the Geodesic Active Contour model involves many very complex mathematical techniques, one of the key issues in the model is the computation of a partial differential equation, which is usually done by using divided differences – not a very complex scheme... The order of approximation in this model is not very good.

In this project we tried to use advanced approximation techniques, namely the spline representation for the equations of the Geodesic Active Contours model.

## Conclusions

Using splines we can achieve smoother solution, and avoid almost completely re-initializing the level set function into a distance map.

The time step is a little bit smaller, however, since we do not perform so many initializations the overall time is more or less the same.

Overall, it does not do any huge breakthrough in the model.

However, visualization can be improved a lot by using splines, achieving sub-pixel accuracy, and visualization of 3D functions.

Concerning the Geodesic Active Contours model in general, it is good for refining segmentation, but not so much for segmentation without a good initial guess, except for easy images.