Robust Image Segmentation using Active Contours: Level Set Approaches

Abstract

Image segmentation is a fundamental task in image analysis responsible for partitioning an image into multiple sub-regions based on a desired feature. Active contours have been widely used as attractive image segmentation methods because they always produce sub-regions with continuous boundaries, while the kernel-based edge detection methods, e.g. Sobel edge detectors, often produce discontinuous boundaries. The use of level set theory has provided more flexibility and convenience in the implementation of active contours. However, traditional edge-based active contour models have been applicable to only relatively simple images whose sub-regions are uniform without internal edges.

A partial solution to the problem of internal edges is to partition an image based on the statistical information of image intensity measured within sub-regions instead of looking for edges. Although representing an image as a piecewise-constant or unimodal probability density functions produces better results than traditional edge-based methods, the performances of such methods is still poor on images with sub-regions consisting of multiple components, e.g. a zebra on the field. The segmentation of this kind of multispectral images is even a more difficult problem. The object of this work is to develop advanced segmentation methods which provide robust performance on the images with non-uniform sub-regions.

In this work, we propose a framework for image segmentation which partitions an image based on the statistics of image intensity where the statistical information is represented as a mixture of probability density functions defined in a multi-dimensional image intensity space. Depending on the method to estimate the mixture density functions, three active contour models are proposed: unsupervised multi-dimensional histogram method, half-supervised multivariate Gaussian mixture density method, and supervised multivariate Gaussian mixture density method. The implementation of active contours is done using level sets.

The proposed active contour models show robust segmentation capabilities on images where traditional segmentation methods show poor performance. Also, the proposed methods provide a means of autonomous pattern classification by integrating image segmentation and statistical pattern classification.