VRL an eye

Variational Image Segmentation using Boundary Functionals


G. Hewer, C. Kenney, B.S.Manjunath


A general variation framework for image approximation and segmentation is introduced. By using a continuous ``line-process'' to represent edge boundaries, it is possible to formulate a variation theory of image segmentation and approximation in which the boundary function has a simple explicit form in terms of the approximation function. At the same time, this variation framework is general enough to include the most commonly used objective functions. Application is made to Mumford-Shah type functional as well as those considered by Geman and others. Employing arbitrary $L_p$ norms to measure smoothness and approximation allows the user to alternate between a least squares approach and one based on total variation, depending on the needs of a particular image. Since the optimal boundary function, that minimizes the associated objective functional for a given approximation function, can be found explicitly, the objective functional can be expressed in a reduced form that depends only on the approximating function. From this a partial differential equation (PDE) descent method, aimed at minimizing the objective functional, is derived. The method is fast and produces excellent results as illustrated by a number of real and synthetic image problems.


The following figure present results on a face image. The approximation functions $u$ in the figures appear much like an artists' sketch. This simplification means that the approximations are more suitable for face feature extraction than the original images. We are currently using the approximation and boundary information in our work on face image tracking.

(a) original (b) approximation (c) boundary function

An example of segmenting out kidney X-ray CT images is shown below. The proposed segmentation approach is used in identifying regions containing kidneys in these CT studies and to localize problems such as a cyst. Combined with simple domain specific heuristics, this approach provides a robust classification algorithm which is currenly being incorporated into the development of a medical image database system.

(a) original (b) approximation (c) boundary function


These materials are presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each authors copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder. G. A. Hewer, C.Kenney and B. S.Manjunath, " Variational image segmentation using boundary functions," IEEE Transactions on Image Processing, vol.7, (no.9), pp.1269-82, Sep 1998. [abstract] G. Hewer, C. Kenney, and B. S. Manjunath, "Image segmentation via functionals based on boundary functions," Proc. Third IEEE international conference on Image processing, ICIP 96, Vol. I, pp. 813-816, Lausanne, Switzerland, Sep 1996. [abstract] "Variational Image Segmentation using Boundary Functions", ECE Technical Report #9607, May 1996. (report figures)