Isophotes Selection and Reaction-Diffusion Model for Object Boundaries Estimation

• Authors: Charles Kervrann;Mark Hoebeke;Alain Trubuil
• Venue: International Journal of Computer Vision
• Year: 2002

This paper investigates generic region-based segmentation schemes using area-minimization constraint and background modeling, and develops a computationally efficient framework based on level lines selection coupled with biased anisotropic diffusion. A common approach to image segmentation is to construct a cost function whose minima yield the segmented image. This is generally achieved by competition of two terms in the cost function, one that punishes deviations from the original image and another that acts as a regularization term. We propose a variational framework for characterizing global minimizers of a particular segmentation energy that can generates irregular object boundaries in image segmentation. Our motivation comes from the observation that energy functionals are traditionally complex, for which it is usually difficult to precise global minimizers corresponding to “best” segmentations. In this paper, we prove that the set of curves that minimizes the basic energy model under concern is a subset of level lines or isophotes, i.e. the boundaries of image level sets. The connections of our approach with region-growing techniques, snakes and geodesic active contours are also discussed. Moreover, it is absolutely necessary to regularize isophotes delimiting object boundaries and to determine piecewise smooth or constant approximations of the image data inside the objects boundaries for vizualization and pattern recognition purposes. Thus, we have constructed a reaction-diffusion process based on the Perona-Malik anisotropic diffusion equation. In particular, a reaction term has been added to force the solution to remain close to the data inside object boundaries and to be constant in non-informative regions, that is the background region. In the overall approach, diffusion requires the design of the background and foreground regions obtained by segmentation, and segmentation of the adaptively smoothed image is performed after each iteration of the diffusion process. From an application point of view, the sound initialization-free algorithm is shown to perform well in a variety of imaging contexts with variable texture, noise and lighting conditions, including optical imaging, medical imaging and meteorological imaging. Depending on the context, it yields either a reliable segmentation or a good pre-segmentation that can be used as initialization for more sophisticated, application-dependent segmentation models.