A New Active Convex Hull Model for Image Regions

This paper presents a new active convex hull model with the following advantages: invariant with respect to the number of pixels to be enveloped; the number of time iterations is invariant, with respect to the image size; time-cheap for large image regions. The model is based on the geometric heat differential equations, derived from parabolic equation, and parameterized by arc length. To prevent the active contour from intruding into concavities and evolve it to the proper convex hull we use a vector field given as a difference between normal and tangent forces. The vector field is also used to segment an image to shells, such that a single region is present in each shell. A penalty function is developed to stop evolvement of those arc segments, whose vectors encountered boundary points of an image region. Based on the model a discrete algorithm is designed and coded by Mathematica 5.2. A condition is developed, with respect to the image size, to guarantee stable convergence of the active contour to the convex hull of the desired region. To validate the advantages and contributions a set of experiments is performed using synthetic, groundwater and medical images of different size and modalities. The paper concludes with a discussion and comparison of the active convex hull model with set of existing convex hull algorithms. Nikolay M. Sirakov received B.S. degree from School of Mathematics and Informatics-Sofia University in 1982, M.S. degree from the same University in the field of Coding Theory in 1983, and Ph.D. degree from Institute of Mechanics-Bulgarian Academy of Sciences in the field of 3D modeling and recognition in 1991. He had research and teaching positions at the Institute of Mechanics (1984–2000—Associate Professor since 1999), International Lab of Artificial Intelligence-Slovak Academy of Sciences (1990), Instituto Superior Technico–CVRM-Portugal (1993, 1998–2000), and Northern Arizona University (2001–2004). Currently Dr. Sirakov is an Assistant Professor of Mathematics and Computer Science at Texas A&M University Commerce. His research interests fall in Active Contours/Surfaces Models to image segmentation and features extraction, 3D reconstruction and visualization, 2D/3D objects matching and classification, Image Processing and Analysis, and Content Based Image Retrieval. He published over seventy papers and was a co-author of two books in the above listed fields.