Mathematical Methods for Images and Surfaces 2011

The study of biomedical imaging and biological surfaces is a rapidly growing interdisciplinary field that has attracted considerable interest from mathematical, engineering, and medicine communities. Many research problems in this field are application oriented and thus the results have practical values but are challenging due to physical and biological constraints and the large scale nature of massive biomedical and biomolecular data. To efficiently solve these problems, advanced mathematical models and fast and efficient computational algorithms are indispensable tools. This special issue was called to address mathematical difficulties and challenges in image and surface analysis. We would like to share with the readers the recent advances in topics such as topological-gradients-based edge/contour detection, partial differential-equation-transform-based feature separation , blind multiple-source reconstruction in biolumines-cence tomography, partial-differential-equation-based cere-bral cortex reconstruction, nonlinear elasto-mammography for characterization of breast tissue properties, and protein surface characterization. We would like to thank the authors for their excellent contributions and patience that make this special issue possible. The time, effort, and valuable work of all anonymous reviewers on these papers are also very greatly acknowledged. This special issue constitutes ten papers. The paper entitled " Contour detection and completion for inpainting and segmentation based on topological gradient and fast marching algorithms " by D. Auroux et al. introduces a contour functional that is based on topological gradient and couples it with a fast marching algorithm to determine the minimal path for the purpose of generating connected contours. This offers a hybrid scheme for edge detection and contour completion. Two specific applications are considered for image processing. For image segmentation, the topological gradient is shown to be more efficient than the standard gradient approaches. For image inpainting, the hybrid scheme particularly improves the quality of the inpainted images. The paper entitled " Protein surface characterization using an invariant descriptor " by Z. Abu Deeb et al. develops a new invariant descriptor for the characterization of protein surfaces. It is suitable for various analysis tasks, such as protein functional classification and search and retrieval of protein surfaces over a large database. Its novelty is the combination of the power of residue-distance cooccurrence-based local and global surface descriptors. The proposed method not only reduces the computational complexity of matching 3D structures, but also facilitates direct comparison between protein structures of different sizes. The comparison with other methods on three protein families indicates that this method is effective. The paper entitled " Extending …