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Abstract: Fuzzy connectedness (FC) constitutes an important class of image segmentation schemas. Although affinity functions represent the core aspect (main variability parameter) of FC algorithms, they have not been studied systematically in the literature. In this paper, we began filling this gap by introducing and studying the notion of equivalent affinities: if any two equivalent affinities are used in the same FC schema to produce two versions of the algorithm, then these algorithms are equivalent in the sense that they lead to identical segmentations. We give a complete and elegant characterization of the affinity equivalence. We also demonstrate that any segmentation obtained via a relative fuzzy connectedness (RFC) algorithm can be viewed as segmentation obtained via absolute fuzzy connectedness (AFC) algorithm with an automatic and adaptive threshold detection. Since the main goal of the paper is to identify, by formal mathematical arguments, the affinity functions that are equivalent, extensive experimental confirmations are not needed — they show completely identical segmentations — and as such, only relevant examples of the theoretical results are provided. [Copyright &y& Elsevier]

A new linear-time algorithm is presented in this paper that simultaneously labels connected components (to be referred to merely as components in this paper) and their contours in binary images. The main step of this algorithm is to use a contour tracing technique to detect the external contour and possible internal contours of each component, and also to identify and label the interior area of each component. Labeling is done in a single pass over the image, while contour points are revisited more than once, but no more than a constant number of times. Moreover, no re-labeling is required throughout the entire process, as it is required by other algorithms. Experimentation on various types of images (characters, half-tone pictures, photographs, newspaper, etc.) shows that our method outperforms methods that use the equivalence technique. Our algorithm not only labels components but also extracts component contours and sequential orders of contour points, which can be useful for many applications. [Copyright &y& Elsevier]

Algorithms for geometric matching and feature extraction that work by recursively subdividing transformation space and bounding the quality of match have been proposed in a number of different contexts and become increasingly popular over the last few years. This paper describes matchlist-based branch-and-bound techniques and presents a number of new applications of branch-and-bound methods, among them, a method for globally optimal partial line segment matching under bounded or Gaussian error, point matching under a Gaussian error model with subpixel accuracy and precise orientation models, and a simple and robust technique for finding multiple distinct object instances. It also contains extensive reference information for the implementation of such matching methods under a wide variety of error bounds and transformations. In addition, the paper contains a number of benchmarks and evaluations that provide new information about the runtime behavior of branch-and-bound matching algorithms in general, and that help choose among different implementation strategies, such as the use of point location data structures and space/time tradeoffs involving depth-first search. [Copyright &y& Elsevier]

This paper designs an object-oriented, continuous-time, full simulation model for addressing a wide range of clinical, procedural, administrative, and financial decisions in health care at a high level of biological, clinical, and administrative detail. The full model has two main parts, which with some simplification can be designated “physiology models” and “models of care processes.” The models of care processes, although highly detailed, are mathematically straightforward. However, the mathematics that describes human biology, diseases, and the effects of interventions are more difficult. This paper describes the mathematical formulation and methods for deriving equations, for a variety of different sources of data. Although Archimedes was originally designed for health care applications, the formulation, and equations are general and can be applied to many natural systems. [Copyright &y& Elsevier]

This paper presents a new model for image blending based on warping. The model is represented by partial differential equations (PDEs) and gives a sequence of images, which has the properties of both blending of image intensities and warping of image shapes. We modified the energy functional in [W.-H. Liao, A. Khuu, M. Bergsneider, L. Vese, S.-C. Huang, S. Osher, From Landmark Matching to Shape and Open Curve Matching: A Level Set Approach, Computational and Applied Mathematics (CAM) Technical Reports 02-59, UCLA, 2002.] in order to adapt the idea of the shape warping to the image blending. The PDEs from the proposed energy functional cover not only overlapped images but also non-overlapped ones. [Copyright &y& Elsevier]

Abstract: This paper describes a variational method with active curve evolution and level sets for the estimation, segmentation, and 3D interpretation of optical flow generated by independently moving rigid objects in space. Estimation, segmentation, and 3D interpretation are performed jointly. Segmentation is based on an estimate of optical flow consistent with a single rigid motion in each segmentation region. The method, which allows both viewing system and viewed objects to move, results in three steps iterated until convergence: (a) evolution of closed curves via level sets and, in each region of the segmentation, (b) linear least squares computation of the essential parameters of rigid motion, (c) estimation of optical flow consistent with a single rigid motion. The translational and rotational components of rigid motion and regularized relative depth are recovered analytically for each region of the segmentation from the estimated essential parameters and optical flow. Several examples with real image sequences are provided which verify the validity of the method. [Copyright &y& Elsevier]

Abstract: To microarray expression data analysis, it is well accepted that biological knowledge-guided clustering techniques show more advantages than pure mathematical techniques. In this paper, Gene Ontology is introduced to guide the clustering process, and thus a new algorithm capturing both expression pattern similarities and biological function similarities is developed. Our algorithm was validated on two well-known public data sets and the results were compared with some previous works. It is shown that our method has advantages in both the quality of clusters and the precision of biological annotations. Furthermore, the clustering results can be adjusted according to different stringency requirements. It is expected that our algorithm can be extended to other biological knowledge, for example, metabolic networks. [Copyright &y& Elsevier]

We present a novel “dynamic learning” approach for an intelligent image database system to automatically improve object segmentation and labeling without user intervention, as new examples become available, for object-based indexing. The proposed approach is an extension of our earlier work on “learning by example,” which addressed labeling of similar objects in a set of database images based on a single example. The proposed dynamic learning procedure utilizes multiple example object templates to improve the accuracy of existing object segmentations and labels. Multiple example templates may be images of the same object from different viewing angles, or images of related objects. This paper also introduces a new shape similarity metric called normalized area of symmetric differences (NASD), which has desired properties for use in the proposed “dynamic learning” scheme, and is more robust against boundary noise that results from automatic image segmentation. Performance of the dynamic learning procedures has been demonstrated by experimental results. [Copyright &y& Elsevier]

The non-rigid registration of surfaces is a complex and difficult task for which there are many important applications, such as comparing shape between deformable objects and comparing associated function. This paper presents a new approach for brain surface matching by determining the correspondence of 3D point sets between pairs of surfaces. The algorithm is based on shape using a combination of geodesic distance and surface curvature. There are two major procedures involved. An initial sparse set of corresponding points is first generated by matching local geometrical features. Geodesic distance interpolation is then employed hierarchically in order to capture the complex surface. By this scheme, surface correspondence and triangulation are computed simultaneously. Experiments applied to human cerebral cortical surfaces are shown to evaluate the approach. It is shown that the proposed method performs well for both surface matching and surface shape recovery. [Copyright &y& Elsevier]