It is shown how a contour can be estimated from a few edge positions. The technique fits a cubic spline to edges using the position and orientations of edges (tangent slopes) and computes tangent magnitudes by a minimization based on the second derivatives. Cubic splines (piecewise third-order polynomials) are used because they are the lowest-order polynomials that can deal with inflection points. For assuring a smooth overall contour, the polynomial segments are joined such that the continuity of the first derivative is preserved and discontinuity in the second derivative is minimized. This technique can be used as an efficient means for entering and editing contours which are tied to the underlying data through the edge orientations. The time required for computing the edge orientations and the time for finding the curve parameters are linearly proportional to the number of edge fragments. The algorithm was applied to medical images, and the results are compared with the conic splines and the B-splines and the distance approximation to the cubic splines.>

Interpolation of X-ray motion pictures of the heart (cineventiculograms of the left ventricle) is complicated by the low contrast of the images and the elastic motion of the heart. Here, the problem of placing the heart boundary in each frame of the motion sequence is described by a framework for the application of knowledge in the form of diagnostically relevant models of the heart in motion. A blackboard architecture is utilized as a basis for the image interpretation. In this architecture, local features such as edges are grouped to build a complete description of the moving heart; the knowledge is organized in a hierarchy with knowledge sources (KSs) operating on different levels of the hierarchy and opportunistic problem-solving techniques are used to control the order of activation of both data-directed and goal-driven sources.>

Energy-Minimizing Active Contour Models (snakes) have recently been proposed by Kass et al. [8] as a top-down mechanism for locating features of interest in images. The Kass et al.’s algorithm involves four steps: setting up a variational integral on the continuous plane, deriving a pair of Euler equations, discretizing them, and solving the discrete equations iteratively until convergence. This algorithm suffers from a number of problems. We discuss these problems and present an algoIithm for active contours based on dynamic programming. The optimization problem is set up as a discrete multi-stage decision process and is solved by a “time-delayed” discrete dynamic programming algorithm. This formulation leads to a stable behavior for the active contours over iterations, in addition to allowing for hard constraints to be enforced on the behavior of the solution. Results of the application of the proposed algorithm to real images is presented.