This paper presents new solutions to the following three problems in image morphing: feature specification, warp generation, and transition control. To reduce the burden of feature specification, we first adopt a computer vision technique called snakes. We next propose the use of multilevel free-form deformations (MFFD) to achieve C 2 -continuous and one-to-one warps among feature point pairs.The resulting technique, based on B-spline approximation, is simpler and faster than previous warp generation methods. Finally, we simplify the MFFD method to construct C 2 -continuous surfaces for deriving transition functions to control geometry and color blending.

This paper presents a new image morphing method using a two‐dimensional deformation technique which provides an intuitive model for a warp. The deformation technique derives aC1‐continuous and one‐to‐one warp from a set of point pairs overlaid on two images. The resulting in‐between image precisely reflects the correspondence of features specified by an animator. We also control the transition behaviour in a metamorphosis sequence by taking another deformable surface model, which is simpler and thus more efficient than the deformation technique for a warp. The proposed method separates transition control from feature interpolation and is easier to use than the previous techniques. The multigrid relaxation method is employed to solve a linear system in deriving a warp or transition rates. This method makes our image morphing technique fast enough for an interactive environment.

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We study the problems of computing two non-convex enclosing shapes with the minimum area; the L-shape and the rectilinear convex hull. Given a set of n points in the plane, we find an L-shape enclosing the points or a rectilinear convex hull of the point set with minimum area over all orientations. We show that the minimum enclosing shapes for fixed orientations change combinatorially at most O (n) times while rotating the coordinate system. Based on this, we propose efficient algorithms that compute both shapes with the minimum area over all orientations. The algorithms provide an efficient way of maintaining the set of extremal points, or the staircase, while rotating the coordinate system, and compute both minimum enclosing shapes in O (n 2 ) time and O (n) space. We also show that the time complexity of maintaining the staircase can be improved if we use more space.

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We investigate the problem of scheduling broadcasts in data delivering systems via broadcast, where a number of requests from several clients can be simultaneously satisfied by one broadcast of a server. Most of prior work has focused on minimizing the total flow time of requests. It assumes that once a request arrives, it will be held until satisfied. In this paper, we are concerned with the situation that clients may leave the system if their requests are still unsatisfied after waiting for some time, that is, each request has a deadline. The problem of maximizing the throughput, for example, the total number of satisfied requests, is developed, and there are given online algorithms achieving constant competitive ratios.

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