This paper is concerned with the simulation of the partial differential equation driven evolution of a closed surface by means of an implicit representation. In most applications, the natural choice for the implicit representation is the signed distance function to the closed surface. Osher and Sethian have proposed to evolve the distance function with a Hamilton-Jacobi equation. Unfortunately the solution to this equation is not a distance function. As a consequence, the practical application of the level set method is plagued with such questions as When do we have to reinitialize the distance function? How do we reinitialize the distance function?, which reveal a disagreement between the theory and its implementation. This paper proposes an alternative to the use of Hamilton-Jacobi equations which eliminates this contradiction: in our method the implicit representation always remains a distance function by construction, and the implementation does not differ from the theory anymore. This is achieved through the introduction of a new equation. Besides its theoretical advantages, the proposed method also has several practical advantages which we demonstrate in three applications: (i) the segmentation of the human cortex surfaces from MRI images using two coupled surfaces (X. Zeng, et al., in
This paper introduces a new digital halftoning technique that uses space filling curves to generate aperiodic patterns of clustered dots. This method allows the parameterization of the size of pixel clusters. which can vary in one pixel steps. The algorithm unities, in this way, the dispersed and clustered-dot dithering techniques.
In this paper we introduce variable resolution 4‐k meshes, a powerful structure for the representation of geometric objects at multiple levels of detail. It combines most properties of other related descriptions with several advantages, such as more flexibility and greater expressive power. The main unique feature of the 4‐k mesh structure lies in its variable resolution capability, which is crucial for adaptive computation. We also give an overview of the different methods for constructing the 4‐k mesh representation, as well as the basic algorithms necessary to incorporate it in modeling and graphics applications.
In this chapter we are going to discuss the problem of image encoding and compression. We will present the classical methods for image compression based on transformation to the frequency domain (i.e. Discrete Cosine Transform) and exploiting multiresolution decomposition (i.e., the Wavelet Transform). These methods are employed respectively on the JPEG compression and JPEG 2000 compression standards.
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