| Image interpolation and discrete surface smoothing are fundamental operations in computer graphics and image processing. Image interpolation can be used to improve the quality of an image and noise removing for a discrete surface will help to smooth the surface. Moreover, discrete surface smoothing will improve the efficiency of many other operations for digital geometry processing. In this thesis, we propose new algorithms for image interpolation and discrete surface smoothing:1. A subdivision approach to image interpolation.2. Shrinkage free mesh and point surface smoothing with feature preservation. We propose a novel method for image interpolation by extending normal basedsubdivision scheme for curve and surface design. Images will be zoomed in by interpolatory subdivision and no intermediate continuous surface model should be established. With proper choices of the subdivision parameters, images can be interpolated with any positive real scale while edges and borders within images can be kept well. Examples and comparisons with some other image interpolation methods show that the advantages of the new image interpolation algorithm lie at its clearance, efficiency and simplicity.We introduce homogeneous barycentric coordinates for discrete surface processing, and any vertex can be expressed as a homogeneous weighting center of its neighboring vertexes and neighboring planes. Based on homogeneous barycentric coordinates, a new geometric variable, sharpness factor, is defined for measuring sharpness of independent vertexes. With the technique of homogeneous barycentric coordinates and sharpness factor, a new filtering algorithm is developed. All vertexes can be restored or filtered by variational normal smoothing and sharpness factor denoising. This new filtering algorithm will reduce to some traditional mesh smoothing methods when all sharpness factors vanish. Not only can this filtering method preserve features and be free of local shrinkage, it also benefits the properties... |
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