On Digital Image Representation by the Delaunay Triangulation
This paper deals with a transformation of raster grey-scale images into a geometric representation by the Delaunay triangulation. It discusses the influence of image filtering techniques and methods for the evaluation of significance of pixels on the conv
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Abstract. This paper deals with a transformation of raster grey-scale images into a geometric representation by the Delaunay triangulation. It discusses the influence of image filtering techniques and methods for the evaluation of significance of pixels on the conversion process. Furthermore, it proposes several novel approaches for a compression of the Delaunay triangulation and compares them with existing solutions. Keywords: image coding, Delaunay triangulation, compression.
1 Introduction A digital image is nowadays usually represented by a rectangular grid of pixels, where each pixel contains a colour value or a greyscale luminance. In order to minimize the storage costs, the grid is very often transferred and stored in a compact form such as well-known GIF, PNG and JPEG. This representation suffers from several disadvantages. First, it cannot be easily processed in its compact form. Next, scaling and rotation operations typically introduce some distortion to the image. Therefore, many researchers have focused recently on alternative geometric representations, such as triangular meshes. Geometric representations are applicable since the pixels of an image can be considered 3D points in a space in which x and ycoordinates are the rows and columns of the image, and z-coordinate is either the grey level or colour value. As it would not be very useful to represent an image with N pixels by a triangulation with the same number of vertices, a triangulation such that it has fewer vertices but it still sufficiently approximates the original mesh is very often needed to be found. From this triangulation, the corresponding image can be easily reconstructed by the interpolation among vertices of the mesh. Let us note that, if bilinear interpolation is exploited, this can be done in real time (especially, if graphics adapters are exploited). Existing methods for the conversion of digital images from the traditional raster representation into a geometric representation can be subdivided into three main categories according to the goal they want to achieve as follows. First, there are methods that produce geometric representations that enhance the quality of further image processing. The representations are not compact as they contain usually as many vertices as the raster. Majority of these methods creates the data dependent D. Mery and L. Rueda (Eds.): PSIVT 2007, LNCS 4872, pp. 826–840, 2007. © Springer-Verlag Berlin Heidelberg 2007
On Digital Image Representation by the Delaunay Triangulation
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triangulation (DDT) where triangle edges match the edges in the image and they differ only in cost functions used to detect an edge and optimisations [1], [16], [17]. In the second category, there are methods that produce compact (i.e., only a subset of vertices is kept) but highly imprecise representations. They find its use in applications of non-photorealistic rendering where details are unwanted because they make an understanding of the information presented by the image more difficult. A typical application of such repr
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