Approximation of granular textures by quadric surfaces

摘要

The method to compute the best biquadratic form approximating an image on neighbourhoods of sizes 3 × 3 to 9 × 9 pixels is given. When this quadric surface is an elliptic paraboloid, various geometric parameters are expressed in terms of quadric coefficients, they are the exact position of the apex, the height, direction, eccentricity, projected area, and mean and Gaussian curvatures. Two examples of approximation by elliptic paraboloids are then presented on two kinds of images: radiographs of metallic pieces and histological sections.