Global Shape Description of Digital Objects

Latest options for global shape description of three-dimensional digital objects are displayed. The form of an object is first represented by using a digital surface in which the faces are either triangles or quadrilaterals. Tips for computing a high-quality parameterization of the surface are developed and this kind of parameterization is required to approximate the form of the object. Spherical harmonics are utilized as basis functions for estimates of the coordinate functions. Information regarding the worldwide shape is going to be captured through the coefficients in the spherical harmonics expansions. For the starshaped object it is usually shown just how a parameterization could be computed by using a projection from the surface on top of the unit sphere. A formula for computing the location in which the centre of the sphere needs to be located, is displayed. This algorithm is equipped for digital voxel objects. Many of the effort is involved with digital objects whose surfaces are homeomorphic for the sphere. The conventional option for computing parameterizations of those surfaces is proven to fail on many objects. This is because of the large distortions to the mathematical properties of the surface that usually occur using this method. Algorithms to handle this problem are suggested. Non-linear optimization methods are utilized to discover a mapping between a surface and the sphere that minimizes geometric distortion and is also useful like a parameterization of the surface….

Contents: Global Shape Description of Digital Objects

1 Introduction
2 Surface Parameterization Techniques
2.1 Convex and Starshaped Objects
2.2 Parameterization and Shape Description of Digital Objects
2.2.1 Deﬁnition and Construction of the Surface
2.2.2 Initial Parameterization
2.2.3 Optimization and Approximation
3 Contributions in This Thesis
3.1 Paper I
3.2 Paper II
3.3 Paper III
3.4 Paper IV
4 Acknowledgement
5 Summary in Swedish: Global formbeskrivning av digitala objekt