Book chapters

1. Discrete skeletons from distance transforms in 2D and 3D
   Authors: Gunilla Borgefors, Ingela Nyström, Gabriella Sanniti di Baja (1)
   (1) Istituto di Cibernetica, CNR, Pozzuoli, Italy
   Book: Medial Representations: Mathematics, Algorithms and Applications, pp. 155-190
   Publisher: Springer-Verlag
   Abstract: We present discrete methods to compute the digital skeleton of shapes in 2D and 3D images. In 2D, the skeleton is a set of curves, while in 3D it will be a set of surfaces and curves, the surface skeleton, or a set of curves, the curve skeleton. A general scheme could, in principle, be followed for both 2D and 3D discrete skeletonization. However, we will describe one approach for 2D skeletonization, mainly based on marking in the distance transform the shape elements that should be assigned to the skeleton, and another approach for 3D skeletonization, mainly based on iterated element removal. In both cases, the distance transform of the image will play a key role to obtain skeletons reflecting important shape features such as symmetry, elongation, and width.

2. Neighborhood sequences in the diamond grid
   Authors: Benedek Nagy (1), Robin Strand
   (1) Dept. of Computer Science, Faculty of Informatics, University of Debrecen, Hungary
   Book: Image analysis - from theory to applications, pp. 187-195
   Publisher: Research Publishing, Singapore, Chennai
   Abstract: In digital image processing digital distances are useful; distances based on neighborhood sequences are widely used.

   In this paper the diamond grid is considered, that is the three-dimensional grid of Carbon atoms in the diamond crystal. An algorithm to compute a shortest path defined by a neighborhood sequence between any two points in the diamond grid is presented. A formula to compute the distance based on neighborhood sequences is given. A necessary and sufficient condition to have a metric distance function is proved.