A Pyramidal Approach to Convex Hull and Filling Algorithms M.G. Albanesi, M. Ferretti, L. Zangrandi Dipartimento di Informatica e Sistemistica, University of Pavia, Via Abbiategrasso 209, 1-27100 Italy Abstract In the paper, a class of algorithms for filling concavities in binary images is presented. The paradigm of computation is a serial, multi- resolution approach. Among the algorithms which have been implemented, the most significant one is fully described, while for the others, some hints are given on the computational complexity. The algorithm for the approximation of the convex hull has a complexity which is linear in the image dimensions, provided that the multi-resolution is already available. The performance of the algorithms has been measured on a broad set of images and experimental results are reported. Final considerations about parallelization are also given. 1 Preliminary considerations In binary images, the problem of describing objects often is formulated in terms of an efficient characterization of silhouettes, which are identified by their convex contour. Therefore, in the analysis of the image, the determination of the convex hull of the shape or the filling of concavities are used in many applications. It is useful, for the following discussion, to distinguish between two classes of approach; planar and hierarchical. In the first class, the data structure involved in the computation is a bi-dimensional array, in which operations may occur locally or globally. On the contrary, in the hierarchical approach, a multi-resolution version of the input image is built, and the computation occurring on a generic level of resolution usually exploits information provided by other levels. Planar versions of algorithms for the computation of filling have been proposed [2] [3], in which computation occurs locally and iteratively in a 3 x 3 neighbourhood. A hierarchical approach [4] applies iteratively the planar algorithm [3] in each level, followed by a projection operation to pass to the higher resolution level. The new methods for convex hull and filling here proposed belong to the serial paradigm of computation, performed in multi-resolution. In particular, three algorithms have been implemented for the filling task (named Fill1, Fill2 and Fill3, respectively), and in the following section the one with best performance (Fill3) is described carefully. For the other two (Fill1 and Fill2), which have been preliminary in our study of hierarchical approaches, we will give some hints on their computation complexity.