Statistical Characterization of Morphological Operator Sequences ⋆ Xiang Gao 1 , Visvanathan Ramesh 2 , and Terry Boult 1 1 Vision And Software Technology Laboratory Lehigh University, Bethlehem, PA, 18015, USA {xig3,tboult}@eecs.lehigh.edu 2 Imaging & Visualization Department Siemens Corporate Research, Princeton, NJ, 08540, USA Visvanathan.Ramesh@scr.siemens.com Abstract. Detection followed by morphological processing is commonly used in machine vision. However, choosing the morphological operators and parameters is often done in a heuristic manner since a statistical characterization of their per- formance is not easily derivable. If we consider a morphology operator sequence as a classifier distinguishing between two patterns, the automatic choice of the operator sequence and parameters is possible if one derives the misclassification distribution as a function of the input signal distributions, the operator sequence, and parameter choices. The main essence of this paper is the illustration that mis- classification statistics, the distribution of bit errors measured by the Hamming distance, can be computed by using an embeddable Markov chain approach. Li- cense plate extraction is used as a case study to illustrate the utility of the theory on real data. 1 Introduction Pixel neighborhood level feature detection followed by a region level grouping and/or morphological filtering (see [4], [9], [13], [17]) is a typical operation sequence in a variety of video and image analysis systems (e.g. document image analysis, video surveillance and monitoring, machine vision and inspection, etc.). The robustness of these algorithms is often questionable because of the use of arbitrary tuning constants that are set by trial and error. Automating the selection of the operators and their algorithms require a sys- tems level analysis or performance characterization. While performance characterization for vision systems in general is being addressed by a growing number of researchers (e.g. [1], [2], [15]), there has been limited research in performance characterization of morphological algorithm sequences. Statistical characterization of morphological op- erators is critical to the task of automating the choice of tuning parameters in various applications. We view the characterization of the morphological operator sequence as the deriva- tion of the output image statistics as a function of the input image statistics, the operator sequence and its tuning parameters. The difficulty is in defining the statistical models ⋆ This work is supported by a research grant from Siemens Corporate Research Inc. A. Heyden et al. (Eds.): ECCV 2002, LNCS 2353, pp. 590–605, 2002. c  Springer-Verlag Berlin Heidelberg 2002