A New Framework for Connected Components Labeling of Binary Images

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Given a binary image of n pixels, assign integral labels to all pixels so that any background pixel has label 0 and any two foreground pixels have the same positive integral labels, if and only if they belong to the same connected components. This problem is referred to as ’Connected Components Labeling’ and it is one of the most fundamental problems in image processing and analysis. This paper presents a new algorithmic framework for the problem. From an algorithmic point of view, the problem can be solved in O(n) time and O(n) space. We propose new algorithms which use smaller work space without much sacrifice of the running time. More specifically, assuming that an input binary image is given by a read-only array, our algorithm outputs correct labels in the raster order in O(n logn) time using only \(O(\sqrt{n})\) work space. Some applications of the algorithms are also given.