Comparative Study and Proof of Single-Pass Connected Components Algorithms

Abstract

Union-find algorithms form the basis of managing sets of equivalent labels within most connected components labelling algorithms. The new class of single-pass connected components analysis (CCA) algorithms (where a feature vector of each component is extracted during processing) are analysed and compared within this context. Such algorithms have been developed for stream processing, using customised hardware architectures. Many of these use an improved union-find algorithm requiring only a single lookup for its find operation. This paper analyses this optimisation and formally proves that the resulting single lookup connected components algorithm associates each pixel with its correct component when extracting the components’ feature vectors. Analysis of the algorithm led to a new double lookup algorithm that reduces the total number of memory accesses and is a step towards unifying pixel-based methods and run-based methods. State-of-the-art CCA algorithms are compared in terms of the number of memory accesses, which is a limiting factor for hardware-based acceleration, with key implementation trade-offs identified between hardware resources and worst-case processing speed.