On the performance of connected components grouping

The paper provides, for the first time, an analysis of the connected components (CC) grouping process, capable of predicting the grouping quality in terms of measurable, meaningful quantities. The results may also be used for design, and specifically for choosing the parameters controlling the grouping process. Unlike most previous statistical methods in computer vision, which were based on an independence assumption, we confront the predictions with the actual results and show that a model, which takes into account statistical dependence, may predict performance better. This paper is concerned with simple grouping processes based on the connected components graph algorithm. Such processes are very fast and are linear in the number of data features. The performance of the algorithm is considered under a probabilistic setting where both the image and the grouping cues are random variables, it focuses on analyzing the quality of the groups extracted by this algorithm, and shows that quantitative and meaningful measures of grouping quality may be predicted and even, within certain constraints, controlled. In particular, we consider two measures of grouping quality: the number of background features, which are falsely added to the true groups and the number of parts to which a smooth curve (i.e. true group) is fragmented