#5839. An analytical proof on suitability of Cauchy-Schwarz Divergence as the aggregation criterion in Region Growing Algorithm

July 2026publication date
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Journal’s subject area:
Computer Vision and Pattern Recognition;
Signal Processing;
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Abstract:
Region Growing Algorithm (RGA) is a popular, fast and strongly formed object segmentation method. In RGA, the region is grown from the seed points to adjacent points depending on an aggregation criterion. Despite the huge literature on RGA, none of the proposed aggregation criteria have been analytically proved to be suitable for an ideal segmentation. In this paper, Cauchy-Schwarz Divergence (CSD) is proved to be suitable as an aggregation criterion in RGA for object segmentation. First, RGA is formulated in this context. The Cauchy-Schwarz-based criterion is proposed here in the continuous case for a bimodal image that contains one object in the background while both regions are normally distributed with different parameters (while the assumption of normal distribution of object and background has been used by many researchers in minimum error thresholding method). Then, a proof is given that in the mentioned formulated case, the proposed RGA will lead to an ideal segmentation.
Keywords:
Aggregation criterion; Cauchy-Schwarz divergence; Image segmentation; Region Growing Algorithm

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