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A Critical Connectivity Radius for Segme...
Murphy, Robert A....

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A Critical Connectivity Radius for Segmenting Randomly-Generated, High Dimensional Data Points by Murphy, Robert A. ( Author )
Lemonjar Open Access
Australian National University
08-08-2023
Motivated by a $2$-dimensional (unsupervised) image segmentation task whereby local regions of pixels are clustered via edge detection methods, a more general probabilistic mathematical framework is devised. Critical thresholds are calculated that indicate strong correlation between randomly-generated, high dimensional data points that have been projected into structures in a partition of a bounded, $2$-dimensional area, of which, an image is a special case. A neighbor concept for structures in the partition is defined and a critical radius is uncovered. Measured from a central structure in localized regions of the partition, the radius indicates strong, long and short range correlation in the count of occupied structures. The size of a short interval of radii is estimated upon which the transition from short-to-long range correlation is virtually assured, which defines a demarcation of when an image ceases to be "interesting".
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Article
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29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/1602.03822
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