1 January 1992 Morphological image segmentation by local granulometric size distributions
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Morphological granulometries are generated by successively opening a thresholded image by an increasing sequence of structuring elements. The result is a sequence of images, each of which is a subimage of the previous. By counting the number of pixels at each stage of the granulometry, a size distribution is generated that can be employed as a signature of the image. Normalization of the size distribution produces a probability distribution in the usual sense. An adaptation of the method that is appropriate to texture-based segmentation is described. Rather than construct a single size distribution based on the entire image, local size distributions are computed over windows within the image. These local size distributions lead to granulometric moments at pixels within the image, and if the image happens to be partitioned into regions of various texture, the local moments will tend to be homogeneous over any given region. Segmentation results from segmenting images whose gray values are local moments. Especially useful are the means of the local size distributions. Goodness of segmentation depends on the local probability distributions of the granulometricmoment images. Both exact and asymptotic characterizations of these distributions are developed for the mean image of a basic convexity model.
Edward R. Dougherty, Jeff B. Pelz, Francis M. Sand, Arnold Lent, "Morphological image segmentation by local granulometric size distributions," Journal of Electronic Imaging 1(1), (1 January 1992). https://doi.org/10.1117/12.55174

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