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<p><b>Abstract</b>—Thresholding is a popular image segmentation method that converts a gray-level image into a binary image. The selection of optimum thresholds has remained a challenge over decades. Besides being a segmentation tool on its own, often it is also a step in many advanced image segmentation techniques in spaces other than the image space. Most of the thresholding methods reported to date are based on histogram analysis using information-theoretic approaches. These methods have not harnessed the information captured in image morphology. Here, we introduce a novel thresholding method that accounts for both intensity-based class uncertainty—a histogram-based property—and region homogeneity—an image morphology-based property. A scale-based formulation is used for region homogeneity computation. At any threshold, intensity-based class uncertainty is computed by fitting a Gaussian to the intensity distribution of each of the two regions segmented at that threshold. The theory of the optimum thresholding method is based on the postulate that objects manifest themselves with fuzzy boundaries in any digital image acquired by an imaging device. The main idea here is to select that threshold at which pixels with high class uncertainty accumulate mostly around object boundaries. To achieve this, a new threshold energy criterion is formulated using class-uncertainty and region homogeneity such that, at any image location, a high energy is created when both class uncertainty and region homogeneity are high or both are low. Finally, the method selects that threshold which corresponds to the minimum overall energy. The method has been compared to a recently-published maximum segmented image information (<tmath>$MSII$</tmath>) method. Superiority of the proposed method was observed both qualitatively on clinical medical images as well as quantitatively on 250 realistic phantom images generated by adding different degrees of blurring, noise, and background variation to real objects segmented from clinical images.</p>
Image segmentation, thresholding, uncertainty, scale, homogeneity, threshold energy, segmented image information.

P. K. Saha and J. K. Udupa, "Optimum Image Thresholding via Class Uncertainty and Region Homogeneity," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 23, no. , pp. 689-706, 2001.
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