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The kernel graph cut method provides good performance in image segmentation. However, its efficiency strongly depends on the data term and regularization term in the objective function. The data term maps the standard deviation of the data of each region to the transformation space. The regularization term is responsible for smoothing the boundaries. The regularization term, based on a constant coefficient, is added to the data term. Allocating a fixed coefficient for all images leads to inappropriate image segmentation. In this regard, we deal with the automatic adjustment of the regularization term coefficient in the kernel graph cut method based on image energy. This approach is useful in image segmentation with thin structures. The laboratory results were taken on three datasets: fingerprint, coronary artery, and real. The efficiency evaluation of the algorithm, compared with other methods in the field of energy-based algorithms, shows a maximum score of 88.27 in Dice, 79.67 in Jaccard, 75.67 in accuracy, 61.06 in peak-signal-to noise ratio, and a minimum score of 0.06 in mean sum of squared distance on the mentioned datasets. The proposed method also takes advantage of appropriate computing load in the methods based on a graph cut. [ABSTRACT FROM AUTHOR]