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Under-segmentation of an image with multiple objects is a common problem in image segmentation algorithms. This paper presents a novel approach for the splitting of clumps formed by multiple objects due to under-segmentation. The algorithm includes two steps: finding a pair of points for clump splitting, and joining the pair of selected points. In the first step, a pair of points for splitting is detected using a bottleneck rule, under the assumption that the desired objects have roughly convex shape. In the second step, the selected pair of splitting points is joined by finding the optimal splitting line between them, based on minimizing an image energy. The performance of this method is evaluated using images from various applications. Experimental results show that the proposed approach has several advantages over existing splitting methods in identifying points for splitting as well as finding an accurate split line.