We propose a novel and effective method for segmentation of connected convex objects. In this method, we find the convex hull of the regions of the connected objects and then extract the convex deficient regions i.e., convex deficiencies which are then used for segmenting the connected objects at appropriate places. It is found that the shortest pairs of tips of different convex deficient regions are the appropriate places for segmentation. This method does not introduce any problem of over and under segmentation issues usually faced in many homogeneous region image segmentation methods such as Watershed segmentation. The proposed method has been applied in segmenting connected soyabeans grains and the connected grains are segmented at appropriate places as expected.