Multiple Domain Segmentation Using Topological Derivatives

Abstract

The topological derivative (TD) has been employed in shape analysis, image segmentation, and restoration. The characteristics of an image can be described by analyzing several features such as image intensity, color, and edge, and each feature can be interpreted as a domain. Therefore, in order to consider various characteristics for image segmentation, we propose an effective scheme that uses multiple domain-based TDs. We employ 2D filters and convolution in our proposed scheme to avoid the high computational complexity that may result from the increased number of domains. Specifically, the proposed scheme assumes that the multiple domains are independent of each other, and the total cost of the segmentation is computed from the summation of the cost of each domain. The sign of the weighted total derivative is used to update the input domains with the class elements. The segmentation is optimized iteratively, and the segmented image is labeled according to the optimized domains and classes until convergence is achieved. Experimental results show that the proposed scheme for TD-based segmentation has better segmentation performance than state of the art methods. In addition, the computational complexity of the proposed approach depends linearly on the low-complexity scheme for TD-based segmentation. Furthermore, multiple magnetic resonance imaging (MRI) images are used to verify the effectiveness of the multiple domain-based approach. Therefore, we believe that the proposed scheme can be a useful tool for effective TD-based segmentation.