Joint edge detection and motion estimation of cardiac MR image sequence by a phase field method

In this paper a variational framework for joint segmentation and motion estimation is employed for inspecting heart in Cine MRI sequences. A functional including Mumford-Shah segmentation and optical flow based dense motion estimation is approximated using the phase-field technique. The minimizer of the functional provides an optimum motion field and edge set by considering both spatial and temporal discontinuities. Exploiting calculus of variation principles, multiple partial differential equations associated with the Euler-Lagrange equations of the functional are extracted, first. Next, the finite element method is used to discretize the resulting PDEs for numerical solution. Several simulation runs are used to test the convergence and the parameter sensitivity of the method. It is further applied to a comprehensive set of clinical data in order to compare with conventional cascade methods. Developmental constraints are identified as memory usage and computational complexities, which may be resolved utilizing sparse matrix manipulations and similar techniques. Based on the results of this study, joint segmentation and motion estimation outperforms previously reported cascade approaches especially in segmentation. Experimental results substantiated that the proposed method extracts the motion field and the edge set more precisely in comparison with conventional cascade approaches. This superior result is the consequence of simultaneously considering the discontinuity in both motion field and image space and including consequent frames (usually five) in our joint process functional.