Periodicity constrained and block accelerated thin plate spline approach for cardiac motion estimation

In this paper, we propose a periodicity constrained and block accelerated Thin Plate Spline (TPS) approach for cardiac motion estimation from periodic medical image sequences. The TPS transformation is confined to specific sub-blocks to cover the motion range of the matching points during the cardiac cycle, which captured sufficient motion information while preserving computational efficiency. A periodic constraint is introduced to ensure motional consistency throughout the entire cardiac motion. The feasibility of the proposed approach was validated using the Lenna test image, further validation was conducted using MRI datasets from the Cardiac Motion Analysis Challenge (CMAC), demonstrating accurate motion estimation capability with an endpoint error ($EE$) of less than 1 pixel and an angular error ($AE$) of less than 5 degrees. Finally, this approach was applied to real cardiac MRI data, and the motion estimation results were shown to be consistent with the assessment of medical experts. Experimental validation demonstrates that the proposed approach provides enhanced computational flexibility in motion estimation, while expert input ensures an optimal balance between computational efficiency and precision.