This study introduces BM-RED, a Block-Matching method combining Energy Distance with the Riemannian metric. By mapping optical flow vectors onto a unit sphere in Riemannian space, it captures nonlinear motion characteristics. Evaluated on the Sintel dataset, BM-RED excels in subtle movements (e.g., facial expressions) and complex motion (e.g., tree and background scenes), improving stability and sensitivity. Results show that Riemannian Energy Distance (RED) provides a robust geometric representation, achieving accurate estimates in challenging scenarios like occlusion and non-uniform motion.