Motion estimation is essential in computer vision, with block matching algorithms (BMA) widely used for their simplicity and efficiency. Traditional BMA cost functions, however, face challenges like noise and illumination changes. This article presents a novel Energy Distance Matrix (BM-EDM) approach that strengthens BMA by using structural information within blocks to improve matching accuracy. Unlike pixel-wise comparisons, BM-EDM generates distance matrices and calculates energy distances to find the best match. Experiments on the Sintel dataset show that BM-EDM significantly outperforms traditional methods, especially in complex local and global motion scenarios, enhancing both accuracy and efficiency. This approach proves highly applicable to real-world tasks such as surveillance, medical imaging, and video compression, where robust motion estimation is critical.