Our study focuses on isolating swallowing dynamics from interfering patient motion in videofluoroscopy, an X-ray technique that records patients swallowing a radiopaque bolus. These recordings capture multiple motion sources, including head movement, anatomical displacements, and bolus transit. To enable precise analysis of swallowing physiology, we aim to eliminate distracting motion, particularly head movement, while preserving essential swallowing-related dynamics. Optical flow methods fail due to artifacts like flickering and instability, making them unreliable for distinguishing different motion groups. We evaluated markerless tracking approaches (CoTracker, PIPs++, TAP-Net) and quantified tracking accuracy in key medical regions of interest. Our findings demonstrate that even sparse tracking points can generate morphing displacement fields that outperform leading registration methods, including ANTs, LDDMM, and VoxelMorph. To compare all approaches, we evaluated their performance using MSE and SSIM metrics after registration. We introduce a novel motion correction algorithm that effectively removes disruptive motion while preserving swallowing dynamics and surpassing competitive registration techniques. Our code is openly available at https://github.com/neuluna/markerless-motion-correction .