A fundamental issue in differential motion analysis is the compromise between the flexibility of the matching criterion for image regions and the ability of recovering the motion. Localized matching criteria, e.g., pixel-based SSD, may enable the recovery of all motion parameters, but it does not tolerate much appearance changes. On the other hand, global criteria, e.g., matching histograms, can accommodate dramatic appearance changes, but may be blind to some motion parameters, e.g., scaling and rotation. This paper presents a novel differential approach that integrates the advantages of both in a principled way based on a spatial-appearance model (SAM) that combines local appearances variations and global spatial structures. This model can capture a large variety of appearance variations that are attributed to the local non-rigidity. At the same time, this model enables efficient recovery of all motion parameters. A maximum likelihood matching criterion is defined and rigorous analytical results are obtained that lead to a closed form solution to motion tracking. Very encouraging results demonstrate the effectiveness and efficiency of the proposed method for tracking non-rigid objects that exhibit dramatic appearance deformations, large object scale changes and partial, occlusions.