Tracking deforming objects involves estimating the global motion of the object and its local deformations as a function
of time. Tracking algorithms using Graph Cut have been proposed. However, because of its globally optimal nature, it is
prone to capture outlying areas similar to the object of interest. Constraint was introduced to confine the standard graph
cut technique in many methods. In this paper, narrow band is introduced to constrain the standard graph cut where it is
build on. With the narrow band constraint, segmentation is ensured to remain in it, which is useful when the result is not
robust using standard graph cut. Secondly, Graph Cut is built based on the band region, compared with traditionally
method, calculation cost is reduced. Thirdly, formulations are adjusted to distinguish between different parts of the
narrow band, which improve the segmentation quality.