Linear solution to scale and rotation invariant object matching

Images of an object undergoing ego- or camera-motion often appear to be scaled, rotated, and deformed versions of each other. To detect and match such distorted patterns to a single sample view of the object requires solving a hard computational problem that has eluded most object matching methods. We propose a linear formulation that simultaneously finds feature point correspondences and global geometrical transformations in a constrained solution space. Further reducing the search space based on the lower convex hull property of the formulation, our method scales well with the number of candidate features. Our results on a variety of images and videos demonstrate that our method is accurate, efficient, and robust over local deformation, occlusion, clutter, and large geometrical transformations.