Estimation of affine geometric transformations of several objects from global measurements

We consider the problem of jointly estimating the affine transformations of multiple objects from a single noisy observation, where each object is undergoing a different affine transformation. The derived algorithm is employed directly, such that prior segmentation of the observation into the distinct objects is avoided. Explicit expressions recovering the parameters of the transformation of each object are derived, assuming only knowledge of the template of each object. In the absence of noise the solution is exact and is not affected by the magnitudes of the deformations. In the presence of noise, the parameters are obtained using a linear least squares solution.