  Aligning partially overlapping point sets where there is no prior information
about the value of the transformation is a challenging problem in computer
vision. To achieve this goal, we first reduce the objective of the robust point
matching algorithm to a function of a low dimensional variable. The resulting
function, however, is only concave over a finite region including the feasible
region. To cope with this issue, we employ the inner approximation optimization
algorithm which only operates within the region where the objective function is
concave. Our algorithm does not need regularization on transformation, and thus
can handle the situation where there is no prior information about the values
of the transformations. Our method is also $\epsilon-$globally optimal and thus
is guaranteed to be robust. Moreover, its most computationally expensive
subroutine is a linear assignment problem which can be efficiently solved.
Experimental results demonstrate the better robustness of the proposed method
over state-of-the-art algorithms. Our method is also efficient when the number
of transformation parameters is small.
