An Algebraic Approach to Affine Registration of Point Sets

This paper proposes a new affine registration algorithm for matching two point sets in IR2 or IR3. The input point sets are represented as probability density functions, using either Gaussian mixture models or discrete density models, and the problem of registering the point sets is treated as aligning the two distributions. Since polynomials transform as symmetric tensors under an affine transformation, the distributions’ moments, which are the expected values of polynomials, also transform accordingly. Therefore, instead of solving the harder problem of aligning the two distributions directly, we solve the softer problem of matching the distributions’ moments. By formulating a least-squares problem for matching moments of the two distributions up to degree three, the resulting cost function is a polynomial that can be efficiently optimized using techniques originated from algebraic geometry: the global minimum of this polynomial can be determined by solving a syst...

• Type: Conference
• Year: 2009
• Where: ICCV
• Authors: Jeffrey Ho, Adrian Peter, Anand Rangarajan, Ming-Hsuan Yang
• Keywords: Affine Registration, Computer Vision, ICCV 2009