Linear time symmetric axis search based on palindrome detection

We present a method searching for the main symmetric axis in an image based on the SAX representation which converts pixels to symbols and a classical linear time palindrome detecting algorithm. This method generates a curve outlining the axis by dynamic programming and produces a straight axis by RANSAC, a linear fitting method tolerates outliers. The computational complexity is O(mn) on an m×n image, which is linear to the pixel number. This method can be extended to multiple symmetric axes detection. Comparing with state-of-the-art symmetry detection methods, our method has a comparable precision and is much faster.