Summation invariant and its applications to shape recognition

A novel summation invariant of curves under transformation group action is proposed. This new invariant is less sensitive to noise than the differential invariant and does not require an analytical expression for the curve as the integral invariant does. We exploit this summation invariant to define a shape descriptor called a semi-local summation invariant and use it as a new feature for shape recognition. Tested on a database of noisy shapes of fish, it was observed that the summation invariant feature exhibited superior discriminating power compared to that of wavelet-based invariant features.