Reduction of numerical errors in zernike invariants computed via complex-valued integral images

Abstract

Floating-point arithmetics may lead to numerical errors when numbers involved in an algorithm vary strongly in their orders of magnitude. In the paper we study numerical stability of Zernike invariants computed via complex-valued integral images according to a constant-time technique from [2], suitable for object detection procedures. We indicate numerically fragile places in these computations and identify their cause, namely—binomial expansions. To reduce numerical errors we propose piecewise integral images and derive a numerically safer formula for Zernike moments. Apart from algorithmic details, we provide two object detection experiments. They confirm that the proposed approach improves accuracy of detectors based on Zernike invariants.