Extended Zernike invariants backed with complex-valued integral images for detection tasks

Abstract

We consider the problem of computationally fast extraction of rotationally invariant features for object detection procedures based on the sliding window. The central point of interest are Zernike moments (ZMs), which can serve to generate rotationally invariant features. However, the definition-based computations of ZMs are linear with respect to the number of pixels in the image window, and therefore are too slow to be applied directly. The method, we have proposed, computes each feature in constant-time — O(1), and thereby does not depend on the number of pixels. This is owed to a suitable construction of complex-valued integral images that we perform prior to the detection procedure. The approach can be referred to extraction of well known Haar-like features (HFs), but our actual computations are more intricate, and obviously the HFs are not rotationally invariant. This paper constitutes a follow-up study and a refinement of our former research. We enrich our initial ideas by proposing an extended space of Zernike invariants backed with integral images. This feature space includes not only the moduli of Zernike moments but also real and imaginary parts of suitable moment products. We demonstrate the rotational invariance property of these products and provide all necessary algorithmic details, such as: a suitable indexation scheme, feature extraction procedures, and feature counts. Finally, we present a road sign detection experiment confirming that the extended space of features contributes to more accurate detection of objects regardless of their rotation.