Rotation Invariant Angular Descriptor Via A Bandlimited Gaussian-like Kernel

TL;DR

This paper introduces a new band-limited, Gaussian-like kernel for angular distribution estimation that is rotation invariant and improves upon traditional histogram methods in image processing tasks.

Contribution

A novel band-limited Gaussian-like kernel enabling exact Fourier series representation of angular distributions for rotation-invariant image analysis.

Findings

Outperforms gradient histograms in patch matching

Enhances person detection accuracy

Improves texture segmentation results

Abstract

We present a new smooth, Gaussian-like kernel that allows the kernel density estimate for an angular distribution to be exactly represented by a finite number of its Fourier series coefficients. Distributions of angular quantities, such as gradients, are a central part of several state-of-the-art image processing algorithms, but these distributions are usually described via histograms and therefore lack rotation invariance due to binning artifacts. Replacing histograming with kernel density estimation removes these binning artifacts and can provide a finite-dimensional descriptor of the distribution, provided that the kernel is selected to be bandlimited. In this paper, we present a new band-limited kernel that has the added advantage of being Gaussian-like in the angular domain. We then show that it compares favorably to gradient histograms for patch matching, person detection, and texture segmentation.