On the Subspace of Image Gradient Orientations

TL;DR

This paper proposes a PCA method based on image gradient orientations and cosine distance, which is more robust to noise than traditional intensity-based PCA, while maintaining computational efficiency.

Contribution

It introduces a novel PCA approach using gradient orientations and cosine distance, improving robustness to non-Gaussian noise in image data.

Findings

More reliable low-dimensional subspace estimation in noisy images

Comparable computational efficiency to standard PCA

Enhanced robustness to non-Gaussian noise

Abstract

We introduce the notion of Principal Component Analysis (PCA) of image gradient orientations. As image data is typically noisy, but noise is substantially different from Gaussian, traditional PCA of pixel intensities very often fails to estimate reliably the low-dimensional subspace of a given data population. We show that replacing intensities with gradient orientations and the $\ell_2$ norm with a cosine-based distance measure offers, to some extend, a remedy to this problem. Our scheme requires the eigen-decomposition of a covariance matrix and is as computationally efficient as standard $\ell_2$ PCA. We demonstrate some of its favorable properties on robust subspace estimation.