Subspace learning from image gradient orientations

We introduce the notion of subspace learning from image gradient orientations for appearance-based object recognition. As image data is typically noisy and noise is substantially different from Gaussian, traditional subspace learning from pixel intensities fails very often to estimate reliably the low-dimensional subspace of a given data population. We show that replacing pixel intensities with gradient orientations and the 2 norm with a cosine-based distance measure offers, to some extend, a remedy to this problem. Within this framework, which we coin IGO (Image Gradient Orientations) subspace learning, we ﬿rst formulate and study the properties of Principal Component Analysis of image gradient orientations (IGO-PCA). We then show its connection to previously proposed robust PCA techniques both theoretically and experimentally. Finally, we derive a number of other popular subspace learning techniques, namely Linear Discriminant Analysis (LDA), Locally Linear Embedding (LLE) and Laplacian Eigenmaps (LE). Experimental results show that our algorithms outperform signi﬿cantly popular methods such as Gabor features and Local Binary Patterns and achieve state-of-the-art performance for dif﬿cult problems such as illumination- and occlusion-robust face recognition. In addition to this, the proposed IGO-methods require the eigen-decomposition of simple covariance matrices and are as computationally ef﬿cient as their corresponding 2 norm intensity-based counterparts. Matlab code for the methods presented in this paper can be found at http://ibug.doc.ic.ac.uk/resources