Abstract
We introduce the notion of subspace learning from image gradient orientations for appearance-based object recognition. As image data are typically noisy and noise is substantially different from Gaussian, traditional subspace learning from pixel intensities very often fails to estimate reliably the low-dimensional subspace of a given data population. We show that replacing pixel intensities with gradient orientations and the ℓ₂ norm with a cosine-based distance measure offers, to some extend, a remedy to this problem. Within this framework, which we coin Image Gradient Orientations (IGO) subspace learning, we first 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 significantly outperform popular methods such as Gabor features and Local Binary Patterns and achieve state-of-the-art performance for difficult problems such as illumination and occlusion-robust face recognition. In addition to this, the proposed IGO-methods require the eigendecomposition of simple covariance matrices and are as computationally efficient as their corresponding ℓ₂ norm intensity-based counterparts. Matlab code for the methods presented in this paper can be found at http://ibug.doc.ic.ac.uk/resources.
Highlights
S UBSPACE learning for computer vision applications has recently attracted a lot of interest in the scientific community [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15]
Gaussian; for data corrupted by outliers, such as occlusions, illumination changes and cast shadows, the estimated subspace can be arbitrarily biased. To remedy this problem, we introduce a new framework for appearancebased object recognition: subspace learning from image gradient orientations (IGO subspace learning)
We formalize and statistically verify the observation that local orientation mismatches caused by outliers can be well-described by a uniform distribution which, under a number of mild assumptions, is cancelled out when the cosine kernel is applied. This last observation has been noticed in recently proposed schemes for image registration [22] and provides the basis for a robust measure of visual correlation. Based on this line of research, we show that a cosinebased distance measure has a functional form which enables us to define an explicit mapping from the space of gradient orientations into a subset of a high-dimensional sphere where essentially linear or non-linear dimensionality reduction is performed
Summary
S UBSPACE learning for computer vision applications has recently attracted a lot of interest in the scientific community [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15]. Manifold learning algorithms [1], [2], [3], [4], [19], [7], [11], [12] assume that input data points are samples from a low-dimensional manifold embedded in a high-dimensional space. This assumption is not unreasonable in computer vision where large amounts of collected data often result from changes in very few degrees of freedom. Typical examples include Isomap [2], Locally Linear Embedding (LLE) [1], [4] and Laplacian Eigenmaps (LE) [3]
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