While several methods have been proposed for modeling and recognizing image sets, the success of these methods relies heavily on how well the image data follows the assumptions of the underlying models. Among the models that, have been utilized by many image set, classification methods, the physically inspired subspace model assumes that the images of an object lie on a union of low-dimensional subspaces. Despite their successful performance in controlled environments, the performance of such subspace-based classifiers suffers in practical unconstrained settings, where the data may not strictly follow the assumptions necessary for the subspace model to hold. In this paper, we propose Nonlinear Subspace Feature Enhancement (NSFE), an approach for nonlinearly embedding image sets into a space where they adhere to a more discriminative subspace structure. In turn, this improves the performance of subspace-based classifiers such as sparse representation-based classification. We describe how the structured loss function of NSFE can be optimized in a batch-by-batch fashion by a two-step alternating algorithm. The algorithm makes very few assumptions about the form of the embedding to be learned and is compatible with stochastic gradient descent and back-propagation. This makes NSFE usable with deep, feedforward embeddings and trainable in an end-to-end fashion. We experiment, with two different, types of features and nonlinear embeddings over three image set datasets and we show that our method compares favorably to state-of-the-art image set classification methods.
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