A Variational Bayesian Approach for Classification with Corrupted Inputs

Classification of corrupted images, for example due to occlusion or noise, is a challenging problem. Most existing methods tackled this problem using a two-step strategy: image reconstruction and classification of reconstructed images. However, their performances heavily relied on the accuracy of reconstruction and parameter estimation. We present a full Bayesian approach which infers the class label from the corrupted image by marginalizing the original image and parameters. Overfitting is effectively overcome through Bayesian integration. Our system consists of two models. The original image model, which specifies the original image generation process, is described by a Gaussian mixture model. The observation model, which relates the corrupted image to the original image, is depicted by an additive deviation model. Normal pixel and corrupted pixel values are elegantly handled by the covariance of the Gaussian deviation. We employ variational approximation to make the Bayesian integration tractable. The advantage of the proposed method is demonstrated by classification tests on the USPS digit database and PIE face database with pose and illumination variations.