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Abstract. 2DRP (two-dimensional random projection) is two-dimensional extension of one-dimensional RP (random projection) to keep biometric images from being reshaped to vectors before RP for recognition. We propose a novel method called (2D) 2 RP (two-directional two-dimensional random projection) for feature extraction of biometrics. (2D) 2 RP directly projects the image matrix from high-dimensional space to low-dimensional space to extract optimal projective vectors at row-direction and column-direction. (2D) 2 RP, similar to RP, can also avoid the problems of singularity, SSS (small sample size) and overfitting; furthermore it has much less storage and computational cost than RP. Besides, the variations of (2D) 2 RP combined with 2DPCA and 2DLDA are developed. Experimental results and comparison discussion among (2D) 2 RP and its variations on face and palmprint databases confirm the performance and effectiveness of (2D) 2 RP and its variations.

This work presents a new robust PCA method for foreground-background separation on freely moving camera video with possible dense and sparse corruptions. Our proposed method registers the frames of the corrupted video and then encodes the varying perspective arising from camera motion as missing data in a global model. This formulation allows our algorithm to produce a panoramic background component that automatically stitches together corrupted data from partially overlapping frames to reconstruct the full field of view. We model the registered video as the sum of a low-rank component that captures the background, a smooth component that captures the dynamic foreground of the scene, and a sparse component that isolates possible outliers and other sparse corruptions in the video. The low-rank portion of our model is based on a recent low-rank matrix estimator (OptShrink) that has been shown to yield superior low-rank subspace estimates in practice. To estimate the smooth foreground component of our model, we use a weighted total variation framework that enables our method to reliably decouple the true foreground of the video from sparse corruptions. We perform extensive numerical experiments on both static and moving camera video subject to a variety of dense and sparse corruptions. Our experiments demonstrate the state-of-the-art performance of our proposed method compared to existing methods both in terms of foreground and background estimation accuracy.

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