Extrinsic Methods for Coding and Dictionary Learning on Grassmann Manifolds

Sparsity-based representations have recently led to notable results in various visual recognition tasks. In a separate line of research, Riemannian manifolds have been shown useful for dealing with features and models that do not lie in Euclidean spaces. With the aim of building a bridge between the two realms, we address the problem of sparse coding and dictionary learning over the space of linear subspaces, which form Riemannian structures known as Grassmann manifolds. To this end, we propose to embed Grassmann manifolds into the space of symmetric matrices by an isometric mapping. This in turn enables us to extend two sparse coding schemes to Grassmann manifolds. Furthermore, we propose closed-form solutions for learning a Grassmann dictionary, atom by atom. Lastly, to handle non-linearity in data, we extend the proposed Grassmann sparse coding and dictionary learning algorithms through embedding into Hilbert spaces. Experiments on several classification tasks (gender recognition, gesture classification, scene analysis, face recognition, action recognition and dynamic texture classification) show that the proposed approaches achieve considerable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as kernelized Affine Hull Method and graph-embedding Grassmann discriminant analysis.Comment: Appearing in International Journal of Computer Visio

Micro Fourier Transform Profilometry (μ\muFTP): 3D shape measurement at 10,000 frames per second

Recent advances in imaging sensors and digital light projection technology have facilitated a rapid progress in 3D optical sensing, enabling 3D surfaces of complex-shaped objects to be captured with improved resolution and accuracy. However, due to the large number of projection patterns required for phase recovery and disambiguation, the maximum fame rates of current 3D shape measurement techniques are still limited to the range of hundreds of frames per second (fps). Here, we demonstrate a new 3D dynamic imaging technique, Micro Fourier Transform Profilometry ($\mu$FTP), which can capture 3D surfaces of transient events at up to 10,000 fps based on our newly developed high-speed fringe projection system. Compared with existing techniques, $\mu$FTP has the prominent advantage of recovering an accurate, unambiguous, and dense 3D point cloud with only two projected patterns. Furthermore, the phase information is encoded within a single high-frequency fringe image, thereby allowing motion-artifact-free reconstruction of transient events with temporal resolution of 50 microseconds. To show $\mu$FTP's broad utility, we use it to reconstruct 3D videos of 4 transient scenes: vibrating cantilevers, rotating fan blades, bullet fired from a toy gun, and balloon's explosion triggered by a flying dart, which were previously difficult or even unable to be captured with conventional approaches.Comment: This manuscript was originally submitted on 30th January 1

Learning Deep Representations of Appearance and Motion for Anomalous Event Detection

We present a novel unsupervised deep learning framework for anomalous event detection in complex video scenes. While most existing works merely use hand-crafted appearance and motion features, we propose Appearance and Motion DeepNet (AMDN) which utilizes deep neural networks to automatically learn feature representations. To exploit the complementary information of both appearance and motion patterns, we introduce a novel double fusion framework, combining both the benefits of traditional early fusion and late fusion strategies. Specifically, stacked denoising autoencoders are proposed to separately learn both appearance and motion features as well as a joint representation (early fusion). Based on the learned representations, multiple one-class SVM models are used to predict the anomaly scores of each input, which are then integrated with a late fusion strategy for final anomaly detection. We evaluate the proposed method on two publicly available video surveillance datasets, showing competitive performance with respect to state of the art approaches.Comment: Oral paper in BMVC 201