Anomaly detection in moving-camera videos with sparse and low-rank matrix decompositions

This work presents two methods based on sparse decompositions that can detect anomalies in video sequences obtained from moving cameras. The first method starts by computing the union of subspaces (UoS) that best represents all the frames from a reference (anomaly-free) video as a low-rank projection plus a sparse residue. Then it performs a low-rank representation of the target (possibly anomalous) video by taking advantage of both the UoS and the sparse residue computed from the reference video. The anomalies are extracted after post-processing this video with these residual data. Such algorithm provides good detection results while at the same time obviating the need for previous video synchronization. However, this technique looses its detection efficiency when target and reference videos presents more severe misalignments. This may happen due to small uncontrolled camera moviment and shaking during the acquisition phase, which is often common in realworld situations. To extend its applicability, a second contribution is proposed in order to cope with these possible pose misalignments. This is done by modeling the target-reference pose discrepancy as geometric transformations acting on the domain of frames of the target video. A complete matrix decomposition algorithm is presented in order to perform a sparse representation of the target video as a sparse combination of the reference video plus a sparse residue, while taking into account the transformation acting on it. Our method is then verified and compared against state-of-the-art techniques using a challenging video dataset, that comprises recordings presenting the described misalignments. Under the evaluation metrics used, the second proposed method exhibits an improvement of at least 16% over the first proposed one, and 22% over the next best rated method.Apresentamos dois métodos baseados em decomposições esparsas que podem detectar anomalias em sequências de vídeo obtidas por câmeras em movimento. O primeiro método estima a união de subespaços (UdS) que melhor representa todos os quadros de um vídeo de referência (livre de anomalias) como uma projeção de baixo-posto mais um resíduo esparso. Em seguida, é realizada uma representação de baixo-posto do vídeo alvo (possivelmente anômalo) aproveitando a UdS e o resíduo esparso calculado a partir do vídeo de referência. As anomalias são extraídas após o pós-processamento destas informações residuais. Esse algoritmo fornece bons resultados de detecção, além de eliminar a necessidade de uma sincronização prévia dos vídeos. No entanto, essa técnica perde eficiência quando os vídeos de referência e alvo apresentam desalinhamentos mais graves entre si. Isso pode ocorrer devido a pequenos movimentos descontrolados da câmera e tremores durante a fase de aquisição. Para estender sua aplicabilidade, uma segunda contribuição é proposta a fim de lidar com esse possível desalinhamento. Isso é feito modelando a discrepância de pose de câmera entre os vídeos de referência e alvo com transformações geométricas agindo no domínio dos quadros do vídeo alvo. Um algoritmo completo de decomposição de matrizes é apresentado para realizar uma representação esparsa do vídeo alvo como uma combinação esparsa do vídeo de referência, levando em consideração as transformações que atuam sobre seus quadros. Nosso método é então verificado e comparado com técnicas de última geração com auxílio de vídeos de uma base desafiadora, apresentando os desalinhamentos em questão. Sob as métricas de avaliação usadas, o segundo método proposto exibe uma melhoria de pelo menos 16% em relação ao primeiro, e 22% sobre o método melhor avaliado logo em seguida

Using Imagery to Identify Abandoned Property in Public Spaces

Generally, the present disclosure is directed to identifying private property that has been illegally dumped or stored for a prolonged period without use. In particular, in some implementations, the systems and methods of the present disclosure can include or otherwise leverage one or more machine-learned models to predict whether an item has been abandoned in a public right-of-way based on imagery of the item and record of public right-of-way

Message Passing Algorithms for Compressed Sensing

Compressed sensing aims to undersample certain high-dimensional signals, yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a known basis. Currently, the best known sparsity-undersampling tradeoff is achieved when reconstructing by convex optimization -- which is expensive in important large-scale applications. Fast iterative thresholding algorithms have been intensively studied as alternatives to convex optimization for large-scale problems. Unfortunately known fast algorithms offer substantially worse sparsity-undersampling tradeoffs than convex optimization. We introduce a simple costless modification to iterative thresholding making the sparsity-undersampling tradeoff of the new algorithms equivalent to that of the corresponding convex optimization procedures. The new iterative-thresholding algorithms are inspired by belief propagation in graphical models. Our empirical measurements of the sparsity-undersampling tradeoff for the new algorithms agree with theoretical calculations. We show that a state evolution formalism correctly derives the true sparsity-undersampling tradeoff. There is a surprising agreement between earlier calculations based on random convex polytopes and this new, apparently very different theoretical formalism.Comment: 6 pages paper + 9 pages supplementary information, 13 eps figure. Submitted to Proc. Natl. Acad. Sci. US

A Foveated Silicon Retina for Two-Dimensional Tracking

A silicon retina chip with a central foveal region for smooth-pursuit tracking and a peripheral region for saccadic target acquisition is presented. The foveal region contains a 9 x 9 dense array of large dynamic range photoreceptors and edge detectors. Two-dimensional direction of foveal motion is computed outside the imaging array. The peripheral region contains a sparse array of 19 x 17 similar, but larger, photoreceptors with in-pixel edge and temporal ON-set detection. The coordinates of moving or flashing targets are computed with two one-dimensional centroid localization circuits located on the outskirts of the peripheral region. The chip is operational for ambient intensities ranging over six orders of magnitude, targets contrast as low as 10%, foveal speed ranging from 1.5 to 10K pixels/s, and peripheral ON-set frequencies from \u3c0.1 to 800 kHz. The chip is implemented in 2-μm N well CMOS process and consumes 15 mW (V dd = 4 V) in normal indoor light (25 μW/cm2). It has been used as a person tracker in a smart surveillance system and a road follower in an autonomous navigation system

Weighted Low-Rank Approximation of Matrices and Background Modeling

We primarily study a special a weighted low-rank approximation of matrices and then apply it to solve the background modeling problem. We propose two algorithms for this purpose: one operates in the batch mode on the entire data and the other one operates in the batch-incremental mode on the data and naturally captures more background variations and computationally more effective. Moreover, we propose a robust technique that learns the background frame indices from the data and does not require any training frames. We demonstrate through extensive experiments that by inserting a simple weight in the Frobenius norm, it can be made robust to the outliers similar to the $\ell_1$ norm. Our methods match or outperform several state-of-the-art online and batch background modeling methods in virtually all quantitative and qualitative measures.Comment: arXiv admin note: text overlap with arXiv:1707.0028