Gal Mishne

Multiscale Anomaly Detection Using Diffusion Maps

We propose a multiscale approach to anomaly detection in images, combining spectral dimensionality reduction and a nearest-neighbor-based anomaly score. We use diffusion maps to embed the data in a low dimensional representation, which separates the anomaly from the background. The diffusion distance between points is then used to estimate the local density of each pixel in the new embedding. The diffusion map is constructed based on a subset of samples from the image and then extended to all other pixels. Due to the interpolative nature of extension methods, this may limit the ability of the diffusion map to reveal the presence of the anomaly in the data. To overcome this limitation, we propose a multiscale approach based on Gaussian pyramid representation, which drives the sampling process to ensure separability of the anomaly from the background clutter. The algorithm is successfully tested on side-scan sonar images of sea-mines.

Graph-Based Supervised Automatic Target Detection

In this paper, we propose a detection method based on data-driven target modeling, which implicitly handles variations in the target appearance. Given a training set of images of the target, our approach constructs models based on local neighborhoods within the training set. We present a new metric using these models and show that, by controlling the notion of locality within the training set, this metric is invariant to perturbations in the appearance of the target. Using this metric in a supervised graph framework, we construct a low-dimensional embedding of test images. Then, a detection score based on the embedding determines the presence of a target in each image. The method is applied to a data set of side-scan sonar images and achieves impressive results in the detection of sea mines. The proposed framework is general and can be applied to different target detection problems in a broad range of signals.

Hierarchical Coupled-Geometry Analysis for Neuronal Structure and Activity Pattern Discovery

In the wake of recent advances in experimental methods in neuroscience, the ability to record in-vivo neuronal activity from awake animals has become feasible. The availability of such rich and detailed physiological measurements calls for the development of advanced data analysis tools, as commonly used techniques do not suffice to capture the spatio-temporal network complexity. In this paper, we propose a new hierarchical coupled-geometry analysis that implicitly takes into account the connectivity structures between neurons and the dynamic patterns at multiple time scales. Our approach gives rise to the joint organization of neurons and dynamic patterns in data-driven hierarchical data structures. These structures provide local to global data representations, from local partitioning of the data in flexible trees through a new multiscale metric to a global manifold embedding. The application of our techniques to in-vivo neuronal recordings demonstrate the capability of extracting neuronal activity patterns and identifying temporal trends, associated with particular behavioral events and manipulations introduced in the experiments.

Multiscale anomaly detection using diffusion maps and saliency score

Recently, we presented a multiscale approach to anomaly detection in images, combining diffusion maps for dimensionality reduction and a nearest-neighbor-based anomaly score in the reduced dimension. When applying diffusion maps to images, usually a process of sampling and out-of-sample extension is used, which has limitations in regards to anomaly detection. To overcome the limitations, a multiscale approach was proposed, which drives the sampling process to ensure separability of the anomaly from the background clutter. In this paper, we propose a new anomaly score used in the diffusion map space, which shows increased performance. We show that this algorithm enables improved detection when tested on side-scan sonar images of sea-mines and compare it with competing algorithms.

Automated cellular structure extraction in biological images with applications to calcium imaging data

Recent advances in experimental methods in neuroscience enable measuring in-vivo activity of large populations of neurons at cellular level resolution. To leverage the full potential of these complex datasets and analyze the dynamics of individual neurons, it is essential to extract high-resolution regions of interest, while addressing demixing of overlapping spatial components and denoising of the temporal signal of each neuron. In this paper, we propose a data-driven solution to these challenges, by representing the spatiotemporal volume as a graph in the image plane. Based on the spectral embedding of this graph calculated across trials, we propose a new clustering method, Local Selective Spectral Clustering, capable of handling overlapping clusters and disregarding clutter. We also present a new nonlinear mapping which recovers the structural map of the neurons and dendrites, and global video denoising. We demonstrate our approach on in-vivo calcium imaging of neurons and apical dendrites, automatically extracting complex structures in the image domain, and denoising and demixing their time-traces.

Improving resolution in supervised patch-based target detection

Recently, a supervised graph-based target detection method was proposed based on a new affinity measure between a set of target training patches and a test image. In this paper, we propose a new high-resolution detection score, which enhances the performance of the previous method by utilizing the known locations of the targets in the training images. We show that our new score is more reliable and spatially accurate, not only improving the detection resolution of true targets, but also reducing the number of false alarms. The method is successfully tested on side-scan sonar images of sea-mines, demonstrating an improved true detection rate. Our approach is general and can improve the detection resolution of the target in other patch-based detection algorithms for various signals and applications.

Multi-channel wafer defect detection using diffusion maps

Detection of defects on patterned semiconductor wafers is a critical step in wafer production. Many inspection methods and apparatus have been developed for this purpose. We recently presented an anomaly detection approach based on geometric manifold learning techniques. This approach is data-driven, with the separation of the anomaly from the background arising from the intrinsic geometry of the image, revealed through the use of diffusion maps. In this paper, we extend our algorithm to 3D data in multichannel wafer defect detection. We test our algorithm on a set of semiconductor wafers and demonstrate that our multiscale multi-channel algorithm has superior performance when compared to single-scale and single-channel approaches.

Iterative diffusion-based anomaly detection

Diffusion maps, when applied to large datasets, are typically constructed by a process of sampling and out-of-sample function extension. However, the performance of anomaly detection in large data when using diffusion maps is sensitive to the chosen samples. In this paper we propose an iterative data-driven approach to improve the sample set and diffusion maps representation. By updating the sample set with suspicious points detected in the previous iteration, the constructed diffusion maps better separate the anomaly from the normal points in each iteration. Experimental results in side-scan sonar images demonstrate the improvement gained by our iterative sampling compared to random sampling and other competing detection algorithms.