The Ensemble Kalman Filter: A Signal Processing Perspective

The ensemble Kalman filter (EnKF) is a Monte Carlo based implementation of the Kalman filter (KF) for extremely high-dimensional, possibly nonlinear and non-Gaussian state estimation problems. Its ability to handle state dimensions in the order of millions has made the EnKF a popular algorithm in different geoscientific disciplines. Despite a similarly vital need for scalable algorithms in signal processing, e.g., to make sense of the ever increasing amount of sensor data, the EnKF is hardly discussed in our field. This self-contained review paper is aimed at signal processing researchers and provides all the knowledge to get started with the EnKF. The algorithm is derived in a KF framework, without the often encountered geoscientific terminology. Algorithmic challenges and required extensions of the EnKF are provided, as well as relations to sigma-point KF and particle filters. The relevant EnKF literature is summarized in an extensive survey and unique simulation examples, including popular benchmark problems, complement the theory with practical insights. The signal processing perspective highlights new directions of research and facilitates the exchange of potentially beneficial ideas, both for the EnKF and high-dimensional nonlinear and non-Gaussian filtering in general

Automated design of robust discriminant analysis classifier for foot pressure lesions using kinematic data

In the recent years, the use of motion tracking systems for acquisition of functional biomechanical gait data, has received increasing interest due to the richness and accuracy of the measured kinematic information. However, costs frequently restrict the number of subjects employed, and this makes the dimensionality of the collected data far higher than the available samples. This paper applies discriminant analysis algorithms to the classification of patients with different types of foot lesions, in order to establish an association between foot motion and lesion formation. With primary attention to small sample size situations, we compare different types of Bayesian classifiers and evaluate their performance with various dimensionality reduction techniques for feature extraction, as well as search methods for selection of raw kinematic variables. Finally, we propose a novel integrated method which fine-tunes the classifier parameters and selects the most relevant kinematic variables simultaneously. Performance comparisons are using robust resampling techniques such as Bootstrap$632+$and k-fold cross-validation. Results from experimentations with lesion subjects suffering from pathological plantar hyperkeratosis, show that the proposed method can lead to$sim 96$correct classification rates with less than 10% of the original features

Discriminative Scale Space Tracking

Accurate scale estimation of a target is a challenging research problem in visual object tracking. Most state-of-the-art methods employ an exhaustive scale search to estimate the target size. The exhaustive search strategy is computationally expensive and struggles when encountered with large scale variations. This paper investigates the problem of accurate and robust scale estimation in a tracking-by-detection framework. We propose a novel scale adaptive tracking approach by learning separate discriminative correlation filters for translation and scale estimation. The explicit scale filter is learned online using the target appearance sampled at a set of different scales. Contrary to standard approaches, our method directly learns the appearance change induced by variations in the target scale. Additionally, we investigate strategies to reduce the computational cost of our approach. Extensive experiments are performed on the OTB and the VOT2014 datasets. Compared to the standard exhaustive scale search, our approach achieves a gain of 2.5% in average overlap precision on the OTB dataset. Additionally, our method is computationally efficient, operating at a 50% higher frame rate compared to the exhaustive scale search. Our method obtains the top rank in performance by outperforming 19 state-of-the-art trackers on OTB and 37 state-of-the-art trackers on VOT2014.Comment: To appear in TPAMI. This is the journal extension of the VOT2014-winning DSST tracking metho

Long-term Tracking in the Wild: A Benchmark

We introduce the OxUvA dataset and benchmark for evaluating single-object tracking algorithms. Benchmarks have enabled great strides in the field of object tracking by defining standardized evaluations on large sets of diverse videos. However, these works have focused exclusively on sequences that are just tens of seconds in length and in which the target is always visible. Consequently, most researchers have designed methods tailored to this "short-term" scenario, which is poorly representative of practitioners' needs. Aiming to address this disparity, we compile a long-term, large-scale tracking dataset of sequences with average length greater than two minutes and with frequent target object disappearance. The OxUvA dataset is much larger than the object tracking datasets of recent years: it comprises 366 sequences spanning 14 hours of video. We assess the performance of several algorithms, considering both the ability to locate the target and to determine whether it is present or absent. Our goal is to offer the community a large and diverse benchmark to enable the design and evaluation of tracking methods ready to be used "in the wild". The project website is http://oxuva.netComment: To appear at ECCV 201

Speech rhythms and multiplexed oscillatory sensory coding in the human brain

Cortical oscillations are likely candidates for segmentation and coding of continuous speech. Here, we monitored continuous speech processing with magnetoencephalography (MEG) to unravel the principles of speech segmentation and coding. We demonstrate that speech entrains the phase of low-frequency (delta, theta) and the amplitude of high-frequency (gamma) oscillations in the auditory cortex. Phase entrainment is stronger in the right and amplitude entrainment is stronger in the left auditory cortex. Furthermore, edges in the speech envelope phase reset auditory cortex oscillations thereby enhancing their entrainment to speech. This mechanism adapts to the changing physical features of the speech envelope and enables efficient, stimulus-specific speech sampling. Finally, we show that within the auditory cortex, coupling between delta, theta, and gamma oscillations increases following speech edges. Importantly, all couplings (i.e., brain-speech and also within the cortex) attenuate for backward-presented speech, suggesting top-down control. We conclude that segmentation and coding of speech relies on a nested hierarchy of entrained cortical oscillations

Learning a Family of Detectors

Object detection and recognition are important problems in computer vision. The challenges of these problems come from the presence of noise, background clutter, large within class variations of the object class and limited training data. In addition, the computational complexity in the recognition process is also a concern in practice. In this thesis, we propose one approach to handle the problem of detecting an object class that exhibits large within-class variations, and a second approach to speed up the classification processes. In the first approach, we show that foreground-background classification (detection) and within-class classification of the foreground class (pose estimation) can be jointly solved with using a multiplicative form of two kernel functions. One kernel measures similarity for foreground-background classification. The other kernel accounts for latent factors that control within-class variation and implicitly enables feature sharing among foreground training samples. For applications where explicit parameterization of the within-class states is unavailable, a nonparametric formulation of the kernel can be constructed with a proper foreground distance/similarity measure. Detector training is accomplished via standard Support Vector Machine learning. The resulting detectors are tuned to specific variations in the foreground class. They also serve to evaluate hypotheses of the foreground state. When the image masks for foreground objects are provided in training, the detectors can also produce object segmentation. Methods for generating a representative sample set of detectors are proposed that can enable efficient detection and tracking. In addition, because individual detectors verify hypotheses of foreground state, they can also be incorporated in a tracking-by-detection frame work to recover foreground state in image sequences. To run the detectors efficiently at the online stage, an input-sensitive speedup strategy is proposed to select the most relevant detectors quickly. The proposed approach is tested on data sets of human hands, vehicles and human faces. On all data sets, the proposed approach achieves improved detection accuracy over the best competing approaches. In the second part of the thesis, we formulate a filter-and-refine scheme to speed up recognition processes. The binary outputs of the weak classifiers in a boosted detector are used to identify a small number of candidate foreground state hypotheses quickly via Hamming distance or weighted Hamming distance. The approach is evaluated in three applications: face recognition on the face recognition grand challenge version 2 data set, hand shape detection and parameter estimation on a hand data set, and vehicle detection and estimation of the view angle on a multi-pose vehicle data set. On all data sets, our approach is at least five times faster than simply evaluating all foreground state hypotheses with virtually no loss in classification accuracy