Modified repeated median filters

We discuss moving window techniques for fast extraction of a signal comprising monotonic trends and abrupt shifts from a noisy time series with irrelevant spikes. Running medians remove spikes and preserve shifts, but they deteriorate in trend periods. Modified trimmed mean filters use a robust scale estimate such as the median absolute deviation about the median (MAD) to select an adaptive amount of trimming. Application of robust regression, particularly of the repeated median, has been suggested for improving upon the median in trend periods. We combine these ideas and construct modified filters based on the repeated median offering better shift preservation. All these filters are compared w.r.t. fundamental analytical properties and in basic data situations. An algorithm for the update of the MAD running in time O(log n) for window width n is presented as well. --signal extraction,robust filtering,drifts,jumps,outliers,computational geometry,update algorithm

General highlight detection in sport videos

Attention is a psychological measurement of human reflection against stimulus. We propose a general framework of highlight detection by comparing attention intensity during the watching of sports videos. Three steps are involved: adaptive selection on salient features, unified attention estimation and highlight identification. Adaptive selection computes feature correlation to decide an optimal set of salient features. Unified estimation combines these features by the technique of multi-resolution autoregressive (MAR) and thus creates a temporal curve of attention intensity. We rank the intensity of attention to discriminate boundaries of highlights. Such a framework alleviates semantic uncertainty around sport highlights and leads to an efficient and effective highlight detection. The advantages are as follows: (1) the capability of using data at coarse temporal resolutions; (2) the robustness against noise caused by modality asynchronism, perception uncertainty and feature mismatch; (3) the employment of Markovian constrains on content presentation, and (4) multi-resolution estimation on attention intensity, which enables the precise allocation of event boundaries

Adaptive time-frequency detection and filtering for imaging in heavy clutter

Abstract. We introduce an adaptive approach for the detection of a reflector in a strongly scattering medium using a timefrequency representation of the array response matrix followed by a Singular Value Decomposition (SVD). We use the Local Cosine Transform (LCT) for the time-frequency representation and introduce a detection criterion that identifies anomalies in the top singular values, across frequencies and in different time windows, that are due to the reflector. The detection is adaptive because the time windows that contain the primary echoes from the reflector are not determined in advance. Their location and width is identified by searching through the time-frequency binary tree of the LCT. After detecting the presence of the reflector we filter the array response matrix to retain information only in the time windows that have been selected. We also project the filtered array response matrix to the subspace associated with the top singular value and then image using travel time migration. We show with extensive numerical simulations that this approach to detection and imaging works well in heavy clutter that is calibrated using random matrix theory so as to simulate regimes close to the experiments in [3]. While the detection and filtering algorithm presented here works well in general clutter it has been analyzed theoretically only for the case of randomly layered media [1]

Cross-Scale Cost Aggregation for Stereo Matching

Human beings process stereoscopic correspondence across multiple scales. However, this bio-inspiration is ignored by state-of-the-art cost aggregation methods for dense stereo correspondence. In this paper, a generic cross-scale cost aggregation framework is proposed to allow multi-scale interaction in cost aggregation. We firstly reformulate cost aggregation from a unified optimization perspective and show that different cost aggregation methods essentially differ in the choices of similarity kernels. Then, an inter-scale regularizer is introduced into optimization and solving this new optimization problem leads to the proposed framework. Since the regularization term is independent of the similarity kernel, various cost aggregation methods can be integrated into the proposed general framework. We show that the cross-scale framework is important as it effectively and efficiently expands state-of-the-art cost aggregation methods and leads to significant improvements, when evaluated on Middlebury, KITTI and New Tsukuba datasets.Comment: To Appear in 2013 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). 2014 (poster, 29.88%

Relation between Financial Market Structure and the Real Economy: Comparison between Clustering Methods

We quantify the amount of information filtered by different hierarchical clustering methods on correlations between stock returns comparing it with the underlying industrial activity structure. Specifically, we apply, for the first time to financial data, a novel hierarchical clustering approach, the Directed Bubble Hierarchical Tree and we compare it with other methods including the Linkage and k-medoids. In particular, by taking the industrial sector classification of stocks as a benchmark partition, we evaluate how the different methods retrieve this classification. The results show that the Directed Bubble Hierarchical Tree can outperform other methods, being able to retrieve more information with fewer clusters. Moreover, we show that the economic information is hidden at different levels of the hierarchical structures depending on the clustering method. The dynamical analysis on a rolling window also reveals that the different methods show different degrees of sensitivity to events affecting financial markets, like crises. These results can be of interest for all the applications of clustering methods to portfolio optimization and risk hedging.Comment: 31 pages, 17 figure