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The paper provides a specific perspective view on background subtraction for moving object detection, as a building block for many computer vision applications, being the first relevant step for subsequent recognition, classification, and activity analysis tasks. Since color information is not sufficient for dealing with problems like light switches or local gradual changes of illumination, shadows cast by the foreground objects, and color camouflage, new information needs to be caught to deal with these issues. Depth synchronized information acquired by low-cost RGBD sensors is considered in this paper to give evidence about which issues can be solved, but also to highlight new challenges and design opportunities in several applications and research areas.

This paper presents a time-of-flight image sensor based on 8-Tap P-N junction demodulator (PND) pixels, which is designed for hybrid-type short-pulse (SP)-based ToF measurements under strong ambient light. The 8-tap demodulator implemented with multiple p-n junctions used for modulating the electric potential to transfer photoelectrons to eight charge-sensing nodes and charge drains has an advantage of high-speed demodulation in large photosensitive areas. The ToF image sensor implemented using 0.11 µm CIS technology, consisting of an 120 (H) × 60 (V) image array of the 8-tap PND pixels, successfully works with eight consecutive time-gating windows with the gating width of 10 ns and demonstrates for the first time that long-range (>10 m) ToF measurements under high ambient light are realized using single-frame signals only, which is essential for motion-artifact-free ToF measurements. This paper also presents an improved depth-adaptive time-gating-number assignment (DATA) technique for extending the depth range while having ambient-light canceling capability and a nonlinearity error correction technique. By applying these techniques to the implemented image sensor chip, hybrid-type single-frame ToF measurements with depth precision of maximally 16.4 cm (1.4% of the maximum range) and the maximum non-linearity error of 0.6% for the full-scale depth range of 1.0–11.5 m and operations under direct-sunlight-level ambient light (80 klux) have been realized. The depth linearity achieved in this work is 2.5 times better than that of the state-of-the-art 4-tap hybrid-type ToF image sensor.

Climbing and descending stairs are demanding daily activities, and the monitoring of them may reveal the presence of musculoskeletal diseases at an early stage. A markerless system is needed to monitor such stair walking activity without mentally or physically disturbing the subject. Microsoft Kinect v2 has been used for gait monitoring, as it provides a markerless skeleton tracking function. However, few studies have used this device for stair walking monitoring, and the accuracy of its skeleton tracking function during stair walking has not been evaluated. Moreover, skeleton tracking is not likely to be suitable for estimating body joints during stair walking, as the form of the body is different from what it is when it walks on level surfaces. In this study, a new method of estimating the 3D position of the knee joint was devised that uses the depth data of Kinect v2. The accuracy of this method was compared with that of the skeleton tracking function of Kinect v2 by simultaneously measuring subjects with a 3D motion capture system. The depth data method was found to be more accurate than skeleton tracking. The mean error of the 3D Euclidian distance of the depth data method was 43.2 ± 27.5 mm, while that of the skeleton tracking was 50.4 ± 23.9 mm. This method indicates the possibility of stair walking monitoring for the early discovery of musculoskeletal diseases.

Covariance matrix estimation is one of the most important problems in statistics. To accommodate the complexity of modern datasets, it is desired to have estimation procedures that not only can incorporate the structural assumptions of covariance matrices, but are also robust to outliers from arbitrary sources. In this paper, we define a new concept called matrix depth and then propose a robust covariance matrix estimator by maximizing the empirical depth function. The proposed estimator is shown to achieve minimax optimal rate under Huber’s ε-contamination model for estimating covariance/scatter matrices with various structures including bandedness and sparsity.

Network motifs are often called the building blocks of networks. Analysis of motifs has been found to be an indispensable tool for understanding local network structure, in contrast to measures based on node degree distribution and its functions that primarily address a global network topology. As a result, networks that are similar in terms of global topological properties may differ noticeably at a local level. This phenomenon of the impact of local structure has been recently documented in network fragility analysis and classification. At the same time, many studies of networks still tend to focus on global topological measures, often failing to unveil hidden mechanisms behind vulnerability of real networks and their dynamic response to malfunctions. In this paper, a study of motif-based analysis of network resilience and reliability under various types of intentional attacks is presented, with the goal of shedding light on local dynamics and vulnerability of networks. These methods are demonstrated on electricity transmission networks of 4 European countries, and the results are compared with commonly used resilience and reliability measures.

A depth-based rank sum statistic for multivariate data introduced by Liu and Singh [J. Amer. Statist. Assoc. 88 (1993) 252-260] as an extension of the Wilcoxon rank sum statistic for univariate data has been used in multivariate rank tests in quality control and in experimental studies. Those applications, however, are based on a conjectured limiting distribution, provided by Liu and Singh [J. Amer. Statist. Assoc. 88 (1993) 252-260]. The present paper proves the conjecture under general regularity conditions and, therefore, validates various applications of the rank sum statistic in the literature. The paper also shows that the corresponding rank sum tests can be more powerful than Hotelling's T² test and some commonly used multivariate rank tests in detecting location-scale changes in multivariate distributions.

This paper proposes a new method called depth difference (DeD), for estimating the optimal number of clusters ( k ) in a dataset based on data depth. The DeD method estimates the k parameter before actual clustering is constructed. We define the depth within clusters, depth between clusters, and depth difference to finalize the optimal value of k , which is an input value for the clustering algorithm. The experimental comparison with the leading state-of-the-art alternatives demonstrates that the proposed DeD method outperforms.

This paper studies robust regression in the settings of Huber’s ϵ-contamination models. We consider estimators that are maximizers of multivariate regression depth functions. These estimators are shown to achieve minimax rates in the settings of ϵ-contamination models for various regression problems including nonparametric regression, sparse linear regression, reduced rank regression, etc. We also discuss a general notion of depth function for linear operators that has potential applications in robust functional linear regression.

We propose a new notion called \"extremal depth\" (ED) for functional data, discuss its properties, and compare its performance with existing concepts. The proposed notion is based on a measure of extreme \"outlyingness.\" ED has several desirable properties that are not shared by other notions and is especially well suited for obtaining central regions of functional data and function spaces. In particular: (a) the central region achieves the nominal (desired) simultaneous coverage probability; (b) there is a correspondence between ED-based (simultaneous) central regions and appropriate pointwise central regions; and (c) the method is resistant to certain classes of functional outliers. The article examines the performance of ED and compares it with other depth notions. Its usefulness is demonstrated through applications to constructing central regions, functional boxplots, outlier detection, and simultaneous confidence bands in regression problems. Supplementary materials for this article are available online.

In this paper, we provide an elaboration on the desirable properties of statistical depths for functional data. Although a formal definition has been put forward in the literature, there are still several unclarities to be tackled, and further insights to be gained. Herein, a few interesting connections between the wanted properties are found. In particular, it is demonstrated that the conditions needed for some desirable properties to hold are extremely demanding, and virtually impossible to be met for common depths. We establish adaptations of these properties which prove to be still sensible, and more easily met by common functional depths.