Nonparametric Clustering of Mixed Data Using Modified Chi-square Tests

We propose a non-parametric method to cluster mixed data containing both continuous and discrete random variables. The product space of continuous and categorical sample spaces is approximated locally by analyzing neighborhoods with cluster patterns. Detection of cluster patterns on the product space is determined by using a modified Chi-square test. The proposed method does not impose a global distance function which could be difficult to specify in practice. Results from simulation studies have shown that our proposed methods out-performed the benchmark method, AutoClass, for various settings

Basic Properties of Singular Fractional Order System with order (1,2)

This paper focuses on some properties, which include regularity, impulse, stability, admissibility and robust admissibility, of singular fractional order system (SFOS) with fractional order $1<\alpha<2$. The finitions of regularity, impulse-free, stability and admissibility are given in the paper. Regularity is analysed in time domain and the analysis of impulse-free is based on state response. A sufficient and necessary condition of stability is established. Three different sufficient and necessary conditions of admissibility are proved. Then, this paper shows how to get the numerical solution of SFOS in time domain. Finally, a numerical example is provided to illustrate the proposed conditions.Comment: 28 pages, 2 figures, journa

PAD-Net: Multi-Tasks Guided Prediction-and-Distillation Network for Simultaneous Depth Estimation and Scene Parsing

Depth estimation and scene parsing are two particularly important tasks in visual scene understanding. In this paper we tackle the problem of simultaneous depth estimation and scene parsing in a joint CNN. The task can be typically treated as a deep multi-task learning problem [42]. Different from previous methods directly optimizing multiple tasks given the input training data, this paper proposes a novel multi-task guided prediction-and-distillation network (PAD-Net), which first predicts a set of intermediate auxiliary tasks ranging from low level to high level, and then the predictions from these intermediate auxiliary tasks are utilized as multi-modal input via our proposed multi-modal distillation modules for the final tasks. During the joint learning, the intermediate tasks not only act as supervision for learning more robust deep representations but also provide rich multi-modal information for improving the final tasks. Extensive experiments are conducted on two challenging datasets (i.e. NYUD-v2 and Cityscapes) for both the depth estimation and scene parsing tasks, demonstrating the effectiveness of the proposed approach.Comment: Accepted at CVPR 201

Learning Cross-Modal Deep Representations for Robust Pedestrian Detection

This paper presents a novel method for detecting pedestrians under adverse illumination conditions. Our approach relies on a novel cross-modality learning framework and it is based on two main phases. First, given a multimodal dataset, a deep convolutional network is employed to learn a non-linear mapping, modeling the relations between RGB and thermal data. Then, the learned feature representations are transferred to a second deep network, which receives as input an RGB image and outputs the detection results. In this way, features which are both discriminative and robust to bad illumination conditions are learned. Importantly, at test time, only the second pipeline is considered and no thermal data are required. Our extensive evaluation demonstrates that the proposed approach outperforms the state-of- the-art on the challenging KAIST multispectral pedestrian dataset and it is competitive with previous methods on the popular Caltech dataset.Comment: Accepted at CVPR 201

Monocular Depth Estimation using Multi-Scale Continuous CRFs as Sequential Deep Networks

Depth cues have been proved very useful in various computer vision and robotic tasks. This paper addresses the problem of monocular depth estimation from a single still image. Inspired by the effectiveness of recent works on multi-scale convolutional neural networks (CNN), we propose a deep model which fuses complementary information derived from multiple CNN side outputs. Different from previous methods using concatenation or weighted average schemes, the integration is obtained by means of continuous Conditional Random Fields (CRFs). In particular, we propose two different variations, one based on a cascade of multiple CRFs, the other on a unified graphical model. By designing a novel CNN implementation of mean-field updates for continuous CRFs, we show that both proposed models can be regarded as sequential deep networks and that training can be performed end-to-end. Through an extensive experimental evaluation, we demonstrate the effectiveness of the proposed approach and establish new state of the art results for the monocular depth estimation task on three publicly available datasets, i.e. NYUD-V2, Make3D and KITTI.Comment: arXiv admin note: substantial text overlap with arXiv:1704.0215

Multi-Scale Continuous CRFs as Sequential Deep Networks for Monocular Depth Estimation

This paper addresses the problem of depth estimation from a single still image. Inspired by recent works on multi- scale convolutional neural networks (CNN), we propose a deep model which fuses complementary information derived from multiple CNN side outputs. Different from previous methods, the integration is obtained by means of continuous Conditional Random Fields (CRFs). In particular, we propose two different variations, one based on a cascade of multiple CRFs, the other on a unified graphical model. By designing a novel CNN implementation of mean-field updates for continuous CRFs, we show that both proposed models can be regarded as sequential deep networks and that training can be performed end-to-end. Through extensive experimental evaluation we demonstrate the effective- ness of the proposed approach and establish new state of the art results on publicly available datasets.Comment: Accepted as a spotlight paper at CVPR 201

Learning to Group and Label Fine-Grained Shape Components

A majority of stock 3D models in modern shape repositories are assembled with many fine-grained components. The main cause of such data form is the component-wise modeling process widely practiced by human modelers. These modeling components thus inherently reflect some function-based shape decomposition the artist had in mind during modeling. On the other hand, modeling components represent an over-segmentation since a functional part is usually modeled as a multi-component assembly. Based on these observations, we advocate that labeled segmentation of stock 3D models should not overlook the modeling components and propose a learning solution to grouping and labeling of the fine-grained components. However, directly characterizing the shape of individual components for the purpose of labeling is unreliable, since they can be arbitrarily tiny and semantically meaningless. We propose to generate part hypotheses from the components based on a hierarchical grouping strategy, and perform labeling on those part groups instead of directly on the components. Part hypotheses are mid-level elements which are more probable to carry semantic information. A multiscale 3D convolutional neural network is trained to extract context-aware features for the hypotheses. To accomplish a labeled segmentation of the whole shape, we formulate higher-order conditional random fields (CRFs) to infer an optimal label assignment for all components. Extensive experiments demonstrate that our method achieves significantly robust labeling results on raw 3D models from public shape repositories. Our work also contributes the first benchmark for component-wise labeling.Comment: Accepted to SIGGRAPH Asia 2018. Corresponding Author: Kai Xu ([email protected]

Edge-Preserving Piecewise Linear Image Smoothing Using Piecewise Constant Filters

Most image smoothing filters in the literature assume a piecewise constant model of smoothed output images. However, the piecewise constant model assumption can cause artifacts such as gradient reversals in applications such as image detail enhancement, HDR tone mapping, etc. In these applications, a piecewise linear model assumption is more preferred. In this paper, we propose a simple yet very effective framework to smooth images of piecewise linear model assumption using classical filters with the piecewise constant model assumption. Our method is capable of handling with gradient reversal artifacts caused by the piecewise constant model assumption. In addition, our method can further help accelerated methods, which need to quantize image intensity values into different bins, to achieve similar results that need a large number of bins using a much smaller number of bins. This can greatly reduce the computational cost. We apply our method to various classical filters with the piecewise constant model assumption. Experimental results of several applications show the effectiveness of the proposed method

A new test of f(R)f(R) gravity with the cosmological standard rulers in radio quasars

As an important candidate gravity theory alternative to dark energy, a class of $f(R)$ modified gravity, which introduces a perturbation of the Ricci scalar $R$ in the Einstein-Hilbert action, has been extensively applied to cosmology to explain the acceleration of the universe. In this paper, we focus on the recently-released VLBI observations of the compact structure in intermediate-luminosity quasars combined with the angular-diameter-distance measurements from galaxy clusters, which consists of 145 data points performing as individual cosmological standard rulers in the redshift range $0.023\le z\le 2.80$, to investigate observational constraints on two viable models in $f(R)$ theories within the Palatini formalism: $f_1(R)=R-\frac{a}{R^b}$ and $f_2(R)=R-\frac{aR}{R+ab}$. We also combine the individual standard ruler data with the observations of CMB and BAO, which provides stringent constraints. Furthermore, two model diagnostics, $Om(z)$ and statefinder, are also applied to distinguish the two $f(R)$ models and $\Lambda$CDM model. Our results show that (1) The quasars sample performs very well to place constraints on the two $f(R)$ cosmologies, which indicates its potential to act as a powerful complementary probe to other cosmological standard rulers. (2) The $\Lambda$CDM model, which corresponds to $b=0$ in the two $f(R)$ cosmologies is still included within $1\sigma$ range. However, there still exists some possibility that $\Lambda$CDM may not the best cosmological model preferred by the current high-redshift observations. (3) The information criteria indicate that the cosmological constant model is still the best one, while the $f_1(R)$ model gets the smallest observational support. (4) The $f_2(R)$ model, which evolves quite different from $f_1(R)$ model at early times, still significantly deviates from both $f_1(R)$ and $\Lambda$CDM model at the present time.Comment: 18 pages, 5 figures, accepted for publication in JCA