Mover's Distance Research Articles

Sparse coding model captures V1 population response statistics to natural movies

Local populations of sensory cortical cells exhibit a diverse range of activity patterns. However, classical approaches have neither fully accounted for nor characterized this heterogeneity, especially in response to natural stimuli. First, classical single cell recordings suffered from sampling bias and favored highly responsive cells [1]. Second, common approaches considered mostly the average activity over different cell classes, without a full description of the statistical distribution over the entire population [2]. Recent studies started to address these issues [3,4]. In this study, we make further inroads by recording simultaneous single unit activities across cortical layers in cat V1 in response to natural movies using a silicon polytrode, and comparing the population statistics to the predictions from a dynamical system implementation of the sparse coding model [5,6], with a linear-nonlinear model as control. We analyzed data sets from two recording sessions in anaesthetized cats viewing natural movies. To quantitatively measure the difference between model predictions and the recording, we used the earth mover's distance [7] to quantify the dissimilarities between the distributions of the recorded response and those predicted by sparse coding and linear-nonlinear model. We show that: (1) The population firing rate distribution is close to exponential in both the recorded data and the sparse coding model in response to natural movies; (2) The response correlation between unit activities is small regardless of the size of receptive field overlap, when using a binning window synced to the movie frame. A similar relationship between the response correlation and receptive field overlap is observed in the sparse coding model; (3) A linear-nonlinear model could predict the exponential firing rate distribution, but not the correlation structure.

Kernel Earth Mover's Distance for EEG Classification

Here, we propose a new kernel approach based on the earth mover's distance (EMD) for electroencephalography (EEG) signal classification. The EEG time series are first transformed into histograms in this approach. The distance between these histograms is then computed using the EMD in a pair-wise manner. We bring the distances into a kernel form called kernel EMD. The support vector classifier can then be used for the classification of EEG signals. The experimental results on the real EEG data show that the new kernel method is very effective, and can classify the data with higher accuracy than traditional methods.

Observing damaged beams through their time–frequency extended signatures

We introduce in this paper a method for observing the appearance of damages in cantilever beams. The procedure is based on comparing the natural frequencies extracted from the refined time–frequency spectrum of the non-stationary Gabor transform. The comparison is realized with an algorithm for computing the Earth's mover distance (EMD) metric such that the possibility of ambient effects is canceled. The EMD is used to measure the dissimilarities on signatures of sets with different frequency values for the first 10 vibration modes.

이동 객체 정보 보호를 위한 그리드 기반 시멘틱 클로킹 기법

최근 스마트폰의 발전에 따라서 많은 위치 기반 서비스가 활용되고 있으며, 위치 정보 노출로 인한 문제점이 사회적 이슈로 대두되고 있다. 기존의 잘 알려진 위치 정보 보호를 위한 공간 클로킹 기법은 사용자가 요청한 지역에서 위치 정보를 흐릿하게 처리하였다. 하지만 계속적으로 움직이는 이동 객체의 모든 지역을 클로킹하기에는 범위공간이 무수히 넓어지는 문제를 가진다. 따라서, 본 논문에서는 이동 객체 정보 보호를 위한 그리드 기반 시멘틱 클로킹 기법을 제안한다. 제안 기법은 시멘틱 클로킹을 위하여 EMD 갱신 스키마를 확장하고 이동 객체를 위한 대표 보호지역의 클로킹을 정의하였다. 성능 평가에서는 제안 기법이 기존 기법에 비해 처리 시간과 공간 범위에서 안전성과 효율성을 높였다. 이를 통해, 성공적으로 다양한 적으로부터 지속적으로 움직이는 객체의 위치 개인 정보를 보호하여 기존의 방법을 능가하는 성능을 보인다. Location privacy has been a serious concern for mobile users who use location-based services to acquire geographical location continuously. Spatial cloaking technique is a well-known privacy preserving method, which blurs an exact user location into a cloaked area to meet privacy requirements. However, cloaking for continuous moving object suffers from cloaked area size problem as it is unlikely for all objects travel in the same direction. In this paper, we propose a grid-based privacy preservation method with an improved Earth Mover's Distance(EMD) metric weight update scheme for semantic cloaking. We also define a representative cloaking area which protects continuous location privacy for moving users. Experimental implementation and evaluation exhibit that our proposed method renders good efficiency and scalability in cloaking processing time and area size control. We also show that our proposed method outperforms the existing method by successfully protects location privacy of continuous moving objects against various adversaries.

A Visual-Attention Model Using Earth Mover's Distance-Based Saliency Measurement and Nonlinear Feature Combination

This paper introduces a new computational visual-attention model for static and dynamic saliency maps. First, we use the Earth Mover's Distance (EMD) to measure the center-surround difference in the receptive field, instead of using the Difference-of-Gaussian filter that is widely used in many previous visual-attention models. Second, we propose to take two steps of biologically inspired nonlinear operations for combining different features: combining subsets of basic features into a set of super features using the Lm-norm and then combining the super features using the Winner-Take-All mechanism. Third, we extend the proposed model to construct dynamic saliency maps from videos by using EMD for computing the center-surround difference in the spatiotemporal receptive field. We evaluate the performance of the proposed model on both static image data and video data. Comparison results show that the proposed model outperforms several existing models under a unified evaluation setting.

QUANTIFYING NEARNESS IN VISUAL SPACES

Cybernetic vision systems can be deployed in problem domains where the goal is to achieve results similar to those produced by humans. Fundamentally, these problems consist of evaluation of image content between sets of images. This article contrasts two theoretical frameworks for image comparison, namely, the semantic similarity approach used in the earth mover's distance (EMD) and the integrated region matching (IRM) similarity measure, with the tolerance nearness measure (tNM) based on near set theory. The contribution of this article is a comparison of the image similarity measures EMD, IRM, and tNM, as well as a signature-based approach to calculating the tolerance nearness measure.

A Linear Optimal Transportation Framework for Quantifying and Visualizing Variations in Sets of Images

Transportation-based metrics for comparing images have long been applied to analyze images, especially where one can interpret the pixel intensities (or derived quantities) as a distribution of 'mass' that can be transported without strict geometric constraints. Here we describe a new transportation-based framework for analyzing sets of images. More specifically, we describe a new transportation-related distance between pairs of images, which we denote as linear optimal transportation (LOT). The LOT can be used directly on pixel intensities, and is based on a linearized version of the Kantorovich-Wasserstein metric (an optimal transportation distance, as is the earth mover's distance). The new framework is especially well suited for computing all pairwise distances for a large database of images efficiently, and thus it can be used for pattern recognition in sets of images. In addition, the new LOT framework also allows for an isometric linear embedding, greatly facilitating the ability to visualize discriminant information in different classes of images. We demonstrate the application of the framework to several tasks such as discriminating nuclear chromatin patterns in cancer cells, decoding differences in facial expressions, galaxy morphologies, as well as sub cellular protein distributions.

Tensor-SIFT Based Earth Mover’s Distance for Contour Tracking

Contour tracking in complex environments is a difficult problem due to the cluttered backgrounds, illumination changes, occlusion and camera viewpoint variations etc. This paper presents a region functional based on the Earth Mover's Distance (EMD), computation of which is mathematically modeled as the transportation problem (TP), for robust contour tracking in the challenging conditions. Formulation of EMD-based functional can be described as variational EMD (VEMD) since the contour curve function is involved for optimization. Minimizing the EMD-based functional is nontrivial and we develop a two-phase method for its optimization. In the first phase, letting the candidate contour be fixed, we seek the best solution to the TP by the Simplex algorithm. Then through the shape derivative theory, we make a perturbation analysis of the contour around the best solution to the TP. As a result we obtain a partial differential equation (PDE) that is solved by the level-set algorithm. The two-phase procedure iterates until the appropriate stopping criterions are satisfied. Alongside the EMD-based functional formulation, we introduce a dimensionality reduction method by tensor decomposition, achieving a low-dimensional Tensor-SIFT features for object representation. Applicable to both the color and gray-level images, Tensor-SIFT features are distinctive, insensitive to illumination and viewpoint changes. Finally, we develop an integrated algorithm that combines various techniques, e.g. the Simplex algorithm, narrow-band level set and fast marching algorithms. Particularly, we provide a method for the level-set initialization between two successive frames and the criterions for stopping the iterative functional optimization. Experiments in challenging image sequences show that the proposed work has promising performance.

A Prototype Learning Framework Using EMD: Application to Complex Scenes Analysis

In the last decades, many efforts have been devoted to develop methods for automatic scene understanding in the context of video surveillance applications. This paper presents a novel nonobject centric approach for complex scene analysis. Similarly to previous methods, we use low-level cues to individuate atomic activities and create clip histograms. Differently from recent works, the task of discovering high-level activity patterns is formulated as a convex prototype learning problem. This problem results in a simple linear program that can be solved efficiently with standard solvers. The main advantage of our approach is that, using as the objective function the Earth Mover's Distance (EMD), the similarity among elementary activities is taken into account in the learning phase. To improve scalability we also consider some variants of EMD adopting L1 as ground distance for 1D and 2D, linear and circular histograms. In these cases, only the similarity between neighboring atomic activities, corresponding to adjacent histogram bins, is taken into account. Therefore, we also propose an automatic strategy for sorting atomic activities. Experimental results on publicly available datasets show that our method compares favorably with state-of-the-art approaches, often outperforming them.

Inferring Phenotypic Properties from Single-Cell Characteristics

Flow cytometry provides multi-dimensional data at the single-cell level. Such data contain information about the cellular heterogeneity of bulk samples, making it possible to correlate single-cell features with phenotypic properties of bulk tissues. Predicting phenotypes from single-cell measurements is a difficult challenge that has not been extensively studied. The 6th Dialogue for Reverse Engineering Assessments and Methods (DREAM6) invited the research community to develop solutions to a computational challenge: classifying acute myeloid leukemia (AML) positive patients and healthy donors using flow cytometry data. DREAM6 provided flow cytometry data for 359 normal and AML samples, and the class labels for half of the samples. Researchers were asked to predict the class labels of the remaining half. This paper describes one solution that was constructed by combining three algorithms: spanning-tree progression analysis of density-normalized events (SPADE), earth mover’s distance, and a nearest-neighbor classifier called Relief. This solution was among the top-performing methods that achieved 100% prediction accuracy.

Advanced information criterion for environmental data quality assurance

Abstract. A new method for testing time series of environmental data for internal inconsistencies is presented. The method divides the dataset into several disjunct blocks. By means of a comparison of the blocks' estimated probability density distributions, each block is compared with the others. In order to judge the differences, four different measures are used and compared: Kullback-Leibler Divergence, Jensen-Shannon Divergence, Earth Mover's Distance and the Root Mean Square. By looking at the resulting patterns, conclusions on possible inconsistencies in the data can be drawn. This paper shows some sensitivitiy tests and gives an example for an application to real data. Furthermore, it is shown, in which cases of errors (shift in mean, shift in variance and rounding), which measure performs best.

Mean Shift Trackers with Cross-Bin Metrics

Cross-bin metrics have been shown to be more suitable than bin-by-bin metrics for measuring the distance between histograms in various applications. In particular, a visual tracker that minimizes the earth mover's distance (EMD) between the candidate and reference feature histograms has recently been proposed. This tracker was shown to be more robust than the Mean Shift tracker, which employs a bin-by-bin metric. In each frame, the former tracker iteratively shifts the candidate location by one pixel in the direction opposite to the EMD's gradient until no improvement is made. This optimization process involves the clustering of the candidate feature density in feature space, as well as the computation of the EMD between the candidate and reference feature histograms after each shift of the candidate location. In this paper, alternative trackers that employ cross-bin metrics as well, but that are based on Mean Shift (MS) iterations, are derived. The proposed trackers are simpler and faster due to 1) the use of MS-based optimization, which is not restricted to single pixel shifts, 2) abstention from any clustering of feature densities, and 3) abstention from EMD computations in multidimensional spaces.

Extended cone-curvature based salient points detection and 3D model retrieval

Local feature extraction of 3D model has become a more and more important aspect in terms of 3D model shape feature extraction. Compared with the global feature, it is more suitable to do the partial retrieval and more robust to the model deformation. In this paper, a local feature called extended cone-curvature feature is proposed to describe the local shape feature of 3D model mesh. Based on the extended cone-curvature feature, salient points and salient regions are extracted by using a new salient point detection method. Then extended cone-curvature feature and local shape distribution feature calculated on the salient regions are used together as shape index, and the earth mover's distance is employed to accomplish similarity measure. After many times' retrieval experiments, the new extended cone-curvature descriptor we propose has more efficient and effective performance than shape distribution descriptor and light field descriptor especially on deformable model retrieval.

Vision-based hand pose estimation through similarity search using the earth mover's distance

Vision-based hand pose estimation presents unique challenges, particularly if high-fidelity reconstruction is desired. Searching large databases of synthetic pose candidates for items similar to the input offers an attractive means of attaining this goal. The earth mover's distance is a perceptually meaningful measure of dissimilarity that has shown great promise in content-based image retrieval. It is in general, however, a computationally expensive operation and must be used sparingly. The authors investigate a way of economising on its use while preserving much of its accuracy when applied naively in the context of searching for hand pose candidates in large synthetic databases. In particular, a two-tier search method is proposed which achieves similar accuracy with a speed increase of two orders of magnitude. The system performance is evaluated using real input and the results obtained using the different approaches are compared.

A method to assess the alteration of water-level-fluctuation patterns in lakes

The alteration of natural water-level-fluctuation patterns is a key cause of ecological degradation in lake ecosystems. In this research a method is developed to measure the alteration degree of natural water-level-fluctuation patterns in lakes. Utilizing this method, a series of indicators are developed that can reflect the pattern of water level fluctuation. The dissimilarity between the pre- and post-impacted frequency histograms for each indicator is evaluated using a metric called the Earth Mover's Distance. A case study of Baiyangdian Lake shows the water-level-fluctuation pattern alteration degree calculated by the new method is consistent with the ecological degradation degree, indicating the new method's ability to reflect the ecological degradation degree based only on hydrological data

Optic Disc Detection by Earth Mover's Distance Template Matching

This paper presents a method for the detection of OD in the retina which takes advantage of the powerful preprocessing techniques such as the contrast enhancement, Gabor wavelet transform for vessel segmentation, mathematical morphology and Earth Mover's distance (EMD) as the matching process. The OD detection algorithm is based on matching the expected directional pattern of the retinal blood vessels. Vessel segmentation method produces segmentations by classifying each image pixel as vessel or nonvessel, based on the pixel's feature vector. Feature vectors are composed of the pixel's intensity and 2D Gabor wavelet transform responses taken at multiple scales. A simple matched filter is proposed to roughly match the direction of the vessels at the OD vicinity using the EMD. The minimum distance provides an estimate of the OD center coordinates. The method's performance is evaluated on publicly available DRIVE and STARE databases. On the DRIVE database the OD center was detected correctly in all of the 40 images (100%) and on the STARE database the OD was detected correctly in 76 out of the 81 images, even in rather difficult pathological situations. Keywords—Diabetic retinopathy, Earth Mover's distance, Gabor wavelets, optic disc detection, retinal images

A remodelling metric for angular fibre distributions and its application to diseased carotid bifurcations

Many soft biological tissues contain collagen fibres, which act as major load bearing constituents. The orientation and the dispersion of these fibres influence the macroscopic mechanical properties of the tissue and are therefore of importance in several areas of research including constitutive model development, tissue engineering and mechanobiology. Qualitative comparisons between these fibre architectures can be made using vector plots of mean orientations and contour plots of fibre dispersion but quantitative comparison cannot be achieved using these methods. We propose a 'remodelling metric' between two angular fibre distributions, which represents the mean rotational effort required to transform one into the other. It is an adaptation of the earth mover's distance, a similarity measure between two histograms/signatures used in image analysis, which represents the minimal cost of transforming one distribution into the other by moving distribution mass around. In this paper, its utility is demonstrated by considering the change in fibre architecture during a period of plaque growth in finite element models of the carotid bifurcation. The fibre architecture is predicted using a strain-based remodelling algorithm. We investigate the remodelling metric's potential as a clinical indicator of plaque vulnerability by comparing results between symptomatic and asymptomatic carotid bifurcations. Fibre remodelling was found to occur at regions of plaque burden. As plaque thickness increased, so did the remodelling metric. A measure of the total predicted fibre remodelling during plaque growth, TRM, was found to be higher in the symptomatic group than in the asymptomatic group. Furthermore, a measure of the total fibre remodelling per plaque size, TRM/TPB, was found to be significantly higher in the symptomatic vessels. The remodelling metric may prove to be a useful tool in other soft tissues and engineered scaffolds where fibre adaptation is also present.

Indexing the earth mover's distance using normal distributions

Querying uncertain data sets (represented as probability distributions) presents many challenges due to the large amount of data involved and the difficulties comparing uncertainty between distributions. The Earth Mover's Distance (EMD) has increasingly been employed to compare uncertain data due to its ability to effectively capture the differences between two distributions. Computing the EMD entails finding a solution to the transportation problem, which is computationally intensive. In this paper, we propose a new lower bound to the EMD and an index structure to significantly improve the performance of EMD based K-- nearest neighbor (K--NN) queries on uncertain databases. We propose a new lower bound to the EMD that approximates the EMD on a projection vector. Each distribution is projected onto a vector and approximated by a normal distribution, as well as an accompanying error term. We then represent each normal as a point in a Hough transformed space. We then use the concept of stochastic dominance to implement an efficient index structure in the transformed space. We show that our method significantly decreases K--NN query time on uncertain databases. The index structure also scales well with database cardinality. It is well suited for heterogeneous data sets, helping to keep EMD based queries tractable as uncertain data sets become larger and more complex.

효율적인 내용 기반 이미지 검색을 위한 근사 Earth Mover's Distance

정확한 내용 기반 이미지 검색을 위하여 Earth mover's distance와 Optimal color composition distance와 같은 거리함수들이 제안되었다. 이 거리함수들은 정확도가 높은 검색 결과를 가져오지만 검색 시간이 매우 크기 때문에 대용량 데이터베이스에서 사용하기 어렵다는 문제점을 가지고 있다. 본 논문에서는 이러한 문제를 해결하기 위하여 선형 시간에 근사 Earth mover's distance를 구하기 위한 새로운 거리 함수를 제안한다. 제안하는 방법은 선형 시간에 두 이미지의 거리를 계산하기 위하여 공간 채움 곡선을 이용한다. 다양한 실험을 통하여 본 논문에서 제안하는 방법의 우수성을 검증한다. 실험 결과, 제안하는 기법이 Earth mover's distance에 비해 약 160배 정도의 검색 속도 향상 효과를 보이면서도 매우 유사한 결과를 검색하는 것으로 나타났다. For content-based image retrieval, the earth mover's distance and the optimal color composition distance are proposed to measure the dissimilarity. Although providing good retrieval results, both methods are too time-consuming to be used in a large image database. To solve the problem, we propose a new distance function that calculates an approximate earth mover's distance in linear time. To calculate the dissimilarity in linear time, the proposed approach employs the space-filling curve. We have performed extensive experiments to show the effectiveness and efficiency of the proposed approach. The results reveal that our approach achieves almost the same results with the EMD in linear time.

Feature-based 3D motif filtering for ribosomal RNA

RNA 3D motifs are recurrent substructures in an RNA subunit and are building blocks of the RNA architecture. They play an important role in binding proteins and consolidating RNA tertiary structures. RNA 3D motif searching consists of two steps: candidate generation and candidate filtering. We proposed a novel method, known as Feature-based RNA Motif Filtering (FRMF), for identifying motifs based on a set of moment invariants and the Earth Mover's Distance in the second step. A positive set of RNA motifs belonging to six characteristic types, with eight subtypes occurring in HM 50S, is compiled by us. The proposed method is validated on this representative set. FRMF successfully finds most of the positive fragments. Besides the proposed new method and the compiled positive set, we also recognize some new motifs, in particular a π-turn and some non-standard A-minor motifs are found. These newly discovered motifs provide more information about RNA structure conformation. Matlab code can be downloaded from www.cs.cityu.edu.hk/~yingshen/FRMF.html cshswong@cityu.edu.hk Supplementary data are available at Bioinformatics online.