Learning non-metric visual similarity for image retrieval

Measuring visual similarity between two or more instances within a data distribution is a fundamental task in image retrieval. Theoretically, non-metric distances are able to generate a more complex and accurate similarity model than metric distances, provided that the non-linear data distribution is precisely captured by the system. In this work, we explore neural networks models for learning a non-metric similarity function for instance search. We argue that non-metric similarity functions based on neural networks can build a better model of human visual perception than standard metric distances. As our proposed similarity function is differentiable, we explore a real end-to-end trainable approach for image retrieval, i.e. we learn the weights from the input image pixels to the final similarity score. Experimental evaluation shows that non-metric similarity networks are able to learn visual similarities between images and improve performance on top of state-of-the-art image representations, boosting results in standard image retrieval datasets with respect standard metric distances.     

Word spotting for historical documents

Searching and indexing historical handwritten collections are a very challenging problem. We describe an approach called word spotting which involves grouping word images into clusters of similar words by using image matching to find similarity. By annotating “interesting” clusters, an index that links words to the locations where they occur can be built automatically. Image similarities computed using a number of different techniques including dynamic time warping are compared. The word similarities are then used for clustering using both K-means and agglomerative clustering techniques. It is shown in a subset of the George Washington collection that such a word spotting technique can outperform a Hidden Markov Model word-based recognition technique in terms of word error rates. An erratum to this article can be found at     

撒布型无线传感器网络节点定位算法

针对撒布型无线传感器网络提出了基于非度量多维标度的NMDS-MAP算法及NMDS-MAP（P）算法,两种方法采用TDOA等测距技术测量节点间距,利用非度量多维标度技术对未知节点进行定位,前者是集中式算法,后者是分布式算法。理论分析与仿真实验表明,两种算法具有较高的定位精度与健壮性。     

基于非度量多维标度的室内多标签协同定位算法

与有源标签相比,无源RFID标签成本较小,本文选取后者作为待定位标签。但是由于无源RFID标签之间无法通信,目前大多数传统的RFID定位算法一次只能定位一个标签而无法实现多标签同时定位。针对这一问题,提出了基于非度量多维标度(NMDS)的室内RFID多标签协同定位算法。利用到达相位差(PDOA)法拟合在多径存在环境下的测距误差,将待定位标签之间的距离差欧氏距离与非度量多维标度算法结合,计算出待定位标签的位置坐标。仿真结果表明,提出的算法可以通过一次非度量多维标度计算得到所有待定位标签的坐标,同时定位精度高于经典多维标度定位算法和传统三边定位算法。     

A multiresolution framework for local similarity based image denoising

In this paper, we present a generic framework for denoising of images corrupted with additive white Gaussian noise based on the idea of regional similarity. The proposed framework employs a similarity function using the distance between pixels in a multidimensional feature space, whereby multiple feature maps describing various local regional characteristics can be utilized, giving higher weight to pixels having similar regional characteristics. An extension of the proposed framework into a multiresolution setting using wavelets and scale space is presented. It is shown that the resulting multiresolution multilateral (MRM) filtering algorithm not only eliminates the coarse-grain noise but can also faithfully reconstruct anisotropic features, particularly in the presence of high levels of noise.     

Dimension Reduction and Construction of Feature Space for Image Pattern Recognition

We mathematically and experimentally evaluate the validity of dimension-reduction methods for the computation of similarity in image pattern recognition. Image pattern recognition identifies instances of particular objects and distinguishes differences among images. This recognition uses pattern recognition techniques for the classification and categorisation of images. In numerical image pattern recognition techniques, images are sampled using an array of pixels. This sampling procedure derives vectors in a higher-dimensional metric space from image patterns. To ensure the accuracy of pattern recognition techniques, the dimension reduction of the vectors is an essential methodology since the time and space complexities of processing depend on the dimension of the data. Dimension reduction causes information loss of topological and geometrical features of image patterns. Through both theoretical and experimental comparisons, we clarify that dimension-reduction methodologies that preserve the topology and geometry in the image pattern space are essential for linear pattern recognition. For the practical application of methods of dimension reduction, the random projection works well compared with downsampling, the pyramid transform, the two-dimensional random projection, the two-dimensional discrete cosine transform and nonlinear multidimensional scaling if we have no a priori information on the input data.     

Projected Field Similarity for Comparative Visualization of Multi‐Run Multi‐Field Time‐Varying Spatial Data

The purpose of multi‐run simulations is often to capture the variability of the output with respect to different initial settings. Comparative analysis of multi‐run spatio‐temporal simulation data requires us to investigate the differences in the dynamics of the simulations' changes over time. To capture the changes and differences, aggregated statistical information may often be insufficient, and it is desirable to capture the local differences between spatial data fields at different times and between different runs. To calculate the pairwise similarity between data fields, we generalize the concept of isosurface similarity from individual surfaces to entire fields and propose efficient computation strategies. The described approach can be applied considering a single scalar field for all simulation runs or can be generalized to a similarity measure capturing all data fields of a multi‐field data set simultaneously. Given the field similarity, we use multi‐dimensional scaling approaches to visualize the similarity in two‐dimensional or three‐dimensional projected views as well as plotting one‐dimensional similarity projections over time. Each simulation run is depicted as a polyline within the similarity maps. The overall visual analysis concept can be applied using our proposed field similarity or any other existing measure for field similarity. We evaluate our measure in comparison to popular existing measures for different configurations and discuss their advantages and limitations. We apply them to generate similarity maps for real‐world data sets within the overall concept for comparative visualization of multi‐run spatio‐temporal data and discuss the results.     

Effective proximity retrieval by ordering permutations

We introduce a new probabilistic proximity search algorithm for range and K-nearest neighbor (K-NN) searching in both coordinate and metric spaces. Although there exist solutions for these problems, they boil down to a linear scan when the space is intrinsically high-dimensional, as is the case in many pattern recognition tasks. This, for example, renders the K-NN approach to classification rather slow in large databases. Our novel idea is to predict closeness between elements according to how they order their distances towards a distinguished set of anchor objects. Each element in the space sorts the anchor objects from closest to farthest to it, and the similarity between orders turns out to be an excellent predictor of the closeness between the corresponding elements. We present extensive experiments comparing our method against state-of-the-art exact and approximate techniques, both in synthetic and real, metric and non-metric databases, measuring both CPU time and distance computations. The experiments demonstrate that our technique almost always improves upon the performance of alternative techniques, in some cases by a wide margin.     

RankVisu: Mapping from the neighborhood network

Most multidimensional scaling methods focus on the preservation of dissimilarities to map high dimensional items in a low-dimensional space. However, the mapping function usually does not consider the preservation of small dissimilarities as important, since the cost is small with respect to the preservation of large dissimilarities. As a consequence, an item's neighborhoods may be sacrificed for the benefit of the overall mapping. We have subsequently designed a mapping method devoted to the preservation of neighborhood ranks rather than their dissimilarities: RankVisu. A mapping of data is obtained in which neighborhood ranks are as close as possible according to the original space.A comparison with both metric and non-metric MDS highlights the pros (in particular, cluster enhancement) and cons of RankVisu.     

MatchSim: a novel similarity measure based on maximum neighborhood matching

Measuring object similarity in a graph is a fundamental data- mining problem in various application domains, including Web linkage mining, social network analysis, information retrieval, and recommender systems. In this paper, we focus on the neighbor-based approach that is based on the intuition that ??similar objects have similar neighbors?? and propose a novel similarity measure called MatchSim. Our method recursively defines the similarity between two objects by the average similarity of the maximum-matched similar neighbor pairs between them. We show that MatchSim conforms to the basic intuition of similarity; therefore, it can overcome the counterintuitive contradiction in SimRank. Moreover, MatchSim can be viewed as an extension of the traditional neighbor-counting scheme by taking the similarities between neighbors into account, leading to higher flexibility. We present the MatchSim score computation process and prove its convergence. We also analyze its time and space complexity and suggest two accelerating techniques: (1) proposing a simple pruning strategy and (2) adopting an approximation algorithm for maximum matching computation. Experimental results on real-world datasets show that although our method is less efficient computationally, it outperforms classic methods in terms of accuracy.     

Using extended feature objects for partial similarity retrieval

In this paper, we introduce the concept of extended feature objects for similarity retrieval. Conventional approaches for similarity search in databases map each object in the database to a point in some high-dimensional feature space and define similarity as some distance measure in this space. For many similarity search problems, this feature-based approach is not sufficient. When retrieving partially similar polygons, for example, the search cannot be restricted to edge sequences, since similar polygon sections may start and end anywhere on the edges of the polygons. In general, inherently continuous problems such as the partial similarity search cannot be solved by using point objects in feature space. In our solution, we therefore introduce extended feature objects consisting of an infinite set of feature points. For an efficient storage and retrieval of the extended feature objects, we determine the minimal bounding boxes of the feature objects in multidimensional space and store these boxes using a spatial access structure. In our concrete polygon problem, sets of polygon sections are mapped to 2D feature objects in high-dimensional space which are then approximated by minimal bounding boxes and stored in an R-tree. The selectivity of the index is improved by using an adaptive decomposition of very large feature objects and a dynamic joining of small feature objects. For the polygon problem, translation, rotation, and scaling invariance is achieved by using the Fourier-transformed curvature of the normalized polygon sections. In contrast to vertex-based algorithms, our algorithm guarantees that no false dismissals may occur and additionally provides fast search times for realistic database sizes. We evaluate our method using real polygon data of a supplier for the car manufacturing industry. Edited by R. Güting. Received October 7, 1996 / Accepted March 28, 1997     

基于广义超曲面树的相似性搜索算法

相似性搜索是数据挖掘的主要领域之一.它在数据库中检索出相似的数据,发现数据间的相似性.它可以应用于图像数据库、空间数据库和时间序列分析.对于欧氏空间(一种特殊的度量空间),相似性搜索算法中基于R-tree的方法,在低维时是高效的,当维数增加时,R-tre e的方法将退化为线性扫描.该现象被称为维数灾难(dimensionality curse),主要原因是存在数据重复.当数据量很大且维数很高时,距离计算和I/O操作将非常费时.提出了度量空间上新的空间分割方法和索引结构rgh-tree,利用数据库的数据对象与很少几个固定参考对象的距离信息进行数据分割和分布,产生一个各节点没有数据重复的平衡树.另外,在rgh-tree的基础上提出了相应的相似性搜索算法,该算法具有较小的I/O代价和距离计算次数,平均复杂性近似为o(n^0.58).解决了目前算法存在的一些问题.     

Fuzzy Diffusion Distance Learning for Cartoon Similarity Estimation

In this paper,a novel method called fuzzy diffusion maps (FDM) is proposed to evaluate cartoon similarity,which is critical to the applications of cartoon recognition,cartoon clustering and cartoon reusing.We find that the features from heterogeneous sources have different influence on cartoon similarity estimation.In order to take all the features into consideration,a fuzzy consistent relation is presented to convert the preference order of the features into preference degree,from which the weights are calculated.Based on the features and weights,the sum of the squared differences (L2) can be calculated between any cartoon data.However,it has been demonstrated in some research work that the cartoon dataset lies in a low-dimensional manifold,in which the L2 distance cannot evaluate the similarity directly.Unlike the global geodesic distance preserved in Isomap,the local neighboring relationship preserved in Locally Linear Embedding,and the local similarities of neighboring points preserved in Laplacian Eigenmaps,the diffusion maps we adopt preserve diffusion distance summing over all paths of length connecting the two data.As a consequence,this diffusion distance is very robust to noise perturbation.Our experiment in cartoon classification using Receiver Operating Curves shows fuzzy consistent relation’s excellent performance on weights assignment.The FDM’s performance on cartoon similarity evaluation is tested on the experiments of cartoon recognition and clustering.The results show that FDM can evaluate the cartoon similarity more precisely and stably compared with other methods.     

Discovery of a perceptual distance function for measuring image similarity

For more than a decade, researchers have actively explored the area of image/video analysis and retrieval. Yet one fundamental problem remains largely unsolved: how to measure perceptual similarity between two objects. For this purpose, most researchers employ a Minkowski-type metric. Unfortunately, the Minkowski metric does not reliably find similarities in objects that are obviously alike. Through mining a large set of visual data, our team has discovered a perceptual distance function. We call the discovered function the dynamic partial function (DPF). When we empirically compare DPF to Minkowski-type distance functions in image retrieval and in video shot-transition detection using our image features, DPF performs significantly better. The effectiveness of DPF can be explained by similarity theories in cognitive psychology.     

Phase Space Projection of Dynamical Systems

Dynamical systems are commonly used to describe the state of time-dependent systems. In many engineering and control problems, the state space is high-dimensional making it difficult to analyze and visualize the behavior of the system for varying input conditions. We present a novel dimensionality reduction technique that is tailored to high-dimensional dynamical systems. In contrast to standard general purpose dimensionality reduction algorithms, we use energy minimization to preserve properties of the flow in the high-dimensional space. Once the projection operator is optimized, further high-dimensional trajectories are projected easily. Our 3D projection maintains a number of useful flow properties, such as critical points and flow maps, and is optimized to match geometric characteristics of the high-dimensional input, as well as optional user constraints. We apply our method to trajectories traced in the phase spaces of second-order dynamical systems, including finite-sized objects in fluids, the circular restricted three-body problem and a damped double pendulum. We compare the projections with standard visualization techniques, such as PCA, t-SNE and UMAP, and visualize the dynamical systems with multiple coordinated views interactively, featuring a spatial embedding, projection to subspaces, our dimensionality reduction and a seed point exploration tool.     

一种利用极限学习机的数据可视化方法

提出一种利用极限学习机ELM的数据可视化方法,该方法利用多维尺度分析MDS、Pearson相关性、Spearman相关性代替常用的均方误差MSE实现高维数据投影到2-维平面的数据可视化。将所提方法与近期流行的随机邻域嵌入SNE及其改进的t-SNE方法对比,并通过局部连续元准则LCMC进行质量评测。结果表明:该方法的数据可视化结果及计算性能明显优于SNE及t-SNE方法;而在提出的三种学习规则中,基于MDS的学习规则效果最好。     

Collaborative image retrieval via regularized metric learning

In content-based image retrieval (CBIR), relevant images are identified based on their similarities to query images. Most CBIR algorithms are hindered by the semantic gap between the low-level image features used for computing image similarity and the high-level semantic concepts conveyed in images. One way to reduce the semantic gap is to utilize the log data of users' feedback that has been collected by CBIR systems in history, which is also called “collaborative image retrieval.” In this paper, we present a novel metric learning approach, named “regularized metric learning,” for collaborative image retrieval, which learns a distance metric by exploring the correlation between low-level image features and the log data of users' relevance judgments. Compared to the previous research, a regularization mechanism is used in our algorithm to effectively prevent overfitting. Meanwhile, we formulate the proposed learning algorithm into a semidefinite programming problem, which can be solved very efficiently by existing software packages and is scalable to the size of log data. An extensive set of experiments has been conducted to show that the new algorithm can substantially improve the retrieval accuracy of a baseline CBIR system using Euclidean distance metric, even with a modest amount of log data. The experiment also indicates that the new algorithm is more effective and more efficient than two alternative algorithms, which exploit log data for image retrieval.     

Local and global mappings of topology representing networks

As data analysis tasks often have to deal with complex data structures, the nonlinear dimensionality reduction methods play an important role in exploratory data analysis. In the literature a number of nonlinear dimensionality reduction techniques have been proposed (e.g. Sammon mapping, Locally Linear Embedding). These techniques attempt to preserve either the local or the global geometry of the original data, and they perform metric or non-metric dimensionality reduction. Nevertheless, it is difficult to apply most of them to large data sets. There is a need for new algorithms that are able to combine vector quantisation and mapping methods in order to visualise the data structure in a low-dimensional vector space. In this paper we define a new class of algorithms to quantify and disclose the data structure, that are based on the topology representing networks and apply different mapping methods to the low-dimensional visualisation. Not only existing methods are combined for that purpose but also a novel group of mapping methods (Topology Representing Network Map) are introduced as a part of this class. Topology Representing Network Maps utilise the main benefits of the topology representing networks and of the multidimensional scaling methods to disclose the real structure of the data set under study. To determine the main properties of the topology representing network based mapping methods, a detailed analysis of classical benchmark examples (Wine and Optical Recognition of Handwritten Digits data set) is presented.     

矢量地图水印的数据质量评价研究

含水印数据的质量评价是衡量水印嵌入隐蔽性和数据可用性的重要指标。峰值信噪比（PSNR）等基于能量的度量指标在应用于矢量地图水印系统时具有一定的局限性。从形状的角度考虑了矢量地图水印的数据质量评价问题,借鉴时间序列聚类和形状相似性匹配的思想,提出了基于距离度量的水印地图数据评价指标。算法从2维矢量地图中提取1维特征函数,通过度量水印嵌入前后特征函数的形状差异来评价含水印地图的数据质量。实验结果证明,本文提出的度量方法更符合矢量数据的特点,能够得到比现有方法更准确的度量结果。     

基于张量积扩散与纹理元相似的医学图像检索

针对医学图像检索中相似性表达的自身困难,以及噪声影响的问题,提出一种通过张量积图进行扩散,利用其他数据点的上下信息改进基于纹理元的成对相似性度量的方法。首先,采用纹理元的统计方法进行医学图像特征描述和提取,并通过对纹理元相似性加权,得到图像的成对相似性;然后,利用张量积图沿着数据点的内在流形进行相似性的传播,实现全局的相似性度量。在ImageCLEFmed 2009上的实验结果表明,该算法与基于Gabor的检索算法相比,其类平均精度提高了32%,与基于尺度不变特征转换(SIFT)的检索算法相比,其类平均精度提高了19%,能良好地应用于医学图像检索。