Clustering is the unsupervised classification of patterns (observations, data items, or feature vectors) into groups (clusters). The clustering problem has been addressed in many contexts and by researchers in many disciplines; this reflects its broad appeal and usefulness as one of the steps in exploratory data analysis. However, clustering is a difficult problem combinatorially, and differences in assumptions and contexts in different communities has made the transfer of useful generic concepts and methodologies slow to occur. This paper presents an overview of pattern clustering methods from a statistical pattern recognition perspective, with a goal of providing useful advice and references to fundamental concepts accessible to the broad community of clustering practitioners. We present a taxonomy of clustering techniques, and identify cross-cutting themes and recent advances. We also describe some important applications of clustering algorithms such as image segmentation, object recognition, and information retrieval.

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Data clustering: a review

A general non-parametric technique is proposed for the analysis of a complex multimodal feature space and to delineate arbitrarily shaped clusters in it. The basic computational module of the technique is an old pattern recognition procedure: the mean shift. For discrete data, we prove the convergence of a recursive mean shift procedure to the nearest stationary point of the underlying density function and, thus, its utility in detecting the modes of the density. The relation of the mean shift procedure to the Nadaraya-Watson estimator from kernel regression and the robust M-estimators; of location is also established. Algorithms for two low-level vision tasks discontinuity-preserving smoothing and image segmentation - are described as applications. In these algorithms, the only user-set parameter is the resolution of the analysis, and either gray-level or color images are accepted as input. Extensive experimental results illustrate their excellent performance.

Mean shift: a robust approach toward feature space analysis

Computer vision applications have come to rely increasingly on superpixels in recent years, but it is not always clear what constitutes a good superpixel algorithm. In an effort to understand the benefits and drawbacks of existing methods, we empirically compare five state-of-the-art superpixel algorithms for their ability to adhere to image boundaries, speed, memory efficiency, and their impact on segmentation performance. We then introduce a new superpixel algorithm, simple linear iterative clustering (SLIC), which adapts a k-means clustering approach to efficiently generate superpixels. Despite its simplicity, SLIC adheres to boundaries as well as or better than previous methods. At the same time, it is faster and more memory efficient, improves segmentation performance, and is straightforward to extend to supervoxel generation.

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SLIC Superpixels Compared to State-of-the-Art Superpixel Methods

This paper presents a database containing 'ground truth' segmentations produced by humans for images of a wide variety of natural scenes. We define an error measure which quantifies the consistency between segmentations of differing granularities and find that different human segmentations of the same image are highly consistent. Use of this dataset is demonstrated in two applications: (1) evaluating the performance of segmentation algorithms and (2) measuring probability distributions associated with Gestalt grouping factors as well as statistics of image region properties.

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A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics

This paper addresses the problem of generating possible object locations for use in object recognition. We introduce selective search which combines the strength of both an exhaustive search and segmentation. Like segmentation, we use the image structure to guide our sampling process. Like exhaustive search, we aim to capture all possible object locations. Instead of a single technique to generate possible object locations, we diversify our search and use a variety of complementary image partitionings to deal with as many image conditions as possible. Our selective search results in a small set of data-driven, class-independent, high quality locations, yielding 99 % recall and a Mean Average Best Overlap of 0.879 at 10,097 locations. The reduced number of locations compared to an exhaustive search enables the use of stronger machine learning techniques and stronger appearance models for object recognition. In this paper we show that our selective search enables the use of the powerful Bag-of-Words model for recognition. The selective search software is made publicly available (Software: http://disi.unitn.it/~uijlings/SelectiveSearch.html ).

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Selective Search for Object Recognition

The sparse representation has been widely used in many areas and utilized for visual tracking. Tracking with sparse representation is formulated as searching for samples with minimal reconstruction errors from learned template subspace. However, the computational cost makes it unsuitable to utilize high dimensional advanced features which are often important for robust tracking under dynamic environment. Based on the observations that a target can be reconstructed from several templates, and only some of the features with discriminative power are significant to separate the target from the background, we propose a novel online tracking algorithm with two stage sparse optimization to jointly minimize the target reconstruction error and maximize the discriminative power. As the target template and discriminative features usually have temporal and spatial relationship, dynamic group sparsity (DGS) is utilized in our algorithm. The proposed method is compared with three state-of-art trackers using five public challenging sequences, which exhibit appearance changes, heavy occlusions, and pose variations. Our algorithm is shown to outperform these methods.

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Robust and fast collaborative tracking with two stage sparse optimization

The systems described herein include tools for computer-assisted evaluation of objective characteristics of pathologies A diagnostic system arranged according to the teachings herein provides computer support for those tasks well suited to objective analysis, along with human decision making where substantial discretion is involved Collaborative diagnosis may be provided through shared access to data and shared control over a diagnostic tool, such as a telemicroscope, and messaging service for clinicians who may be at remote locations These aspects of the system, when working in cooperation with one another, may achieve improved diagnostic accuracy or early detection for pathologies such as lymphoma

Collaborative diagnostic systems

We present an algorithm to estimate the parameters of a linear model in the presence of heteroscedastic noise, i.e., each data point having a different covariance matrix. The algorithm is motivated by the recovery of bilinear forms, one of the fundamental problems in computer vision which appears whenever the epipolar constraint is imposed, or a conic is fit to noisy data points. We employ the errors-in-variables (EIV) model and show why already at moderate noise levels most available methods fail to provide a satisfactory solution. The improved behavior of the new algorithm is due to two factors: taking into account the heteroscedastic nature of the errors arising from the linearization of the bilinear form, and the use of generalized singular value decomposition (GSVD) in the computations. The performance of the algorithm is compared with several methods proposed in the literature for ellipse fitting and estimation of the fundamental matrix. It is shown that the algorithm achieves the accuracy of nonlinear optimization techniques at much less computational cost.

Heteroscedastic Regression in Computer Vision: Problems with Bilinear Constraint

A novel multiresolution image analysis technique based on hierarchies of irregular tessellations generated in parallel by independent stochastic processes is presented. Like traditional image pyramids these hierarchies are constructed in a number of steps on the order of log(image-size) steps. However, the structure of a hierarchy is adapted to the image content and artifacts of rigid resolution reduction are avoided. Two applications of these techniques are presented: connected component analysis of labeled images and segmentation of gray level images. In labeled images, every connected component is reduced to a separate root, with the adjacency relations among the components also extracted. In gray level images the output is a segmentation of the image into a small number of classes as well as the adjacency graph of the classes. >

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Hierarchical image analysis using irregular tessellations

The original mean shift algorithm is widely applied for nonparametric clustering in vector spaces. In this paper we generalize it to data points lying on Riemannian manifolds. This allows us to extend mean shift based clustering and filtering techniques to a large class of frequently occurring non-vector spaces in vision. We present an exact algorithm and prove its convergence properties as opposed to previous work which approximates the mean shift vector. The computational details of our algorithm are presented for frequently occurring classes of manifolds such as matrix Lie groups, Grassmann manifolds, essential matrices and symmetric positive definite matrices. Applications of the mean shift over these manifolds are shown.

Peter Meer

Papers

Robust and fast collaborative tracking with two stage sparse optimization

Collaborative diagnostic systems

Heteroscedastic Regression in Computer Vision: Problems with Bilinear Constraint

Hierarchical image analysis using irregular tessellations

Nonlinear Mean Shift over Riemannian Manifolds