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

Two new techniques based on nonparametric estimation of probability densities are introduced which improve on the performance of equivalent robust methods currently employed in computer vision. The first technique draws from the projection pursuit paradigm in statistics, and carries out regression M-estimation with a weak dependence on the accuracy of the scale estimate. The second technique exploits the properties of the multivariate adaptive mean shift, and accomplishes the fusion of uncertain measurements arising from an unknown number of sources. As an example, the two techniques are extensively used in an algorithm for the recovery of multiple structures from heavily corrupted data.

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Robust Computer Vision through Kernel Density Estimation

Robust and fast 3D tracking of deformable objects, such as heart, is a challenging task because of the relatively low image contrast and speed requirement. Many existing 2D algorithms might not be directly applied on the 3D tracking problem. The 3D tracking performance is limited due to dramatically increased data size, landmarks ambiguity, signal drop-out or complex nonrigid deformation. In this paper, we present a robust, fast, and accurate 3D tracking algorithm: prediction based collaborative trackers (PCT). A novel one-step forward prediction is introduced to generate the motion prior using motion manifold learning. Collaborative trackers are introduced to achieve both temporal consistency and failure recovery. Compared with tracking by detection and 3D optical flow, PCT provides the best results. The new tracking algorithm is completely automatic and computationally efficient. It requires less than 1.5 s to process a 3D volume which contains millions of voxels. In order to demonstrate the generality of PCT, the tracker is fully tested on three large clinical datasets for three 3D heart tracking problems with two different imaging modalities: endocardium tracking of the left ventricle (67 sequences, 1134 3D volumetric echocardiography data), dense tracking in the myocardial regions between the epicardium and endocardium of the left ventricle (503 sequences, roughly 9000 3D volumetric echocardiography data), and whole heart four chambers tracking (20 sequences, 200 cardiac 3D volumetric CT data). Our datasets are much larger than most studies reported in the literature and we achieve very accurate tracking results compared with human experts' annotations and recent literature.

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Prediction Based Collaborative Trackers (PCT): A Robust and Accurate Approach Toward 3D Medical Object Tracking

A new method for 3D rigid motion estimation is derived under the most general assumption that the measurements are corrupted by inhomogeneous and anisotropic, i.e., heteroscedastic noise. This is the case, for example, when the motion of a calibrated stereo-head is to be determined from image pairs. Linearization in the quaternion space transforms the problem into a multivariate, heteroscedastic errors-in-variables (HEIV) regression, from which the rotation and translation estimates are obtained simultaneously. The significant performance improvement is illustrated, for real data, by comparison with the results of quaternion, subspace and renormalization based approaches described in the literature. Extensive use as made of bootstrap, an advanced numerical tool from statistics, both to estimate the covariances of the 3D data points and to obtain confidence regions for the rotation and translation estimates. Bootstrap enables an accurate recovery of these information using only the two image pairs serving as input.

Optimal rigid motion estimation and performance evaluation with bootstrap

A general method for eliminating the bias of nonlinear estimators using bootstrap is presented. Instead of the traditional mean bias we consider the definition of bias based on the median. The method is applied to the problem of fitting ellipse segments to noisy data. No assumption beyond being independent identically distributed is made about the error distribution and experiments with both synthetic and real data prove the effectiveness of the technique.

Unbiased estimation of ellipses by bootstrapping

Automatic image analysis of histopathology specimens would help the early detection of blood cancer. The first step for automatic image analysis is segmentation. However, touching cells bring the difficulty for traditional segmentation algorithms. In this paper, we propose a novel algorithm which can reliably handle touching cells segmentation. Robust estimation and color active contour models are used to delineate the outer boundary. Concave points on the boundary and inner edges are automatically detected. A concave vertex graph is constructed from these points and edges. By minimizing a cost function based on morphological characteristics, we recursively calculate the optimal path in the graph to separate the touching cells. The algorithm is computationally efficient and has been tested on two large clinical dataset which contain 207 images and 3898 images respectively. Our algorithm provides better results than other studies reported in the recent literature.

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Peter Meer

Papers

Robust Computer Vision through Kernel Density Estimation

Prediction Based Collaborative Trackers (PCT): A Robust and Accurate Approach Toward 3D Medical Object Tracking

Optimal rigid motion estimation and performance evaluation with bootstrap

Unbiased estimation of ellipses by bootstrapping

Automatic Image Analysis of Histopathology Specimens Using Concave Vertex Graph