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

We present a new algorithm to detect humans in still images utilizing covariance matrices as object descriptors. Since these descriptors do not lie on a vector space, well known machine learning techniques are not adequate to learn the classifiers. The space of d-dimensional nonsingular covariance matrices can be represented as a connected Riemannian manifold. We present a novel approach for classifying points lying on a Riemannian manifold by incorporating the a priori information about the geometry of the space. The algorithm is tested on INRIA human database where superior detection rates are observed over the previous approaches.

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Human Detection via Classification on Riemannian Manifolds

Guiding image segmentation with edge information is an often employed strategy in low level computer vision. To improve the trade-off between the sensitivity of homogeneous region delineation and the over-segmentation on of the image, we have incorporated a recently proposed edge magnitude/confidence map into a color image segmenter based on the mean shift procedure. The new method can recover regions with weak but sharp boundaries and thus can provide a more accurate input for high level interpretation modules. The edge detection and image segmentation (EDISON) system, available for download, implements the proposed technique and provides a complete toolbox for discontinuity preserving filtering, segmentation and edge detection.

http://rutgersscholar.rutgers.edu/volume04/chrimeer/ChrisMeer.pdf

Synergism in low level vision

Computing the weighted average of the pixel values in a window is a basic module in many computer vision operators. The process is reformulated in a linear vector space and the role of the different subspaces is emphasized. Within this framework wellknown artifacts of the gradient-based edge detectors, such as large spurious responses can be explained quantitatively. It is also shown that template matching with a template derived from the input data is meaningful since it provides an independent measure of confidence in the presence of the employed edge model. The widely used three-step edge detection procedure - gradient estimation, non-maxima suppression, hysteresis thresholding - is generalized to include the information provided by the confidence measure. The additional amount of computation is minimal and experiments with several standard test images show the ability of the new procedure to detect weak edges.

Edge detection with embedded confidence

We present two solutions for the scale selection problem in computer vision. The first one is completely nonparametric and is based on the the adaptive estimation of the normalized density gradient. Employing the sample point estimator, we define the Variable Bandwidth Mean Shift, prove its convergence, and show its superiority over the fixed bandwidth procedure. The second technique has a semiparametric nature and imposes a local structure on the data to extract reliable scale information. The local scale of the underlying density is taken as the bandwidth which maximizes the magnitude of the normalized mean shift vector. Both estimators provide practical tools for autonomous image and quasi real-time video analysis and several examples are shown to illustrate their effectiveness.

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The variable bandwidth mean shift and data-driven scale selection

A clustering algorithm based on the minimum volume ellipsoid (MVE) robust estimator is proposed. The MVE estimator identifies the least volume region containing h percent of the data points. The clustering algorithm iteratively partitions the space into clusters without prior information about their number. At each iteration, the MVE estimator is applied several times with values of h decreasing from 0.5. A cluster is hypothesized for each ellipsoid. The shapes of these clusters are compared with shapes corresponding to a known unimodal distribution by the Kolmogorov-Smirnov test. The best fitting cluster is then removed from the space, and a new iteration starts. Constrained random sampling keeps the computation low. The clustering algorithm was successfully applied to several computer vision problems formulated in the feature space paradigm: multithresholding of gray level images, analysis of the Hough space, and range image segmentation. >

Peter Meer

Papers

Human Detection via Classification on Riemannian Manifolds

Synergism in low level vision

Edge detection with embedded confidence

The variable bandwidth mean shift and data-driven scale selection

Robust clustering with applications in computer vision