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.

/pdf/data-clustering-a-review-4c452f5cab.pdf

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.

/pdf/slic-superpixels-compared-to-state-of-the-art-superpixel-5d8sq04am9.pdf

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.

/pdf/a-database-of-human-segmented-natural-images-and-its-2ve1vk356s.pdf

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 ).

/pdf/selective-search-for-object-recognition-3yqeb0u837.pdf

Selective Search for Object Recognition

Real-world visual data are often corrupted and require the use of estimation techniques that are robust to noise and outliers. Robust methods are well studied for Euclidean spaces and their use has also been extended to Riemannian spaces. In this chapter, we present the necessary mathematical constructs for Grassmann manifolds, followed by two different algorithms that can perform robust estimation on them. In the first one, we describe a nonlinear mean shift algorithm for finding modes of the underlying kernel density estimate (KDE). In the second one, a user-independent robust regression algorithm, the generalized projection-based M-estimator (gpbM), is detailed. We show that the gpbM estimates are significantly improved if KDE optimization over the Grassmann manifold is also included. The results for a few real-world computer vision problems are shown to demonstrate the importance of performing robust estimation using Grassmann manifolds.

Robust Estimation for Computer Vision Using Grassmann Manifolds

The problem of parallel, bottom-up construction of hierarchical structures adapted to the content of an input image is addressed. This principle is essential in image analysis and understanding. For each level of the structure, which is related to a resolution level, the region adjacency graph of a segmentation of the input image is defined. All segmentation and resolution reduction operations are local, and therefore a complete input-dependent hierarchy can be built in O[log(image-size)]. The region adjacency graph contraction is achieved by extracting a maximal independent set (MIS) of the graph. A new parallel probabilistic method for MIS computation is proposed and discussed. The representation uncertainty introduced by the probabilistic component of the hierarchy construction is reduced through consensus among an ensemble of outputs obtained from the same input image.

Hierarchical Shape Analysis in Grey-level Images

Simulation of constant size multi-resolution representations on image pyramids

Robust recovery of 3d geometric primitives from point cloud

Random Sample Consensus (RANSAC) is the most widely used robust regression algorithm in computer vision. However, RANSAC has a few drawbacks which make it difficult to use for practical applications. Some of these problems have been addressed through improved sampling algorithms or better cost functions, but an important difficulty still remains. The algorithm is not user independent, and requires knowledge of the scale of the inlier noise. We propose a new robust regression algorithm, the projection based M-estimator (pbM). The pbM algorithm is derived by building a connection to the theory of kernel density estimation and this leads to an improved cost function, which gives better performance. Furthermore, pbM is user independent and does not require any knowledge of the scale of noise corrupting the inliers. We propose a general framework for the pbM algorithm which can handle heteroscedastic data and multiple linear constraints on each data point through the use of Grassmann manifold theory. The performance of pbM is compared with RANSAC and M-Estimator Sample Consensus (MSAC) on various real problems. It is shown that pbM gives better results than RANSAC and MSAC in spite of being user independent.

Peter Meer

Papers

Robust Estimation for Computer Vision Using Grassmann Manifolds

Hierarchical Shape Analysis in Grey-level Images

Simulation of constant size multi-resolution representations on image pyramids

Robust recovery of 3d geometric primitives from point cloud

Projection Based M-Estimators