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46
Face alignment through subspace constrained mean-shifts
- in Proc. Int. Conf. Computer Vision
"... Deformable model fitting has been actively pursued in the computer vision community for over a decade. As a result, numerous approaches have been proposed with varying degrees of success. A class of approaches that has shown substantial promise is one that makes independent predictions regarding loc ..."
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Cited by 93 (10 self)
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Deformable model fitting has been actively pursued in the computer vision community for over a decade. As a result, numerous approaches have been proposed with varying degrees of success. A class of approaches that has shown substantial promise is one that makes independent predictions regarding locations of the model’s landmarks, which are combined by enforcing a prior over their joint motion. A common theme in innovations to this approach is the replacement of the distribution of probable landmark locations, obtained from each local detector, with simpler parametric forms. This simplification substitutes the true objective with a smoothed version of itself, reducing sensitivity to local minima and outlying detections. In this work, a principled optimization strategy is proposed where a nonparametric representation of the landmark distributions is maximized within a hierarchy of smoothed estimates. The resulting update equations are reminiscent of mean-shift but with a subspace constraint placed on the shape’s variability. This approach is shown to outperform other existing methods on the task of generic face fitting. 1.
Gaussian mean shift is an EM algorithm
- IEEE Trans. on Pattern Analysis and Machine Intelligence
, 2005
"... The mean-shift algorithm, based on ideas proposed by Fukunaga and Hostetler (1975), is a hill-climbing algorithm on the density defined by a finite mixture or a kernel density estimate. Mean-shift can be used as a nonparametric clustering method and has attracted recent attention in computer vision ..."
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Cited by 42 (4 self)
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The mean-shift algorithm, based on ideas proposed by Fukunaga and Hostetler (1975), is a hill-climbing algorithm on the density defined by a finite mixture or a kernel density estimate. Mean-shift can be used as a nonparametric clustering method and has attracted recent attention in computer vision applications such as image segmentation or tracking. We show that, when the kernel is Gaussian, mean-shift is an expectationmaximisation (EM) algorithm, and when the kernel is non-gaussian, mean-shift is a generalised EM algorithm. This implies that mean-shift converges from almost any starting point and that, in general, its convergence is of linear order. For Gaussian mean-shift we show: (1) the rate of linear convergence approaches 0 (superlinear convergence) for very narrow or very wide kernels, but is often close to 1 (thus extremely slow) for intermediate widths, and exactly 1 (sublinear convergence) for widths at which modes merge; (2) the iterates approach the mode along the local principal component of the data points from the inside of the convex hull of the data points; (3) the convergence domains are nonconvex and can be disconnected and show fractal behaviour. We suggest ways of accelerating mean-shift based on the EM interpretation.
Nonlinear Mean Shift over Riemannian Manifolds
, 2009
"... 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- ..."
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Cited by 37 (1 self)
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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.
Intrinsic Mean Shift for Clustering on Stiefel and Grassmann Manifolds
"... The mean shift algorithm, which is a nonparametric density estimator for detecting the modes of a distribution on a Euclidean space, was recently extended to operate on analytic manifolds. The extension is extrinsic in the sense that the inherent optimization is performed on the tangent spaces of th ..."
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Cited by 25 (0 self)
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The mean shift algorithm, which is a nonparametric density estimator for detecting the modes of a distribution on a Euclidean space, was recently extended to operate on analytic manifolds. The extension is extrinsic in the sense that the inherent optimization is performed on the tangent spaces of these manifolds. This approach specifically requires the use of the exponential map at each iteration. This paper presents an alternative mean shift formulation, which performs the iterative optimization “on ” the manifold of interest and intrinsically locates the modes via consecutive evaluations of a mapping. In particular, these evaluations constitute a modified gradient ascent scheme that avoids the computation of the exponential maps for Stiefel and Grassmann manifolds. The performance of our algorithm is evaluated by conducting extensive comparative studies on synthetic data as well as experiments on object categorization and segmentation of multiple motions. 1.
Incremental majorization-minimization optimization with application to large-scale machine learning
, 2015
"... Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective function downhill. Such a simple principle is widely applicable ..."
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Cited by 23 (1 self)
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Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective function downhill. Such a simple principle is widely applicable and has been very popular in various scientific fields, especially in signal processing and statistics. We propose an incremental majorization-minimization scheme for minimizing a large sum of continuous functions, a problem of utmost importance in machine learning. We present convergence guarantees for nonconvex and convex optimization when the upper bounds approximate the objective up to a smooth error; we call such upper bounds “first-order surrogate functions.” More precisely, we study asymptotic stationary point guarantees for nonconvex problems, and for convex ones, we provide convergence rates for the expected objective function value. We apply our scheme to composite optimization and obtain a new incremental proximal gradient algorithm with linear convergence rate for strongly convex functions. Our experiments show that our method is competitive with the state of the art for solving machine learning problems such as logistic regression when the number of training samples is large enough, and we demonstrate its usefulness for sparse estimation with nonconvex penalties.
Fast Global Kernel Density Mode Seeking with Application to Localisation and Tracking
- In IEEE International Conference on Computer Vision
, 2005
"... We address the problem of seeking the global mode of a density function using the mean shift algorithm. Mean shift, like other gradient ascent optimisation methods, is susceptible to local maxima, and hence often fails to find the desired global maximum. In this work, we propose a multi-bandwidth me ..."
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Cited by 13 (1 self)
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We address the problem of seeking the global mode of a density function using the mean shift algorithm. Mean shift, like other gradient ascent optimisation methods, is susceptible to local maxima, and hence often fails to find the desired global maximum. In this work, we propose a multi-bandwidth mean shift procedure that avoids this problem, which we term annealed mean shift, as it shares similarities with the annealed importance sampling procedure. The bandwidth of the algorithm plays the same role as the temperature in annealing. We observe that the over-smoothed density function with a sufficiently large bandwidth is uni-modal. Using a continuation principle, the influence of the global peak in the density function is introduced gradually. In this way the global maximum is more reliably located. Generally, the price of this annealing-like procedure is that more iterations are required. Since it is imperative that the computation complexity is minimal in real-time applications such as visual tracking. We propose an accelerated version of the mean shift algorithm. Compared with the conventional mean shift algorithm, annealed mean shift can significantly decrease the number of iterations required for convergence. The proposed algorithm is applied to the problems of visual tracking and object localisation. We empirically show on various data sets that the proposed algorithm can reliably find the true object location when the starting position of mean shift is far away from the global maximum, in contrast with the conventional mean shift algorithm that will usually get trapped in a spurious local maximum.
Featurepreserving MRI denoising: A nonparametric empirical bayes approach
- IEEE Transactions On Medical Imaging
, 2007
"... Abstract—This paper presents a novel method for Bayesian denoising of magnetic resonance (MR) images that bootstraps itself by inferring the prior, i.e., the uncorrupted-image statis-tics, from the corrupted input data and the knowledge of the Rician noise model. The proposed method relies on princi ..."
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Cited by 13 (0 self)
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Abstract—This paper presents a novel method for Bayesian denoising of magnetic resonance (MR) images that bootstraps itself by inferring the prior, i.e., the uncorrupted-image statis-tics, from the corrupted input data and the knowledge of the Rician noise model. The proposed method relies on principles from empirical Bayes (EB) estimation. It models the prior in a nonparametric Markov random field (MRF) framework and estimates this prior by optimizing an information-theoretic metric using the expectation-maximization algorithm. The generality and power of nonparametric modeling, coupled with the EB approach for prior estimation, avoids imposing ill-fitting prior models for denoising. The results demonstrate that, unlike typical denoising methods, the proposed method preserves most of the important features in brain MR images. Furthermore, this paper presents a novel Bayesian-inference algorithm on MRFs, namely iterated conditional entropy reduction (ICER). This paper also extends the application of the proposed method for denoising diffusion-weighted MR images. Validation results and quantita-tive comparisons with the state of the art in MR-image denoising clearly depict the advantages of the proposed method. Index Terms—Denoising, empirical Bayes (EB), information theory, Markov random fields (MRF), nonparametric statistics.
Scale and Orientation Adaptive Mean Shift Tracking
"... Abstract – A scale and orientation adaptive mean shift tracking (SOAMST) algorithm is proposed in this paper to address the problem of how to estimate the scale and orientation changes of the target under the mean shift tracking framework. In the original mean shift tracking algorithm, the position ..."
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Cited by 10 (0 self)
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Abstract – A scale and orientation adaptive mean shift tracking (SOAMST) algorithm is proposed in this paper to address the problem of how to estimate the scale and orientation changes of the target under the mean shift tracking framework. In the original mean shift tracking algorithm, the position of the target can be well estimated, while the scale and orientation changes can not be adaptively estimated. Considering that the weight image derived from the target model and the candidate model can represent the possibility that a pixel belongs to the target, we show that the original mean shift tracking algorithm can be derived using the zero th and the first order moments of the weight image. With the zero th order moment and the Bhattacharyya coefficient between the target model and candidate model, a simple and effective method is proposed to estimate the scale of target. Then an approach, which utilizes the estimated area and the second order center moment, is proposed to adaptively estimate the width, height and orientation changes of the target. Extensive experiments are performed to testify the proposed method and validate its robustness to the
Accelerated Convergence Using Dynamic Mean Shift
"... Abstract. Mean shift is an iterative mode-seeking algorithm widely used in pattern recognition and computer vision. However, its convergence is sometimes too slow to be practical. In this paper, we improve the convergence speed of mean shift by dynamically updating the sample set during the iteratio ..."
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Cited by 6 (0 self)
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Abstract. Mean shift is an iterative mode-seeking algorithm widely used in pattern recognition and computer vision. However, its convergence is sometimes too slow to be practical. In this paper, we improve the convergence speed of mean shift by dynamically updating the sample set during the iterations, and the resultant procedure is called dynamic mean shift (DMS). When the data is locally Gaussian, it can be shown that both the standard and dynamic mean shift algorithms converge to the same optimal solution. However, while standard mean shift only has linear convergence, the dynamic mean shift algorithm has superlinear convergence. Experiments on color image segmentation show that dynamic mean shift produces comparable results as the standard mean shift algorithm, but can significantly reduce the number of iterations for convergence and takes much less time. 1
Kernel Methods for Weakly Supervised Mean Shift Clustering
"... Mean shift clustering is a powerful unsupervised data analysis technique which does not require prior knowledge of the number of clusters, and does not constrain the shape of the clusters. The data association criteria is based on the underlying probability distribution of the data points which is d ..."
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Cited by 6 (1 self)
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Mean shift clustering is a powerful unsupervised data analysis technique which does not require prior knowledge of the number of clusters, and does not constrain the shape of the clusters. The data association criteria is based on the underlying probability distribution of the data points which is defined in advance via the employed distance metric. In many problem domains, the initially designed distance metric fails to resolve the ambiguities in the clustering process. We present a novel semi-supervised kernel mean shift algorithm where the inherent structure of the data points is learned with a few user supplied constraints in addition to the original metric. The constraints we consider are the pairs of points that should be clustered together. The data points are implicitly mapped to a higher dimensional space induced by the kernel function where the constraints can be effectively enforced. The mode seeking is then performed on the embedded space and the approach preserves all the advantages of the original mean shift algorithm. Experiments on challenging synthetic and real data clearly demonstrate that significant improvements in clustering accuracy can be achieved by employing only a few constraints. 1.
