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Mean shift algorithm equipped with the intersection of confidence intervals rule for image segmentation
Abstract
The mean shift algorithm equipped with the intersection of confidence intervals (ICI) rule for image smoothing and segmentation is proposed. Firstly, the ICI rule for bandwidth selection in a multi-dimensional feature space is studied. In the ICI rule, the kernel function is used to estimate the probability density intervals of the pixel feature and find its bandwidth close to the optimal parameter. Secondly, the mean shift algorithm is used for image smoothing and segmentation with the bandwidth determined by the ICI rule. Experimental results show that the structures of the objects in images are preserved and over-segmentation caused by noises and texture can be eliminated effectively. In addition, a comparison between the smoothing results with adaptive bandwidths determined by the ICI rule and with fixed bandwidths is done. The results show that the proposed method is better in the field of image smoothing and segmentation.
... Using the segmentation and classification tools in ArcGIS 10.3, we converted the 58 multi-band Landsat 5 satellite images into 58 unsupervised classifications, which we refer to as "Events", following the BULC and BULC-U work flow [15,20] (Figure 3). Using the Segment Mean Shift tool [25] in ArcGIS 10.3, we identified features in each image that were spectrally distinct and spatially contiguous, with each class being spectrally uniform with little speckling for each class. After identifying the segments, each band was re-computed using the mean value within the segment as the value for all pixels within the segment. ...
... The number of pixels in each class was large enough that BULC-U could relate them to the coverage in the GlobCover 2009 image, but small enough that each unsupervised class tended to be dominated by just one of the LULC classes tracked through the study. Using the Segment Mean Shift tool [25] in ArcGIS 10.3, we identified features in each image that were spectrally distinct and spatially contiguous, with each class being spectrally uniform with little speckling for each class. After identifying the segments, each band was re-computed using the mean value within the segment as the value for all pixels within the segment. ...
Landsat 5 has produced imagery for decades that can now be viewed and manipulated in Google Earth Engine, but a general, automated way of producing a coherent time series from these images—particularly over cloudy areas in the distant past—is elusive. Here, we create a land use and land cover (LULC) time series for part of tropical Mato Grosso, Brazil, using the Bayesian Updating of Land Cover: Unsupervised (BULC-U) technique. The algorithm built backward in time from the GlobCover 2009 data set, a multi-category global LULC data set at 300 m resolution for the year 2009, combining it with Landsat time series imagery to create a land cover time series for the period 1986–2000. Despite the substantial LULC differences between the 1990s and 2009 in this area, much of the landscape remained the same: we asked whether we could harness those similarities and differences to recreate an accurate version of the earlier LULC. The GlobCover basis and the Landsat-5 images shared neither a common spatial resolution nor time frame, But BULC-U successfully combined the labels from the coarser classification with the spatial detail of Landsat. The result was an accurate fine-scale time series that quantified the expansion of deforestation in the study area, which more than doubled in size during this time. Earth Engine directly enabled the fusion of these different data sets held in its catalog: its flexible treatment of spatial resolution, rapid prototyping, and overall processing speed permitted the development and testing of this study. Many would-be users of remote sensing data are currently limited by the need to have highly specialized knowledge to create classifications of older data. The approach shown here presents fewer obstacles to participation and allows a wide audience to create their own time series of past decades. By leveraging both the varied data catalog and the processing speed of Earth Engine, this research can contribute to the rapid advances underway in multi-temporal image classification techniques. Given Earth Engine’s power and deep catalog, this research further opens up remote sensing to a rapidly growing community of researchers and managers who need to understand the long-term dynamics of terrestrial systems.
... The oil tea varieties planted are the Xianglin series, which have high yield, disease resistance, and high quality. density gradient estimation and has been widely used in image smoothing [42], seg tation [43,44], and video tracking [45,46]. However, compared to other algorithms accuracy of clustering and recognition is limited in complex situations. ...
Oil tea (Camellia oleifera) is one of the world’s major woody edible oil plants and is vital in providing food and raw materials and ensuring water conservation. The yield of oil tea can directly reflect the growth condition of oil tea forests, and rapid and accurate yield measurement is directly beneficial to efficient oil tea forest management. Light detection and ranging (LiDAR), which can penetrate the canopy to acquire the geometric attributes of targets, has become an effective and popular method of yield identification for agricultural products. However, the common geometric attribute information obtained by LiDAR systems is always limited in terms of the accuracy of yield identi-fication. In this study, to improve yield identification efficiency and accuracy, the red-green-blue (RGB) and luminance-bandwidth-chrominance (i.e., YUV color spaces) were used to identify the point clouds of oil tea fruits. An optimized mean shift clustering algorithm was constructed for oil tea fruit point cloud extraction and product identification. The point cloud data of oil tea trees were obtained using terrestrial laser scanning (TLS), and field measurements were conducted in Changsha County, central China. In addition, the common mean shift, density-based spatial clus-tering of applications with noise (DBSCAN), and maximum–minimum distance clustering were established for comparison and validation. The results showed that the optimized mean shift clustering algorithm achieved the best identification in both the RGB and YUV color spaces, with detection ratios that were 9.02%, 54.53%, and 3.91% and 7.05%, 62.35%, and 10.78% higher than those of the common mean shift clustering, DBSCAN clustering, and maximum-minimum distance clustering algorithms, respectively. In addition, the improved mean shift clustering algorithm achieved a higher recognition rate in the YUV color space, with an average detection rate of 81.73%, which was 2.4% higher than the average detection rate in the RGB color space. Therefore, this method can perform efficient yield identification of oil tea and provide a new reference for agri-cultural product management.
... This classification method performs detection and delineation, not only based on pixel but also based on object segmentation. Image segmentation techniques using the algorithm Mean-shift [8][9][10] have been used in several forest resource studies, such as the use of unmanned imagery in the inventory of nipah vegetation with overall and kappa accuracy of 76.6 % and 55.7% [11] and environmental management monitoring [12]. Detection of land use changes images Synthetic Aperture Radar (SAR) with mean shifts shows better detection and identification capabilities than classic log ratios [13], detection of forest changes due to storms using OBIA [14]. ...
In the last two decades there has been significant leap on the spatial resolution of the satellite digital images which may be very useful for estimating stand parameter required for forest as well as environment management. This paper describes development of stand volume estimator models using SPOT 6 panchromatic and multispectral images with an object-based digital image analysis (OBIA) and conventional pixel-based approaches. The data used include panchromatic band with1.5m spatial resolution, and multispectral band with6m spatial resolution. The proposed OBIA technique with mean-shift algorithm was functioned to derive a canopy cover variable from the fusion of the panchromatic and multispectral, while the pixel-based vegetation index was used to develop model with an original pixel-size of 6 m. The estimator models were established based on 65 sample plots both measured in the field and images. The study found that the OBIA provides more accurate identification with Kappa Accuracy (KA) of 71% and Overall Accuracy (OA) of 86%. The study concluded that the best stand volume estimation model is the model that developed from the canopy cover (C) derived from OBIA i.e., v = 13.47e0.032C with mean deviation of only 0.92%, better than the model derived from conventional pixel-based approach, i.e., v = 0.0000067e16.48TNDVI with a mean deviation of 5.37%.
... A method that originally proposed this kind of adaptive filtering [19] was shown to efficiently adapt to unknown smoothness of the signal [20] ensuring close to optimal bias-to-variance trade-off [21], getting its name based on its functionality as the intersection of confidence intervals (ICI) method [20]. The goal of the ICI based denoising procedure is to obtain discrete estimatesŷ(t i ) as close as possible to the noise-free signal y(t i ); the ICI method does so by selecting upper and lower boundaries of confidence interval to track non-emptiness of confidence intervals intersection, whose limits can be expressed as: ...
Abstract The brain dynamics in the electroencephalogram (EEG) data are often challenging to interpret, specially when the signal is a combination of desired brain dynamics and noise. Thus, in an EEG signal, anything other than the desired electrical activity, which is produced due to coordinated electrochemical process, can be considered as unwanted or noise. To make brain dynamics more analyzable, it is necessary to remove noise in the temporal location of interest, as well as to denoise data from a specific spatial location. In this paper, we propose a novel method for noisy EEG analysis with accompanying toolbox which includes adaptive, data-driven noise removal technique based on the improved intersection of confidence interval (ICI)-based algorithm. Next, a local entropy-based method for EEG data analysis was designed and included in the toolbox. As shown in the paper, the relative intersection of confidence interval (RICI) procedure retains the dominant dipole activity projected on electrodes, while the local (short-term) Rényi entropy-based analysis of the EEG representation in the time-frequency domain is efficient in detecting the presence of P300 event-related potential (ERP) at specific electrodes. Namely, the P300 are detected as sharp drop of entropy in the temporal domain that enabled accurate calculation of the index of the noise class for the EEG signals.
... The mean shift algorithm obtains the gradient vector by estimating the probability density gradient of feature parameters. The image pixels are clustered along the gradient direction in order to segment the image [PENG, T.G. WU, T.H. 2007]. Conversion of the image from RGB to other colour model will cost more computational time and slow down the classification system. ...
... The mean shift algorithm obtains the gradient vector by estimating the probability density gradient of feature parameters. The image pixels are clustered along the gradient direction in order to segment the image [11]. ...
Foreign fibers in cotton have seriously affected the quality of cotton products. The classification and identification of foreign fibers in cotton is the foundation of cotton foreign fiber automated inspection. The paper takes the typical cotton foreign fibers in China’s textile enterprises as the research object, and acquires the images under simulated actual cotton processing. The various classification features are calculated and analyzed. The results show that aspect ratio, roundness, duty cycle and I1I1 are the effective features for classifying various foreign fibers. The paper puts forward a classifier of cotton foreign fibers based on a support vector machine. A Decision Tree Support Vector Machine (DTSVM) can not only avoid the non-separated region, but also improve the training speed while the training sample number gradually decreases, going through the decision tree. The DTSVM is to be used to identify the sorts of common foreign fibers in cotton. The experimental data set shows that the rates of identifying different kinds of foreign fibers are greater than 92% using the proposed DTSVM.
Defect segmentation results affect the precision of classification in the automatic strip surface defect detection system. In order to obtain a better result, the mean shift algorithm is presented to segment the defects in strip images. The mean shift algorithm is used to smooth the region of interest in the image and detect the defect's edge, and its effectiveness is compared with that of the median filter. Test results show that it can smooth strip images effectively and can detect the edges of defect objects accurately. The mean shift algorithm can work effectively in strip image segmentation.
This paper firstly proposes an algorithm of moving object detection and extraction, and places the extracted object in the mixed reality. The movement tendency of the moving objects is tracked by the value of mean shifting algorithm, so the computation of the frame difference can be reduced. The appropriate threshold is selected and frame difference is improved by using the histogram. The “holes” and “double shadows” phenomena are reduced and the foreground image is enhanced. The experiment shows that this method can not only improve the detection rate, but also have strong robustness.
Snakes have been extensively used for object segmentation and tracking in computer vision and image processing applications. One of these drawbacks is that they converge slowly, since inverse matrix is computed at each iteration. We have introduced a new external force model, called mean-shift flow field (MSFF). This external force model is computed by a novel and fast mean-shift mask. This type of snake has the feature that it can enhance the convergence rates, and at the same time, maintain the properties of the traditional and GVF snakes. A conventional parametric snake model relies on some functions of the object contour gradient; in contrast the proposed method bases on MSFF which offers an automatic and definite termination criterion. To demonstrate the effectiveness of our algorithm, we present the processing results from synthetic and real images. The experimental results show that by incorporating mean-shift information into the snake framework, the new snake model provides excellent convergence speed and stability.
The paper is devoted to developing spatial adaptive estimates for restoring functions from noisy observations. We show that the traditional least square (piecewise polynomial) estimate equipped with adaptively adjusted window pos- sesses simultaneously many attractive adaptive properties, namely, 1) it is near{ optimal within lnn{factor for estimating a function (or its derivative) at a single point; 2) it is spatial adaptive in the sense that its quality is close to that one which could be achieved if smoothness of the underlying function was known in advance; 3) it is optimal in order (in the case of \strong" accuracy measure) or near{optimal within lnn{factor (in the case of \weak" accuracy measure) for estimating whole function (or its derivative) over wide range of the classes and global loss functions. We demonstrate that the \spatial adaptive abilities" of our estimate are, in a sense, the best possible. Besides this, our adaptive estimate is computationally ecient and demonstrates reasonable practical behavior.
We consider bandwidth matrix selection for bivariate kernel density estimators. The majority of work in this area has been directed towards selection of diagonal bandwidth matrices, but full bandwidth matrices can give markedly better performance for some types of target density. Our methodological contribution has been to develop a new version of the plug-in selector for full bandwidth matrices. Our approach has the advantage, in comparison to existing full bandwidth matrix plug-in techniques, that it will always produce a finite bandwidth matrix. Furthermore, it requires computation of significantly fewer pilot bandwidths. Numerical studies indicate that the performance of our bandwidth selector is best when implemented with two pilot estimation stages and applied to sphered data. In this case our methodology performs at least as well as any competing method considered, while being simpler to implement than its competitors.
Progress in selection of smoothing parameters for kernel density estimation has been much slower in the multivariate than univariate setting. Within the context of multivariate density estimation attention has focused on diagonal bandwidth matrices. However, there is evidence to suggest that the use of full (or unconstrained) bandwidth matrices can be beneficial. This paper presents some results in the asymptotic analysis of data-driven selectors of full bandwidth matrices. In particular, we give relative rates of convergence for plug-in selectors and a biased cross-validation selector.
We consider bandwidth matrix selection for bivariate kernel density estimators. The majority of work in this area has been directed towards selection of diagonal bandwidth matrices, but full bandwidth matrices can give markedly better performance for some types of target density. Our methodological contribution has been to develop a new version of the plug-in selector for full bandwidth matrices. Our approach has the advantage, in comparison to existing full bandwidth matrix plug-in techniques, that it will always produce a finite bandwidth matrix. Furthermore, it requires computation of significantly fewer pilot bandwidths. Numerical studies indicate that the performance of our bandwidth selector is best when implemented with two pilot estimation stages and applied to sphered data. In this case our methodology performs at least as well as any competing method considered, while being simpler to implement than its competitors.
We describe a novel approach to solve a problem of bandwidth selection for Altering a signal given with a noise. The local polynomial approximation is used in order to demonstrate the efficiency of the approach. The algorithm is simple to implement and nearly optimal within InJV factor in the point-wise risk for estimating the signal and its derivatives. The adaptive varying bandwidth enables the algorithm to be spatial adaptive in the sense that its quality is close to that which could be achieved if smoothness of the estimated signal was known in advance. It is shown that the cross-validation adjustment of the threshold parameter of the algorithm significantly improves its accuracy. In particular, simulation demonstrates that the adaptive filters with the adjusted threshold parameter performs better than the adaptive wavelet estimators. A generalization for nonlinear observations and robust nonparametric M-estimate filters is proposed.
We propose a new method of kernel density estimation with a varying adaptive window width. This method is different from traditional ones in two aspects. First, we use symmetric as well as nonsymmetric left and right kernels with discontinuities and show that the fusion of these estimates results in accuracy improvement. Second, we develop estimates with adaptive varying window widths based on the so-called intersection of confidence intervals (ICI) rule. Several examples of the proposed method are given for different types of densities and the quality of the adaptive density estimate is assessed by means of numerical simulations.
Allthough nonparametric kernel density estimation is nowadays a standard technique in explorative data--analysis, there is still a big dispute on how to assess the quality of the estimate and which choice of bandwidth is optimal. The main argument is on whether one should use the Integrated Squared Error or the Mean Integrated Squared Error to define the optimal bandwidth. In the last years a lot of research was done to develop bandwidth selection methods which try to estimate the optimal bandwidth obtained by either of this error criterion. This paper summarizes the most important arguments for each criterion and gives an overview over the existing bandwidth selection methods. We also summarize the small sample behaviour of these methods as assessed in several Monte--Carlo studies. These Monte--Carlo studies are all restricted to very small sample sizes due to the fact that the numerical effort of estimating the optimal bandwidth by any of these bandwidth selection methods is proporti...
A new method of kernel density estimation with a varying adaptive window size is proposed. It is based on the so-called intersection of confidence intervals (ICI) rule. Several examples of the proposed method are given for different types of densities and the quality of the adaptive density estimate is assessed by means of numerical simulations.
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
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
Nonparametric density gradient estimation using a generalized kernel approach is investigated. Conditions on the kernel functions are derived to guarantee asymptotic unbiasedness, consistency, and uniform consistency of the estimates. The results are generalized to obtain a simple mcan-shift estimate that can be extended in a k -nearest-neighbor approach. Applications of gradient estimation to pattern recognition are presented using clustering and intrinsic dimensionality problems, with the ultimate goal of providing further understanding of these problems in terms of density gradients.
A new approach toward target representation and localization, the central component in visual tracking of nonrigid objects, is proposed. The feature histogram-based target representations are regularized by spatial masking with an isotropic kernel. The masking induces spatially-smooth similarity functions suitable for gradient-based optimization, hence, the target localization problem can be formulated using the basin of attraction of the local maxima. We employ a metric derived from the Bhattacharyya coefficient as similarity measure, and use the mean shift procedure to perform the optimization. In the presented tracking examples, the new method successfully coped with camera motion, partial occlusions, clutter, and target scale variations. Integration with motion filters and data association techniques is also discussed. We describe only a few of the potential applications: exploitation of background information, Kalman tracking using motion models, and face tracking.
Density Estimation for Statistics and Data Analysis Bandwidth selection in kernel density estimation: A review. Discussion Paper 9317
- B W Silverman
- Chapman
- Hall
- London
- B A Turlach
Silverman, B.W., 1986. Density Estimation for Statistics and Data Analysis. Chapman & Hall, London. Turlach, B.A., 1993. Bandwidth selection in kernel density estimation: A review. Discussion Paper 9317, Institut de Statistique, Voie du Roman Pays 34, B-1348 Louvain-la-Neuve.
Kernel Smoothing. Chapman & Hall, London. Fig. 13. Smoothing and segmentation results. (a) Original; (b) smoothing results with r = 16–24, stp = 1.0; (c) segmentation results
- M P Wand
- M C Jones
Wand, M.P., Jones, M.C., 1995. Kernel Smoothing. Chapman & Hall, London. Fig. 13. Smoothing and segmentation results. (a) Original; (b) smoothing results with r = 16–24, stp = 1.0; (c) segmentation results, r = 16–24, stp = 1.0, M = 40.
The estimation of the gradient of a density function, with applications in pattern recognition
- Fukunaga
Kernel density estimation with varying data-driven bandwidth
- Katkovnik