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JumpPreserving Surface Reconstruction From Noisy Data (Short title: JumpPreserving Surface Reconstruction)
"... A new local smoothing procedure is suggested for jumppreserving surface reconstruction from noisy data. In a neighborhood of a given point in the design space, a plane is fitted by local linear kernel smoothing, giving the conventional local linear kernel estimator of the surface at the point. The ..."
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A new local smoothing procedure is suggested for jumppreserving surface reconstruction from noisy data. In a neighborhood of a given point in the design space, a plane is fitted by local linear kernel smoothing, giving the conventional local linear kernel estimator of the surface at the point. The neighborhood is then divided into two parts by a line passing through the given point and perpendicular to the gradient direction of the fitted plane. In the two parts, two half planes are fitted, respectively, by local linear kernel smoothing, providing two onesided estimators of the surface at the given point. Our surface reconstruction procedure then proceeds in the following two steps. First, the fitted surface is defined by one of the three estimators, i.e., the conventional estimator and the two onesided estimators, depending on the weighted residual means of squares of the fitted planes. The fitted surface of this step preserves the jumps well, but it is a bit noisy, compared to the conventional local linear kernel estimator. Second, the estimated surface values at the original design points obtained in the first step are used as new data, and the above procedure is applied to this data in the same way except that one of the three estimators is selected based on their estimated variances. Theoretical justification and numerical examples show that the fitted surface of the second step preserves jumps well and also removes noise efficiently. Besides two window widths, this procedure does not introduce other parameters. Its surface estimator has an explicit formula. All these features make it convenient to use and simple to compute.
On Image Registration In Magnetic Resonance Imaging
"... Image registration is used in many fields for mapping one image to another. In magnetic resonance imaging (MRI) applications, one of the main uses is for correction of motioninduced artifacts so that subsequent image analysis would be more reliable. This paper gives an introduction to some image reg ..."
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Image registration is used in many fields for mapping one image to another. In magnetic resonance imaging (MRI) applications, one of the main uses is for correction of motioninduced artifacts so that subsequent image analysis would be more reliable. This paper gives an introduction to some image registration problems in MRI and functional MRI applications, describes certain commonly used image registration procedures, and discusses their major features. Two potential research topics for improving current image registration procedures are also discussed. 1.
3d image denoising by local smoothing and nonparametric regression
 Technometrics
, 2011
"... Threedimensional (3D) images are becoming increasingly popular in image applications, such as magnetic resonance imaging (MRI), functional MRI (fMRI), and other image applications. Observed 3D images often contain noise that should be removed beforehand for improving the reliability of subsequent ..."
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Threedimensional (3D) images are becoming increasingly popular in image applications, such as magnetic resonance imaging (MRI), functional MRI (fMRI), and other image applications. Observed 3D images often contain noise that should be removed beforehand for improving the reliability of subsequent image analyses. In the literature, most existing image denoising methods are for 2D images. Their direct extensions to 3D cases generally can not handle 3D images efficiently, because the structure of 3D images is often substantially more complicated than that of 2D images. For instance, edge locations are surfaces in 3D cases, which are much more challenging to handle, compared to edge curves in 2D cases. In this paper, we propose a novel 3D image denoising procedure, based on nonparametric estimation of a 3D jump surface from noisy data. One important feature of this method is its ability to preserve edges and major edge structures, such as intersections of two edge surfaces, pyramids, pointed corners, and so forth. Both theoretical arguments and numerical studies show that it works well in various applications. Software and proofs are available online as supplemental material.
An Adaptive Window Mechanism for Image Smoothing
"... Image smoothing using adaptive windows whose shapes, sizes, and orientations vary with image structure is described. Window size is increased with decreasing gradient magnitude, and window shape and orientation are adjusted in such a way as to smooth most in the direction of least gradient. Rather t ..."
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Image smoothing using adaptive windows whose shapes, sizes, and orientations vary with image structure is described. Window size is increased with decreasing gradient magnitude, and window shape and orientation are adjusted in such a way as to smooth most in the direction of least gradient. Rather than performing smoothing isotropically, smoothing is performed in preferred orientations to preserve region boundaries while reducing random noise within regions. Also, instead of performing smoothing uniformly, smoothing is performed more in homogeneous areas than in detailed areas. The proposed adaptive window mechanism is tested in the context of median, mean, and Gaussian filtering, and experimental results are presented using synthetic and real images and compared with a stateoftheart method.
Using Conventional Edge Detectors And PostSmoothing For Segmentation Of Spotted Microarray Images
"... Segmentation of spotted microarray images is important in generating gene expression data. It aims to distinguish foreground pixels from background pixels for a given spot of a microarray image. Edge detection in the image processing literature is a closely related research area, because spot bounda ..."
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Segmentation of spotted microarray images is important in generating gene expression data. It aims to distinguish foreground pixels from background pixels for a given spot of a microarray image. Edge detection in the image processing literature is a closely related research area, because spot boundary curves separating foregrounds from backgrounds in a microarray image can be treated as edges. However, for generating gene expression data, segmentation methods for handling spotted microarray images are required to classify each pixel as either a foreground or a background pixel; most conventional edge detectors in the image processing literature do not have this classification property, because their detected edge pixels are often scattered in the whole design space and consequently the foreground or background pixels are not defined. In this paper, we propose a general postsmoothing procedure for estimating spot boundary curves from the detected edge pixels of conventional edge detectors, such that these conventional edge detectors together with the proposed postsmoothing procedure can be used for segmentation of spotted microarray images. Numerical studies show that this proposal works well in applications.
An Introduction to Wavelets
 IEEE Computational Science and Engineering
"... frame based scene reconstruction from range data ..."
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MULTISCALE KERNEL SMOOTHING USING A LIFTING SCHEME
"... This paper discusses the idea of a lifting scheme for multiscale implementation of kernel estimation procedures used in statistical estimation. The resulting decomposition is related to the BurtAdelson pyramid, but the design of the filters is well adapted to nonequispaced samples. The proposed dec ..."
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This paper discusses the idea of a lifting scheme for multiscale implementation of kernel estimation procedures used in statistical estimation. The resulting decomposition is related to the BurtAdelson pyramid, but the design of the filters is well adapted to nonequispaced samples. The proposed decomposition has an oversampling rate of 2, where the oversampling can be seen as an alternative to primal lifting steps (update steps) as a tool for stabilising and antialiasing. We then propose an adaptive version of this multiscale kernel estimation with truncated kernels. Truncated kernels allow sharp representations of jumps. Illustrations show that our method is numerically well conditioned, suffers less from visual effects due to false detections, and allows indeed sharp transitions if equiped with an adaptive choice among truncated kernels. All variants of the proposed method have linear computational complexity. Key words: wavelet; lifting; kernel; adaptive; smoothing; thresholding
Jump Regression Analysis
"... Nonparametric regression analysis provides statistical tools for estimating regression curves or surfaces from noisy data. Conventional nonparametric regression procedures, however, are only appropriate for estimating continuous regression functions. When the underlying regression function has jumps ..."
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Nonparametric regression analysis provides statistical tools for estimating regression curves or surfaces from noisy data. Conventional nonparametric regression procedures, however, are only appropriate for estimating continuous regression functions. When the underlying regression function has jumps, functions estimated by the conventional procedures are not statistically consistent at the jump positions. Recently, regression analysis for estimating jump regression functions is under rapid development [1], which is briefly introduced here. 1D Jump Regression Analysis In onedimensional (1D) cases, the jump regression analysis (JRA) model has the form yi = f(xi) + εi, for i = 1, 2,...,n, (1) where {yi, i = 1, 2,..., n} are observations of the response variable y at design points {xi, i = 1, 2,..., n}, f is an unknown regression function, and {εi, i = 1, 2,...,n} are random errors. For simplicity, we assume that the design interval is [0, 1]. In (1), f is assumed to have the expression f(x) = g(x) + p∑ djI(x> sj), for x ∈ [0, 1], (2) j=1 where g is a continuous function in the entire design interval, p is the number of jump points, {sj, j = 1, 2,...,p} are the jump positions, and {dj, j = 1, 2,...,p} are the corresponding jump magnitudes. If p = 0, then f is continuous in the entire design interval. In (2), the function g is called the continuity part of f, and the summation ∑ p j=1 djI(x> sj) is called the jump part of f. The major goal of JRA is to estimate g, p, {sj, j = 1, 2,...,p} and {dj, j = 1, 2,...,p} from the observed data {(xi, yi), i = 1, 2,...,n}. A natural jump detection criterion is Mn(x) = 1 n∑ xi − x
Pseudosphere Filter and Edge Detection
"... Abstract: In this paper, a novel image filter called the pseudosphere filter is presented. An edgepreserving parameter is introduced besides a scale parameter in the pseudosphere filter, and thus a better tradeoff between image smoothing and edge locating can be obtained using it. A pseudosphereb ..."
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Abstract: In this paper, a novel image filter called the pseudosphere filter is presented. An edgepreserving parameter is introduced besides a scale parameter in the pseudosphere filter, and thus a better tradeoff between image smoothing and edge locating can be obtained using it. A pseudospherebased edge detector is formed by replacing the Gaussian filter in the classic Canny edge detector with the Pseudosphere filter. The experiment results in this paper show that, compared with the classic Canny edge detector, in the case of having the same smoothness, the pseudospherebased edge detector offers a better precision for edge locating. Key words: tractrix filter; pseudosphere filter; edge detector