Jump Detection In Blurred Regression Surfaces

We consider the problem of detecting jump location curves of regression surfaces when they are spatially blurred and contaminated pointwise by random noise. This problem is common in various applications, including equi-temperature surface estimation in meteorology and oceanography and edge detection in image processing. In the literature, most existing jump-detection methods are developed under the assumption that there is no blurring involved, or that the blurring mechanism described by a point spread function (psf) is completely specified. In this article, we propose four possible jump detectors, without imposing restrictive assumptions on either the psf or the true regression surface. Their theoretical and numerical properties are studied and compared. We also propose a new quantitative metric for measuring the performance of a jump detector. A data-driven bandwidth selection procedure via the bootstrap is suggested as well. This article has supplementary material online.

[1]  Lih-Chung Wang,et al.  Estimation of 2D jump location curve and 3D jump location surface in nonparametric regression , 2012, Stat. Comput..

[2]  Peihua Qiu,et al.  Jump-preserving surface reconstruction from noisy data , 2009 .

[3]  Peihua Qiu,et al.  Tracking Edges, Corners and Vertices in an Image , 2008 .

[4]  M. Hillebrand,et al.  Outlier robust corner-preserving methods for reconstructing noisy images , 2007, 0708.0481.

[5]  Peihua Qiu,et al.  Jump Detection in Regression Surfaces Using Both First-Order and Second-Order Derivatives , 2007 .

[6]  T. Garlipp,et al.  Detection of linear and circular shapes in image analysis , 2006, Comput. Stat. Data Anal..

[7]  Valen E. Johnson,et al.  Image Restoration and Reconstruction , 2006 .

[8]  D Marr,et al.  Theory of edge detection , 1979, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[9]  Deepika,et al.  Comparison of edge detectors , 2014, 2014 International Conference on Medical Imaging, m-Health and Emerging Communication Systems (MedCom).

[10]  Suchendra M. Bhandarkar,et al.  An edge detection technique using local smoothing and statistical hypothesis testing , 1996, Pattern Recognit. Lett..

[11]  Peihua Qiu,et al.  The Local Piecewisely Linear Kernel Smoothing Procedure for Fitting Jump Regression Surfaces , 2004, Technometrics.

[12]  James J. Clark.  Authenticating Edges Produced by Zero-Crossing Algorithms , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  Tomaso A. Poggio,et al.  On Edge Detection , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[14]  T. Garlipp.  Robust Jump Detection in Regression Surface , 2004 .

[15]  Margaret M. Fleck.  Some Defects in Finite-Difference Edge Finders , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  P. Qiu.  Jump Surface Estimation, Edge Detection, and Image Restoration , 2007 .

[17]  Yazhen Wang,et al.  Change Curve Estimation via Wavelets , 1998 .

[18]  Sudeep Sarkar,et al.  Comparison of Edge Detectors: A Methodology and Initial Study , 1998, Comput. Vis. Image Underst..

[19]  Adrian W. Bowman,et al.  Detecting discontinuities in nonparametric regression curves and surfaces , 2006, Stat. Comput..

[20]  Peihua Qiu,et al.  Nonparametric estimation of a point-spread function in multivariate problems , 2007 .

[21]  Irène Gijbels,et al.  Bandwidth Selection for Changepoint Estimation in Nonparametric Regression , 2004, Technometrics.

[22]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[23]  B. Yandell,et al.  Jump Detection in Regression Surfaces , 1997 .

[24]  P. Qiu.  A Nonparametric Procedure to Detect Jumps in Regression Surfaces , 2002 .

[25]  P. Qiu.  Image processing and jump regression analysis , 2005 .

[26]  D. Ferger.  Boundary estimation based on set-indexed empirical processes , 2004 .

[27]  H.M. Wechsler,et al.  Digital image processing, 2nd ed. , 1981, Proceedings of the IEEE.

[28]  Sudeep Sarkar,et al.  Comparison of edge detectors: a methodology and initial study , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.