Theoretical aspects of vertically invariant gray-level morphological operators and their application on adaptive signal and image filtering

We use vertically invariant morphological filters for time-varying or adaptive signal processing. The morphological filters adopted in this paper are vertically invariant openings and closings. Vertically invariant openings and closings have intuitive geometric interpretations and can provide different filtering scales with respect to different spatial positions. Hence, they are suitable for adaptive signal filtering. To adaptively assign structuring elements of the vertically invariant openings or closings, we develop the progressive umbra-filling (PUF) procedure. Experimental results have shown that our approach can successfully eliminate noise without oversmoothing the important features of a signal.

[1]  Stan Z. Li,et al.  On Discontinuity-Adaptive Smoothness Priors in Computer Vision , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  Edward R. Dougherty,et al.  Morphological methods in image and signal processing , 1988 .

[3]  William A. Sethares,et al.  Smoothing of discontinuous signals: the competitive approach , 1995, IEEE Trans. Signal Process..

[4]  Ja-Ling Wu,et al.  Extraction of Corner-Edge-Surface Structure from Range Images Using Mathematical Morphology , 1995, IEICE Trans. Inf. Syst..

[5]  Aldo W. Morales,et al.  Statistical analysis of morphological openings , 1993, IEEE Trans. Signal Process..

[6]  David C. Wang,et al.  Gradient inverse weighted smoothing scheme and the evaluation of its performance , 1981 .

[7]  Steven K. Feiner,et al.  Computer graphics: principles and practice (2nd ed.) , 1990 .

[8]  Philippe Saint-Marc,et al.  Adaptive Smoothing: A General Tool for Early Vision , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  Thomas Ertl,et al.  Computer Graphics - Principles and Practice, 3rd Edition , 2014 .

[10]  Chu-Song Chen,et al.  A 3D Range Data Acquisition System Combining Laser Lighting and Stereo Vision , 1996 .

[11]  Paul J. Besl,et al.  Surfaces in Range Image Understanding , 1988, Springer Series in Perception Engineering.

[12]  M.-H. Chen,et al.  A Multiscanning Approach Based on Morphological Filtering , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  Emanuele Trucco,et al.  Computer and Robot Vision , 1995 .

[14]  Joseph Ronsin,et al.  Texture Classification and Segmentation Based on Iterative Morphological Decomposition , 1993, J. Vis. Commun. Image Represent..

[15]  Aldo W. Morales,et al.  Nonlinear multiscale filtering using mathematical morphology , 1992, Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[16]  Petros Maragos,et al.  Pattern Spectrum and Multiscale Shape Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  W. Eric L. Grimson,et al.  Discontinuity detection for visual surface reconstruction , 1985, Comput. Vis. Graph. Image Process..

[18]  Edward J. Delp,et al.  The analysis of morphological filters with multiple structuring elements , 1990, Comput. Vis. Graph. Image Process..

[19]  Ja-Ling Wu,et al.  Statistical analysis of space-varying morphological openings with flat structuring elements , 1996, IEEE Trans. Signal Process..

[20]  Henk J. A. M. Heijmans,et al.  The algebraic basis of mathematical morphology : II. Openings and closings , 1991, CVGIP Image Underst..

[21]  Mark A. Roth.  Theoretical advances in *** , 1986, CSC '86.

[22]  Savitri Bevinakoppa,et al.  DIGITAL IMAGE COMPRESSION TECHNIQUES , 2014 .

[23]  Gary Mastin,et al.  Adaptive filters for digital image noise smoothing: An evaluation , 1985, Comput. Vis. Graph. Image Process..

[24]  Alfredo Restrepo,et al.  Adaptive trimmed mean filters for image restoration , 1988, IEEE Trans. Acoust. Speech Signal Process..

[25]  Henk J. A. M. Heijmans,et al.  The algebraic basis of mathematical morphology. I Dilations and erosions , 1990, Comput. Vis. Graph. Image Process..

[26]  Petros Maragos.  A Representation Theory for Morphological Image and Signal Processing , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[27]  Moncef Gabbouj,et al.  Optimal stack filtering and the estimation and structural approaches to image processing , 1989, Sixth Multidimensional Signal Processing Workshop,.

[28]  Richard Alan Peters,et al.  A new algorithm for image noise reduction using mathematical morphology , 1995, IEEE Trans. Image Process..