Lipschitz Filter

Lipschitz Filter

Authors: Mikulas Stencel (mikulas.stencel at gmail.com)
Jiri Janacek (janacek at biomed.cas.cz)

History: 2006/06/21: First version

Source: Lipschitz_.java

Installation: Download Lipschitz_.class to the plugins folder, or subfolder, restart ImageJ, and there will be a new "Lipschitz " command in the Plugins menu, or submenu.

Description: This plugin implements Lipschitz cover of image that is equivalent to a grayscale opening by a cone. The Lipschitz cover can be applied for the elimination of a slowly varying image background by subtraction of the lower Lipschitz cover (a top-hat procedure). Sequential double scan algorithm (according Rosenfeld) was used.
This plug-in is designed to perform filtering on an 8-bit, 16-bit and RGB images with support for ROI and Stacks. Long processing can be stopped with Esc.
Dialog box parameters:

Slope - maximum allowed difference between two neighbouring pixels
TopDown - covering from top to bottom.
TopHat - computes lower (upper) Lipschitz cover.
A PDF document and sample images are available.
References:

Mikulas Stencel, Jiri Janacek: On calculation of chamfer distance and lipschitz covers in digital images. S4G conference, Prague, 2006.
Bloch I.: Fuzzy spatial relationships for image processing and interpretation: a review. Image and Vision Computing 23 (2005), 89-110.
Borgefors G.: Distance transformations in arbitrary dimensions. CVGIP 27 (1984), 321-345.
Borgefors G.: Distance transformations in digital images. CVGIP 34 (1986), 344-371.
Breu H., Gil J., Kirkpatrick D., Werman M.: Linear time euclidean distance transform algorithms, IEEE Trans. PAMI 17 (1995), 529-533.
Danielsson P.-E.: Euclidean distance mapping. CVIP 14 (1980), 227-248.
Moreau P., Ronse C.: Generation of shading-off in images by extrapolation of Lipschitz functions. Graphical Models and Image Processing 58 (1996), 314-333.
Rosenfeld A., Pfaltz J. L.: Sequential Operations in Digital Picture Processing. (1966), 33-61.
Rosenfeld A., Pfaltz J. L.: Distance functions on digital pictures. Pattern Recognition 1 (1968), 33-61.
Sternberg S. R.: Grayscale morphology. CVGIP 35 (1986), 333-355.

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Authors:	Mikulas Stencel (mikulas.stencel at gmail.com) Jiri Janacek (janacek at biomed.cas.cz)
History:	2006/06/21: First version
Source:	Lipschitz_.java
Installation:	Download Lipschitz_.class to the plugins folder, or subfolder, restart ImageJ, and there will be a new "Lipschitz " command in the Plugins menu, or submenu.
Description:	This plugin implements Lipschitz cover of image that is equivalent to a grayscale opening by a cone. The Lipschitz cover can be applied for the elimination of a slowly varying image background by subtraction of the lower Lipschitz cover (a top-hat procedure). Sequential double scan algorithm (according Rosenfeld) was used. This plug-in is designed to perform filtering on an 8-bit, 16-bit and RGB images with support for ROI and Stacks. Long processing can be stopped with Esc. Dialog box parameters: Slope - maximum allowed difference between two neighbouring pixels TopDown - covering from top to bottom. TopHat - computes lower (upper) Lipschitz cover. A PDF document and sample images are available. References: Mikulas Stencel, Jiri Janacek: On calculation of chamfer distance and lipschitz covers in digital images. S4G conference, Prague, 2006. Bloch I.: Fuzzy spatial relationships for image processing and interpretation: a review. Image and Vision Computing 23 (2005), 89-110. Borgefors G.: Distance transformations in arbitrary dimensions. CVGIP 27 (1984), 321-345. Borgefors G.: Distance transformations in digital images. CVGIP 34 (1986), 344-371. Breu H., Gil J., Kirkpatrick D., Werman M.: Linear time euclidean distance transform algorithms, IEEE Trans. PAMI 17 (1995), 529-533. Danielsson P.-E.: Euclidean distance mapping. CVIP 14 (1980), 227-248. Moreau P., Ronse C.: Generation of shading-off in images by extrapolation of Lipschitz functions. Graphical Models and Image Processing 58 (1996), 314-333. Rosenfeld A., Pfaltz J. L.: Sequential Operations in Digital Picture Processing. (1966), 33-61. Rosenfeld A., Pfaltz J. L.: Distance functions on digital pictures. Pattern Recognition 1 (1968), 33-61. Sternberg S. R.: Grayscale morphology. CVGIP 35 (1986), 333-355.