Monotonicity-Enhancing Nonlinear Diffusion

Pavel Mrazek and Mirko Navara
Center for Machine Perception
Czech Technical University
http://cmp.felk.cvut.cz/

Problem formulation

Input:

f, a noisy sampled function of one or two variables (e.g. grey values of an image, range data)
f is expected to be piecewise continuous, piecewise monotone; noise violates these properties

Task:

filter the noise, restore piecewise monotonicity, smooth the data

Linear diffusion

Properties:

+ signal becomes smoother, local extrema gradually removed
- blurs and dislocates edges

Nonlinear diffusion

Properties:

+ smoothes more inside homogeneous regions
+ preserves important discontinuities
+- approaches function (piecewise) constant
- bends growing function segments near the ends

Monotonicity-enhancing nonlinear diffusion

Properties:

+ removes noise, enhances piecewise monotonicity
+ preserves important discontinuities
+- approaches function (piecewise) linear
+ suitable for data expected to be piecewise monotone, with gradual changes of function values, and discontinuities; example: range data.

Further information

Pavel Mrazek: Nonlinear Diffusion for Image Filtering and Monotonicity Enhancement
PhD Thesis, Czech Technical University, Prague, June 2001.
full text [PDF, 4.5MB]

Pavel Mrazek: Monotonicity Enhancing Nonlinear Diffusion
Journal of Visual Communication and Image Representation, Academic Press, 2001. To appear.

Pavel Mrazek: Enhancing monotonicity by nonlinear diffusion of image derivatives.
In Tomas Svoboda, editor, Czech Pattern Recognition Workshop 2000, Czech Pattern Recognition Society, Perslak, Czech Republic, Feb 2000.
[222kB PDF] or [78kB Postscript]

Pavel Mrazek: Monotonicity in Interpolation and Approximation.
Research report K335-CMP/99/179, Czech Technical University, Prague, 1999. [Postscript, 1525kB]

Last modified: May 11, 2000.

Center for Machine Perception
Mail to mrazekp@cmp.felk.cvut.cz