wiener_filter🔗
Short description🔗
wiener_filter — Image restoration by Wiener filtering.
Signature🔗
wiener_filter( image Image, image Psf, image FilteredImage, out image RestoredImage )
Description🔗
wiener_filter produces an estimate of the original image
(= image without noise and blurring) by minimizing the mean square error
between estimated and original image.
wiener_filter can be used to restore images corrupted by
noise and/or blurring (e.g., motion blur, atmospheric turbulence or
out-of-focus blur).
Method and realization of this restoration technique bases on the
following model:
The corrupted image is interpreted as the output of a (disturbed) linear
system. Functionality of a linear system is determined by its specific
impulse response. So the convolution of original image and impulse response
results in the corrupted image. The specific impulse response describes
image acquisition and the occurred degradations. In the presence of additive
noise an additional noise term must be considered. So the corrupted image
can be modeled as the result of
[convolution(impulse_response,original_image)] + noise_term
The noise term encloses two different terms describing image-dependent and
image-independent noise.
According to this model, two terms must be known for restoration by Wiener
filtering:
-
degradation-specific impulse response
-
noise term
So wiener_filter needs a smoothed version of the input image
to estimate the power spectral density of noise and original image. One
can use one of the smoothing HALCON-filters (e.g., eliminate_min_max)
to get this version.
wiener_filter needs further the impulse response that describes
the specific degradation. This impulse response (represented in spatial
domain) must fit into an image of HALCON image type real. There
exist two HALCON-operators for generation of an impulse response for
motion blur and out-of-focus (see gen_psf_motion,
gen_psf_defocus). The representation of the impulse response
presumes the origin in the upper left corner. This results in the following
disposition of an NxM sized image:
-
first rectangle (“upper left”): (image coordinates \(xb = 0..(N/2)-1\), \(yb = 0..(M/2)-1)\)
- conforms to the fourth quadrant of the Cartesian coordinate system, encloses values of the impulse response at position \(x = 0..N/2\) and \(y = 0..-M/2\)
-
second rectangle (“upper right”): (image coordinates \(xb = N/2..N-1\), \(yb = 0..(M/2)-1)\)
- conforms to the third quadrant of the Cartesian coordinate system, encloses values of the impulse response at position \(x = -N/2..-1\) and \(y = -1..-M/2\)
-
third rectangle (“lower left”): (image coordinates \(xb = 0..(N/2)-1\), \(yb = M/2..M-1)\)
- conforms to the first quadrant of the Cartesian coordinate system, encloses values of the impulse response at position \(x = 1..N/2\) and \(y = M/2..0\)
-
fourth rectangle (“lower right”): (image coordinates \(xb = N/2..N-1\), \(yb = M/2..M-1)\)
- conforms to the second quadrant of the Cartesian coordinate system, encloses values of the impulse response at position \(x = -N/2..-1\) and \(y = M/2..1\)
wiener_filter works as follows:
-
estimation of the power spectrum density of the original image by using the smoothed version of the corrupted image,
-
estimation of the power spectrum density of each pixel by subtracting smoothed version from not smoothed version,
-
building the Wiener filter kernel with the quotient of power spectrum densities of noise and original image and with the impulse response,
-
processing the convolution of image and Wiener filter frequency response.
The result image has got image type real.
Attention🔗
Psf must be of image type real and conform to Image
and FilteredImage in image width and height.
Execution information🔗
Execution information
-
Multithreading type: reentrant (runs in parallel with non-exclusive operators).
-
Multithreading scope: global (may be called from any thread).
-
Automatically parallelized on channel level.
Parameters🔗
Image (input_object) (multichannel-)image → object (byte / direction / cyclic / int1 / int2 / uint2 / int4 / real)
Corrupted image.
Psf (input_object) (multichannel-)image → object (real)
impulse response (PSF) of degradation (in spatial domain).
FilteredImage (input_object) (multichannel-)image → object (byte / direction / cyclic / int1 / int2 / uint2 / int4 / real)
Smoothed version of corrupted image.
RestoredImage (output_object) image → object (real)
Restored image.
Example🔗
(C)
/* Restoration of a noisy image (size=256x256), that was blurred by motion*/
Hobject object\;
Hobject restored\;
Hobject psf\;
Hobject noisefiltered\;
/* 1. Generate a Point-Spread-Function for a motion-blur with */
/* parameter a=10 and direction along the x-axis */
gen_psf_motion(&psf,256,256,10,0,3)\;
/* 2. Noisefiltering of the image */
median_image(object,&noisefiltered,"circle",2,0)\;
/* 3. Wiener-filtering */
wiener_filter(object,psf,noisefiltered,&restored)\;
Result🔗
wiener_filter returns 2 (H_MSG_TRUE) if all parameters are
correct. If the input is empty wiener_filter returns with
an error message.
Combinations with other operators🔗
Combinations
Possible predecessors
gen_psf_motion, simulate_motion, simulate_defocus, gen_psf_defocus, optimize_fft_speed
Alternatives
See also
simulate_motion, gen_psf_motion, simulate_defocus, gen_psf_defocus
References🔗
M. Lückenhaus:“Grundlagen des Wiener-Filters und seine Anwendung in der Bildanalyse”; Diplomarbeit; Technische Universität München, Institut für Informatik; Lehrstuhl Prof. Radig; 1995
Azriel Rosenfeld, Avinash C. Kak: Digital Picture Processing, Computer Science and Aplied Mathematics, Academic Press New York/San Francisco/London 1982
Module🔗
Foundation