wiener_filter — Image restoration by Wiener filtering.
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 realisation 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 impuls response. So the convolution of original image and impulse response results in the corrupted image. The specific impulse response describes image acquisition and the occured 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
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 unsmoothed 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'.
Psf must be of image type 'real' and conform to Image and FilteredImage in image width and height.
impulse response (PSF) of degradation (in spatial domain).
Smoothed version of corrupted image.
/* 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);
wiener_filter returns 2 (H_MSG_TRUE) if all parameters are correct. If the input is empty wiener_filter returns with an error message.
gen_psf_motion, simulate_motion, simulate_defocus, gen_psf_defocus, optimize_fft_speed
simulate_motion, gen_psf_motion, simulate_defocus, gen_psf_defocus
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