wiener_filter_ni — Image restoration by Wiener filtering.
wiener_filter_ni (ni = noise-estimation integrated) 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_termThe 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
wiener_filter_ni estimates the noise term as follows: The user defines a region that is suitable for noise estimation within the image (homogeneous as possible, as edges or textures aggravate noise estimation). After smoothing within this region by an (unweighted) median filter and subtracting smoothed version from unsmoothed, the average noise amplitude of the region is processed within wiener_filter_ni. This amplitude together with the average gray value within the region allows estimating the quotient of the power spectral densities of noise and original image (in contrast to wiener_filter wiener_filter_ni assumes a rather constant quotient within the whole image). The user can define width and height of the rectangular (median-)filter mask to influence the noise estimation (MaskWidth, MaskHeight). wiener_filter_ni 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:
estimating the quotient of the power spectrum densities of noise and original image,
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 in width and height. The Region used for noise estimation must lie completely within the image. If MaskWidth or MaskHeight is an even number, it is replaced by the next higher odd number (this allows the unique extraction of the center of the filter mask). Width/height of the mask may not exceed the image width/height or be less than null.
impulse response (PSF) of degradation (in spatial domain).
Region for noise estimation.
Width of filter mask.
Default value: 3
Suggested values: 3, 5, 7, 9
Typical range of values: 0 ≤ MaskWidth ≤ width(Image)
Height of filter mask.
Default value: 3
Suggested values: 3, 5, 7, 9
Typical range of values: 0 ≤ MaskHeight ≤ height(Image)
/* Restoration of a noisy image (size=256x256), that was blurred by motion*/ Hobject object; Hobject restored; Hobject psf; Hobject noise_region; /* 1. Generate a Point-Spread-Function for a motion-blur with */ /* parameter a=10 and direction of the x-axis */ gen_psf_motion(&psf,256,256,10,0,3); /* 2. Segmentation of a region for the noise-estimation */ open_window(0,0,256,256,0,"visible",&WindowHandle); disp_image(object,WindowHandle); draw_region(&noise_region,draw_region); /* 3. Wiener-filtering */ wiener_filter_ni(object,psf,noise_region,&restored,3,3);
wiener_filter_ni returns 2 (H_MSG_TRUE) if all parameters are correct. If the input is empty wiener_filter_ni 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