wiener_filter_niwiener_filter_niwiener_filter_niWienerFilterNiWienerFilterNi (Operator)

Name

wiener_filter_niwiener_filter_niwiener_filter_niWienerFilterNiWienerFilterNi — Image restoration by Wiener filtering.

Signature

Description

wiener_filter_niwiener_filter_niwiener_filter_niWienerFilterNiWienerFilterNi (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_filterwiener_filterwiener_filterWienerFilterWienerFilter 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:

1. degradation-specific impulse response

2. noise term

wiener_filter_niwiener_filter_niwiener_filter_niWienerFilterNiWienerFilterNi 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_niwiener_filter_niwiener_filter_niWienerFilterNiWienerFilterNi. 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_filterwiener_filterwiener_filterWienerFilterWienerFilter wiener_filter_niwiener_filter_niwiener_filter_niWienerFilterNiWienerFilterNi 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 (MaskWidthMaskWidthMaskWidthMaskWidthmaskWidth, MaskHeightMaskHeightMaskHeightMaskHeightmaskHeight). wiener_filter_niwiener_filter_niwiener_filter_niWienerFilterNiWienerFilterNi 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_motiongen_psf_motiongen_psf_motionGenPsfMotionGenPsfMotion, gen_psf_defocusgen_psf_defocusgen_psf_defocusGenPsfDefocusGenPsfDefocus). 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_filterwiener_filterwiener_filterWienerFilterWienerFilter 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'.

Attention

PsfPsfPsfPsfpsf must be of image type 'real' and conform to ImageImageImageImageimage in width and height. The Region used for noise estimation must lie completely within the image. If MaskWidthMaskWidthMaskWidthMaskWidthmaskWidth or MaskHeightMaskHeightMaskHeightMaskHeightmaskHeight 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.

Parallelization

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Multithreading scope: global (may be called from any thread).
• Processed without parallelization.

Parameters

Example (C)

/* 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);

Result

wiener_filter_niwiener_filter_niwiener_filter_niWienerFilterNiWienerFilterNi returns 2 (H_MSG_TRUE) if all parameters are correct. If the input is empty wiener_filter_niwiener_filter_niwiener_filter_niWienerFilterNiWienerFilterNi returns with an error message.

Possible Predecessors

gen_psf_motiongen_psf_motiongen_psf_motionGenPsfMotionGenPsfMotion, simulate_motionsimulate_motionsimulate_motionSimulateMotionSimulateMotion, simulate_defocussimulate_defocussimulate_defocusSimulateDefocusSimulateDefocus, gen_psf_defocusgen_psf_defocusgen_psf_defocusGenPsfDefocusGenPsfDefocus

Alternatives

wiener_filterwiener_filterwiener_filterWienerFilterWienerFilter

See also

simulate_motionsimulate_motionsimulate_motionSimulateMotionSimulateMotion, gen_psf_motiongen_psf_motiongen_psf_motionGenPsfMotionGenPsfMotion, simulate_defocussimulate_defocussimulate_defocusSimulateDefocusSimulateDefocus, gen_psf_defocusgen_psf_defocusgen_psf_defocusGenPsfDefocusGenPsfDefocus

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