Method and system for edge denoising of a digital image

1. A method of denoising an edge in a raw image, the edge comprising a pixel p, the method comprising:

employing a hardware processor for:

(a) determining a direction of a normal to the edge near the pixel p;

(b) determining neighboring pixels in a neighborhood of the pixel p;

(c) projecting the neighboring pixels to the normal to the edge, forming projected pixels;

(d) determining weighted intensities of the neighboring pixels, comprising:

(i) determining a set of weights, comprising applying a one dimensional, 1D, Gaussian filter centered on the pixel p and acting on the projected pixels;

and

(ii) adjusting intensities of the neighboring pixels according to the set of weights; and

(e) determining a denoised value z of the pixel p using the weighted intensities;

thereby denoising the edge of the raw image expediently.

2. The method of claim 1 , further comprising:

replacing the pixel p with respective first shifted pixel p + at a first distance from the pixel p along the normal to the edge, on a brighter side of the edge, and a second shifted pixel p − at a second distance from the pixel p along the normal to the edge, on a darker side of the edge;

applying the steps (b) to (e) to the respective pixels p + and p − to determine a first shifted denoised value z + and a second shifted denoised value z − ;

determining a second order derivative Δ along the normal to the edge, based on the first and second shifted denoised values z − and z + and a distance between the pixels p + and p − ;

determining a sharpened edge denoised value z sharp of the pixel p, comprising adjusting the denoised value z proportionately to the second order derivative Δ.

3. The method of claim 2 , wherein the first distance from the pixel p and the second distance from the pixel p are substantially equal.

4. The method of claim 2 , wherein a sharpened edge denoised value z sharp is determined as z sharp =z+s Δ, wherein “s” is a predefined strength of sharpening.

5. The method of claim 4 , wherein “s” is about 0.6.

6. The method of claim 1 , wherein the determining the direction of the normal to the edge further comprises:

applying a set of linear filters K x , K y , K z , and K w to the raw image, the filters being balanced, resulting in a set of filtered images d x , d y , d z , d w , respectively;

generating a set of estimates of the normal to the edge, based on the set of respective filtered images d x , d y , d z , d w ; and

generating the normal to the edge using the set of filtered images.

7. The method of claim 6 , wherein the applying further comprises choosing a size of each linear filter from about 3 to about 9.

8. The method of claim 2 , wherein the applying comprises applying the set of linear filters K x , K y , K z , K w as follows:

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9. The method of claim 1 , further comprising selecting the neighborhood of the pixel p having a rectangular shape.

10. The method of claim 1 , further comprising choosing a standard deviation for the 1D Gaussian filter from about 1.5 to about 2.

11. A system for denoising an edge in a raw image, the edge comprising a pixel p, the system comprising:

a memory device having computer readable instructions stored thereon for execution by a processor, causing the processor to:

(a) determine a direction of a normal to the edge;

(b) determine neighboring pixels in a neighborhood of the pixel p;

(c) project the neighboring pixels to the normal to the edge, forming projected pixels;

(d) determine weighted intensities of the neighboring pixels, comprising:

(i) determining a set of weights, comprising applying a one dimensional, 1D, Gaussian filter centered on the pixel p and acting on the projected pixels; and

(ii) adjusting intensities of the neighboring pixels according to the set of weights; and

(e) determine a denoised value z of the pixel p using the weighted intensities;

thereby denoising the edge of the raw image expediently.

12. The system of claim 11 , wherein the computer readable instructions further cause the processor to:

replace the pixel p with respective first shifted pixel p + at a first distance from the pixel p along the normal to the edge, on a brighter side of the edge, and a second shifted pixel p− at a second distance from the pixel p along the normal to the edge, on a darker side of the edge;

apply the steps (b) to (e) to the respective pixels p + and p − to determine a first shifted denoised value z + and a second shifted denoised value z − ;

determine a second order derivative Δ along the normal to the edge, based on the first and second shifted denoised values z − and z + and a distance between the pixels p + and p − ;

determine a sharpened edge denoised value z sharp of the pixel p, comprising adjusting the denoised value z proportionately to the second order derivative Δ.

13. The system of claim 12 , wherein the first distance from the pixel p and the second distance from the pixel p are substantially equal.

14. The system of claim 12 , wherein the computer readable instructions further cause the processor to determine a sharpened edge denoised value as: z sharp =z+s Δ, wherein “s” is a predefined strength of sharpening.

15. The system of claim 14 , wherein “s” is about 0.6.

16. The system of claim 11 , wherein the computer readable instructions for determining the direction of the normal to the edge, further cause the processor to:

apply a set of linear filters K x , K y , K z , and K w to the raw image, the filters being balanced, resulting in a set of filtered images d x , d y , d z , d w , respectively;

generate a set of estimates of the normal to the edge, based on the set of respective filtered images d x , d y , d z , d w ; and

generate the normal to the edge using the set of filtered images.

17. The system of claim 16 , wherein a size of each linear filters is from about 3 to about 9.

18. The system of claim 12 , wherein the set of linear filters K x , K y , K z , K w are as follows:

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19. The system of claim 11 , wherein the neighborhood of the pixel p has a rectangular shape.

20. The system of claim 11 , wherein a standard deviation for the 1D Gaussian filter is from about 1.5 to about 2.

21. The method of claim 1 , further comprising blending noise contributions from an approximation part and an edge of the raw image, comprising:

(f) determining a blending weight w b (p) as a function of α(p) and m(p), wherein:

(i) α(p) is a variability of an angle in a direction of a normal to the edge near the pixel p; and

(ii) m(p) is a measure of a similarity between pixels in a neighborhood of the pixel p and a patch with a strong edge separating two flat areas;

and

(g) blending the noise contributions as a function of the blending weight w b (p), thereby expediently denoising the raw image.

22. The method of claim 1 , further comprising removing halos around the edge in the raw image, wherein:

(a) determining a first minimal value z min among the denoised value z of the pixel p and the shifted denoised values z − and z + ;

(b) determining a first maximal intensity among the denoised value z of the pixel p and the shifted denoised values z − and z + ;

(c) determining a second maximal intensity among the sharpened edge denoised value z sharp of the pixel p and the first minimal intensity;

(d) determining a halos removed denoised value of the pixel p as the minimal intensity among the second maximal intensity and the first maximal intensity.

23. A method for blending an approximation noise and an edge noise for a pixel p from an approximation part and an edge of a raw image respectively, the method comprising:

employing a hardware processor for:

(a) determining a blending weight w b (p) for blending the approximation noise and the edge noise as a function of α(p) and m(p), comprising:

(i) determining α(p) as a variability of an angle measure in a direction of a normal to the edge near the pixel p; and

(ii) determining m(p) as a measure of a similarity between pixels in a neighborhood of the pixel p and a patch with a strong edge separating two flat areas;

and

(b) blending the approximation noise and the edge noise as a function of the blending weight w b (p), thereby expediently denoising the raw image.