Bi-Affinity Filter: A Bilateral Type Filter for Color Images

• US 20110243428A1
• Filed: 04/01/2010
• Published: 10/06/2011
• Est. Priority Date: 04/01/2010
• Status: Active Grant

• Current Assignee: Seiko Epson Corporation (Seiko Group)
• Original Assignee: Seiko Epson Corporation (Seiko Group)
• Inventors: Xiao, Jing, Das Gupta, Mithun
• Granted Patent: US 8,285,033 B2
• Time in Patent Office: Days
• US Class Current: 382/162
• CPC Class Codes: G06T 2207/10024 Color image
• CPC Class Codes: G06T 2207/20028 Bilateral filtering
• CPC Class Codes: G06T 2207/20192 Edge enhancement; Edge preservation
• CPC Class Codes: G06T 5/70 Denoising; Smoothing

Abstract

An edge preserving filter that works on the principle of matting affinity allows a better representation of the range filter term in bilateral class filters. The definition of the affinity term can be relaxed to suit different applications. An approximate bi-affinity filter whose output is shown to be very similar to the traditional bilateral filter is defined. The present technique has the added advantage that no color space changes are required and hence an input image can be handled in its original color space. This is a big benefit over the traditional bilateral filter, which needs conversion to perception based spaces, such as CIELAB, to generate results close to the present invention. The full bi-affinity filter preserves very minute details of the input image, and thus permits an enhanced zooming functionality.

Claims

1. A method of processing a digital, input image, comprising:

providing said digital input image, I, in physical memory, said input image having color information in a native color space for each image pixel;

providing a processing device coupled to said physical memory to access said input image I and create an output image, h, by implementing the following steps;

(a) applying the following sequence to said input image I,

2. The method of claim 1, wherein step (a) is applied to said input image I in its native color space.

3. The method of claim 2, wherein said native color space is the RGB color space.

4. The method of claim 1, wherein said laplacian matrix L_xy^ε

follows a 2 color model specifying that pixel color I_i in an input image I can be represented as a linear combination of two colors P and S as follows;

I_i=α

_iP+(1−

α

_i)S, ∀

iε

w, 0≦

α

_i≦

1

where the two colors are piecewise smooth and can be derived from local properties within neighborhood Ω

_x containing the pixel i, and wherein piecewise smooth means smooth within a region of similar in size as window w.

5. The method of claim 4, wherein parameter ε

determines the smoothness of the decomposition into said two color modes as represented by the smoothness of α

estimates.

6. The method of claim 4, wherein α

_i is defined as;

7. The method of claim 6, wherein the α

values are determined according to quadratic cost function J(α

)=α

^TLα

.

8. The method of claim 7, wherein laplacian matrix L is an n×

n matrix, where n is the total number of pixels in input image I whose (ij)^th element is given by

9. The method of claim 8, wherein the laplacian matrix L is further decomposed into a diagonal matrix D and a weight matrix W with the formulation L=D−

W, wherein;

diagonal matrix D is defined with terms D_ii=#[k|iε

w_k] at its diagonal and represents the cardinality of the number of windows of which the pixel i is a member;

individual terms of weight matrix W are given by

10. The method of claim 9, wherein at the local minima, the solution α

* satisfies a first order optimality condition L^Tα

*=0, and the optimal condition is defined as L^Tα

*=(D−

W)^Tα

*.

11. The method of claim 9, wherein terms of W_i,j are evaluated by counting the contribution of only the center pixel'"'"'s local window defined as the window centered about it.

12. The method of claim 11, wherein the local window w is a 3×

3 pixel window requiring O(w²) computations.

13. The method of claim 1, further including:

(b) interpolating said input image I to a resolution higher than its native resolution;

(c) combining the results of step (a) with the interpolated, higher resolution image of step (b).

14. The method of claim 13, wherein step (a) generates detail line information of said input image I, and step (c) adds this line information to the interpolated, higher resolution image.

15. The method of claim 1, wherein the laplacian matrix L is a zero-sum filter kernel.

16. A method of enlarging an input image I, comprising:

providing said digital input image, I, in physical memory, said input image having color information in a native color space for each image pixel;

providing a processing device coupled to said physical memory to access said input image I and create an output image, h, by implementing the following steps;

(a) applying the following sequence to said input image I,

17. The method of claim 16, wherein step (b) generates detail line information of said input image I, and step (c) adds this line information to the interpolated, higher resolution image.

18. The method of claim 16, wherein step (a) is applied to said input image I in its native color space.

19. The method of claim 17, wherein said native color space is the RGB color space.

20. A method of smoothing an input image I, comprising:

providing said digital input image, I, in physical memory, said input image having color information in a native color space for each image pixel;

providing a processing device coupled to said physical memory to access said input image I and create an output image, h, by implementing the following steps;

(a) applying the following sequence to said input image I,

21. The method of claim 20, wherein the local window w is a 3×

3 pixel window.

22. The method of claim 20, wherein regularization factor of ε

is at last 0.1.

23. The method of claim 20, wherein step (a) is applied to said input image I in its native color space.

24. The method of claim 23, wherein said native color space is the RGB color space.