CN104484872A - Interference image edge extending method based on directions - Google Patents

Abstract

The invention relates to an edge extending method based on interference image fringe directions. The edge extending method comprises the following steps of 1, determining the direction of a boundary point; 2, according to the edge contour principle, defining internal pixels and external pixels, and determining the positions; 3, utilizing bilinear interpolation to determine an equation of known pixels and to-be-filled pixels; 4, according to the step 3, respectively establishing the equation of all to-be-filled pixels along the four boundary directions, expressing the equation as a matrix type, and solving the to-be-filled edge pixel values through a matrix solution method; 5, filling the obtained edge pixel values to an image, so as to perform the image edge extension.

Description

Based on the interference image edge extending method in direction

Technical field

The invention belongs to technical field of image processing, be specifically related to a kind of interference image edge extending method based on image direction newly.

Background technology

Optical interference techniques provides contactless, high-acruracy survey, and it is used in various investigation and application field.Interference image is the record result of this technology, and in order to strengthen degree of accuracy and robustness, interference image needs to carry out denoising at pretreatment stage.In multiple interference image noise-removed technology, very efficient and be widely used based on the iteration of partial differential equation and directed noise-removed technology in spatial domain.Such as, but if use traditional image border to fill, zero padding or mirror image are filled, and this noise-removed technology can introduce error in image boundary.Owing to needing to use a large amount of iterationses, error will extend to image inside from image boundary.For process interference image edge, a kind of method based on iterative Fourier transform is suggested, and it fills image boundary by outside derivation interference fringe.But it requires that the band of interference image is narrow, this is all under any circumstance not set up.Due to the streaming structure that interference image has interference fringe such, can contribute to along filling border, interference fringe direction reducing error.Therefore, propose a kind of interference image edge based on edge direction to expand.

Summary of the invention

The present invention will overcome the shortcoming and defect that prior art exists, and proposes a kind of image border fill method based on interference image stripe direction, comprises following basic step:

The first step: by gradient direction method determination edge direction θ (x, y), as follows;

$\mathrm{\θ}(x,y)=\frac{1}{2}\arctan 2\{-\underset{u=x-\mathrm{\ϵ}}{\overset{x+\mathrm{\ϵ}}{\mathrm{\Σ}}}\underset{v=y-\mathrm{\ϵ}}{\overset{y+\mathrm{\ϵ}}{\mathrm{\Σ}}}2f_{\mathrm{x\σ}}(u,v)f_{\mathrm{y\σ}}(u,v),\underset{u=x-\mathrm{\ϵ}}{\overset{x+\mathrm{\ϵ}}{\mathrm{\Σ}}}\underset{v=y-\mathrm{\ϵ}}{\overset{y+\mathrm{\ϵ}}{\mathrm{\Σ}}}[f_{\mathrm{y\σ}}^2(u,v)-f_{\mathrm{x\σ}}^2(u,v)\left]\right\}---\left(1\right)$

Wherein f _σbe through Gauss except the bar graph after making an uproar, f _{x σ}and f _{y σ}f respectively _σfirst-order partial derivative on x direction and y direction.Direction θ (x, y) of point (x, y) is its direction average around in region [x-ε: x+ ε, y-ε: y+ ε ,], and ε represents the range size of peripheral region.

Second step: according to edge level line principle definition interior pixels and external pixels determine its position.For boundary pixel f (x, y), with its interior pixels f (x being in image inside on same level line _i, y _i) be in external pixels f (x outside image boundary _o, y _o) can be expressed as

f(x _i,y _i)＝f(x _o,y _o)＝f(x,y) (2)

x _i＝x-γ,y _i＝y-η (3)

x _o＝x+γ,y _o＝y+η (4)

In formula, γ and η represents the horizontal and vertical range deviation of interior pixels and external pixels and boundary pixel respectively.For external pixels, external pixels has following character:

ω _x(x,y)γ+ω _y(x,y)η＝0 (6)

In formula, a (x, y) represents image background intensity, and b (x, y) represents amplitude, represent phase place, ω _x(x, y) and ω _y(x, y) represents the first-order partial derivative of phase place on x direction and y direction respectively.Because direction θ (x, y) also can be defined as:

θ(x,y)＝atan[ω _x(x,y),-ω _y(x,y)] (7)

γ and η can be expressed as with direction:

γ＝±αcosθ(x,y),η＝±αsinθ(x,y) (8)

α represents the distance of interior pixels and external pixels and boundary pixel.Because ω _x(x, y) and ω _y(x, y) is generally unknown, and direction θ (x, y) is tried to achieve by method in step one.γ and η positive and negative ± from the direction of self, there is different definition according to four borders, can be determined by following table:

3rd step: utilize bilinear interpolation to determine pixel equation to be filled.The bilinear interpolation of external pixels can be expressed as

f(x+γ,y+η)≈(1-|γ|)(1-|η|)f(x,y)+|γ|(1-|η|)f[x+sign(γ),y]

+(1-|γ|)|η|f[x,y+sign(η)]+|γ||η|f[x+sign(γ),y+sign(η)] (9)

Wherein, when parameter be positive number or negative time sign get 1 or-1; According to different boundary directions, f [x+sign (γ), y] and f [x+sign (γ), y+sign (η)] or f [x, y+sign (η)] with f [x+sign (γ), y+sign (η)] be pixel to be filled.F (x+ γ, y+ η) can calculate according to formula (2).

4th step: the system of equations setting up four all edge pixels to be filled of boundary direction according to the 3rd step respectively, is expressed as matrix form by system of equations, and solves edge pixel values to be filled by the method for solution matrix;

5th step: be filled on image by the edge pixel values of acquisition, carries out image border expansion.

Advantage of the present invention is: utilize the existing information of image to carry out the prediction of image change, realizes more accurate edge filling.The existing information of image is with ingenious the showing succinctly of the form in direction.

Accompanying drawing explanation

Fig. 1 is the interior pixels and external pixels that define in the present invention.

Fig. 2 is the level line and image direction that relate in the present invention.

Fig. 3 is the bilinear interpolation schematic diagram used in the present invention.

Fig. 4 be the inventive method result schematic diagram and with additive method result compare schematic diagram.

Embodiment

In the following description, with specific implementation method, the present invention is further explained in detail by reference to the accompanying drawings.But, it should be appreciated that and the invention is not restricted to this application, but can be applicable in the image procossing of many other types and other purposes.

Edge extending method based on interference image stripe direction of the present invention, comprises following basic step:

Step one: according to gradient direction method determination edge direction.Interference image can be expressed as:

In formula, f (x, y) represents pixel (x, y) pixel value, and a (x, y) represents image background intensity, and b (x, y) represents amplitude, represent phase place, n (x, y) represents additive noise.Uniquely known only have f (x, y).Gradient method can estimate direction exactly from the bar graph of band noise, as follows;

$\mathrm{\θ}(x,y)=\frac{1}{2}\arctan 2\{-\underset{u=x-\mathrm{\ϵ}}{\overset{x+\mathrm{\ϵ}}{\mathrm{\Σ}}}\underset{v=y-\mathrm{\ϵ}}{\overset{y+\mathrm{\ϵ}}{\mathrm{\Σ}}}2f_{\mathrm{x\σ}}(u,v)f_{\mathrm{y\σ}}(u,v),\underset{u=x-\mathrm{\ϵ}}{\overset{x+\mathrm{\ϵ}}{\mathrm{\Σ}}}\underset{v=y-\mathrm{\ϵ}}{\overset{y+\mathrm{\ϵ}}{\mathrm{\Σ}}}[f_{\mathrm{y\σ}}^2(u,v)-f_{\mathrm{x\σ}}^2(u,v)\left]\right\}---\left(1\right)$

Wherein f _σbe through Gauss except the bar graph after making an uproar, f _{x σ}and f _{y σ}f respectively _σfirst-order partial derivative on x direction and y direction.Direction θ (x, y) of point (x, y) is its direction average around in region [x-ε: x+ ε, y-ε: y+ ε ,], and ε represents the range size of peripheral region.

Step 2: definition interior pixels and external pixels calculate position.As shown in Figure 1, the straight line in figure is the level line by frontier point.The square representative on the left side is in the interior pixels of image inside, and middle square represents boundary pixel, and the square on the right represents the external pixels be in outside image boundary.Interior pixels and external pixels are all sub-pixels.Because these three pixels are positioned on same level line, they have identical pixel value.For boundary pixel f (x, y), with its interior pixels f (x on same level line _i, y _i) and external pixels f (x _o, y _o) can be expressed as

f(x _i,y _i)＝f(x _o,y _o)＝f(x,y) (12)

_xi＝x-γ,y _i＝y-η (13)

x _o＝x+γ,y _o＝y+η (14)

In formula, γ and η represents the horizontal and vertical range deviation of interior pixels and external pixels and boundary pixel respectively.

As shown in Figure 2, be the level line being positioned at border, in frontier point near zone, can suppose that a (x, y) and b (x, y) is constant, and linear.Because the pixel value on same level line is equal, for external pixels, external pixels has following character:

ω _x(x,y)γ+ω _y(x,y)η＝0 ( ¹⁶)

ω in formula _x(x, y) and ω _y(x, y) represents the first-order partial derivative of phase place on x direction and y direction respectively.Because direction θ (x, y) also can be defined as:

θ(x,y)＝atan[ω _x(x,y),-ω _y(x,y)] ( ¹7)

γ and η can be expressed as with direction:

γ＝±αcosθ(x,y),η＝±αsinθ(x,y) (18)

α represents the distance of interior pixels and external pixels and boundary pixel.Experimentally data show, when α gets 1, the filling result of acquisition is better, and therefore in this embodiment, α value gets 1.Because ω _x(x, y) and ω _y(x, y) is generally unknown, and direction θ (x, y) is tried to achieve by method in step one and formula (11).γ and η positive and negative ± from the direction of self, there is different definition according to four borders, can be determined by following table:

Step 3: utilize bilinear interpolation to determine pixel value to be filled.As shown in Figure 3, the square row representative image boundary pixel in left side, middle square row represent external pixels, and the square row on right side represent pixel to be filled.According to bilinear interpolation, external pixels can be expressed as

f(x+γ,y+η)≈(1-|γ|)(1-|η|)f(x,y)+|γ|(1-|η|)f[x+sign(γ),y]

+(1-|γ|)|η|f[x,y+sign(η)]+|γ||η|f[x+sign(γ),y+sign(η)] (19)

Wherein, when parameter be positive number or negative time sign get 1 or-1.In formula (19), the equation left side is external pixels, and it equals boundary pixel on same level line and interior pixels, is known.Two known boundaries pixels and two unknown pixels to be filled are comprised on the right of equation.According to different boundary directions, f [x+sign (γ), y] and f [x+sign (γ), y+sign (η)] or f [x, y+sign (η)] with f [x+sign (γ), y+sign (η)] be pixel to be filled.As shown in Figure 3, in the equation of adjacent external pixels, unknown pixel repeats.List equation to each external pixels, can obtain n equation, comprise n+2 unknown number, n is the length or wide of image.Summit pixel to be filled can be made to equal the summit pixel of former figure, thus make equation equal with unknown number, can solving equation group.

Step 4: set up the system of equations on four direction according to the 3rd step respectively, system of equations is expressed as matrix form, and solve edge pixel values to be filled by the method for solution matrix.

Step 5: be filled on image by the edge pixel values of acquisition, carries out image border expansion.

As shown in Figure 4, the first pictures be with the inventive method process after the design sketch of picture after iteration noise reduction, used zero padding and mirror image fill method respectively for latter two.Obviously can observe, with the image after the inventive method process after noise reduction, there is better effect.

The invention provides the thinking of a kind of image border extending method, the method and access of this technical scheme of specific implementation is a lot, and the above is only the preferred embodiment of the present invention.It should be pointed out that for those skilled in the art, under the premise without departing from the principles of the invention, can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.

Claims (1)

1., based on the edge extending method of interference image stripe direction, based on the expansion border, direction of image boundary, comprise the steps:

The first step: by gradient direction method determination edge direction θ (x, y), as follows;

$\mathrm{\θ}(x,y)=\frac{1}{2}\arctan 2\{-\underset{u=x-\mathrm{\ϵ}}{\overset{x+\mathrm{\ϵ}}{\mathrm{\Σ}}}\underset{v=y-\mathrm{\ϵ}}{\overset{y+\mathrm{\ϵ}}{\mathrm{\Σ}}}2f_{\mathrm{x\σ}}(u,v)f_{\mathrm{y\σ}}(u,v),\underset{u=x-\mathrm{\ϵ}}{\overset{x+\mathrm{\ϵ}}{\mathrm{\Σ}}}\underset{v=y-\mathrm{\ϵ}}{\overset{y+\mathrm{\ϵ}}{\mathrm{\Σ}}}[f_{\mathrm{y\σ}}^2(u,v)-f_{\mathrm{x\σ}}^2(u,v)\left]\right\}---\left(1\right)$

Wherein f _σbe through Gauss except the bar graph after making an uproar, f _{x σ}and f _{y σ}f respectively _σfirst-order partial derivative on x direction and y direction.Direction θ (x, y) of point (x, y) is its direction average around in region [x-ε: x+ ε, y-ε: y+ ε ,], and ε represents the range size of peripheral region.

Second step: according to edge level line principle definition interior pixels and external pixels determine its position.For boundary pixel f (x, y), with its interior pixels f (x being in image inside on same level line _i, y _i) be in external pixels f (x outside image boundary _o, y _o) can be expressed as

f(x _i,y _i)＝f(x _o,y _o)＝f(x,y) (2)

x _i＝x-γ,y _i＝y-η (3)

x _o＝x+γ,y _o＝y+η (4)

In formula, γ and η represents the horizontal and vertical range deviation of interior pixels and external pixels and boundary pixel respectively.For external pixels, external pixels has following character:

ω _x(x,y)γ+ω _y(x,y)η＝0 (6)

In formula, a (x, y) represents image background intensity, and b (x, y) represents amplitude, represent phase place, ω _x(x, y) and ω _y(x, y) represents the first-order partial derivative of phase place on x direction and y direction respectively.

Because direction θ (x, y) also can be defined as:

θ(x,y)＝atan[ω _x(x,y),-ω _y(x,y)] (7)

γ and η can be expressed as with direction

γ＝±αcosθ(x,y),η＝±αsinθ(x,y) (8)

α represents the distance of interior pixels and external pixels and boundary pixel.Because ω _x(x, y) and ω _y(x, y) is generally unknown, and direction θ (x, y) is tried to achieve by method in step one.γ and η positive and negative ± from the direction of self, there is different definition according to four borders, can be determined by following table:

3rd step: utilize bilinear interpolation to determine pixel equation to be filled.The bilinear interpolation of external pixels can be expressed as

f(x+γ,y+η)≈(1-|γ|)(1-|η|)f(x,y)+|γ|(1-|η|)f[x+sign(γ),y]

(9)

+(1-|γ|)|η|f[x,y+sign(η)]+|γ||η|f[x+sign(γ),y+sign(η)]

Wherein, when parameter be positive number or negative time sign get 1 or-1; According to different boundary directions, f [x+sign (γ), y] and f [x+sign (γ), y+sign (η)] or f [x, y+sign (η)] with f [x+sign (γ), y+sign (η)] be pixel to be filled.F (x+ γ, y+ η) can calculate according to formula (2).

4th step: the system of equations setting up four all edge pixels to be filled of boundary direction according to the 3rd step respectively, is expressed as matrix form by system of equations, and solves edge pixel values to be filled by the method for solution matrix;

5th step: be filled on image by the edge pixel values of acquisition, carries out image border expansion.