CN1763472A - Quick and high-precision method for extracting center of structured light stripe - Google Patents

Abstract

The invention relates to an extraction method of structure optical fringe center, which comprises the following steps: convoluting the z (x ,y) and Gauss differential to obtain rx, ry, rxx, rxy, ryy; adapting the separability of Gauss Function to transfer the two-dimensional convolution of image into one-dimensional convolution; utilizing the recursive method to realize the Gauss one-dimensional convolution; solving the characteristic value and characteristic vector of Hessian matrix to obtain the fringe normal direction (nx, ny); solving the inferior pixel coordinate of optical fringe center according to the Taylor expansion formula. The invention reduces the operand, which realizes the rapid extraction of structure optical fringe center line.

Description

A kind of structural light stripes center quick and high-precision method for extracting

Technical field

The invention belongs to measuring technique, relate to improvement structural light stripes center extracting method.

Background technology

In active vision system based on the triangulation principle, structural light stripes is owing to the change in depth on testee surface is modulated, be reflected to distortion has then taken place in the image, the degree of its distortion has comprised the relative position information between laser instrument, the ccd video camera and the depth information on testee surface.Seek out these information, must at first from the image that contains striation, obtain the accurate position at striations center.Therefore, in structured light vision detection, a very important Flame Image Process task is exactly to obtain the accurate location information at structural light stripes center.Common striations center line extraction method has gray threshold method, extremum method, Grads threshold method etc. (seeing: Yu Qifeng, Lu Hongwei, Liu Xiaolin, " based on the precision measurement and the motion measurement of image) ", Beijing: Science Press, 2002.).These methods realize simple, but precision is not high.He Junji (sees: He Junji, Zhang Guangjun, " optical strip image Study on processing method in the structured light three-dimensional vision detection ", the journal .2003 of BJ University of Aeronautics ﹠ Astronautics, 29 (7): 593-597.) grade is carried out Gauss or fitting of parabola on the striation cross section, by asking its extreme point to obtain the sub-pixel location at striations center, this method only is suitable for the little straight line striations of normal direction variation in the image again.Hu Bin (Hu Bin, Li Dehua, Buddha's warrior attendant, Hu Hanping, " based on the structural light stripes center detection method of direction template ", computer engineering and application, 2002,11:59-60.) wait the structural light stripes center detection method that has proposed based on direction template, use a plurality of direction templates to detect the sub-pixel location that normal direction changes striations center greatly, this method noise resisting ability is strong, has certain broken line repairing ability, but calculates more complicated.Striation in the image can be understood as curvilinear structures or the lines of certain width is arranged.Steger (STEGER C, " An Unbiased Detector of Curvilinear Structures ", IEEE Transactions on Pattern Analysis and machine Intelligence.1998,20 (2): 113-125.) utilize the Hessian matrix to obtain the normal direction of striations in the image, ask extreme point on the normal direction to obtain the sub-pixel location of striations center line then.Advantages such as the Steger method has the precision height, and robustness is good are widely applied to literal identification, the road Identification in take photo by plane image or the satellite image, the fields such as extraction of medical image medium vessels, bone.The major defect of this algorithm is that operand is big, is difficult to the rapid extraction of implementation structure striations center line, is difficult to the higher application scenario of requirement of real time.

Summary of the invention

The objective of the invention is: propose a kind of structural light stripes center rapid extracting method, further improve the real-time requirement that Machine Vision Detection is used.

Technical scheme of the present invention is: a kind of structural light stripes center rapid extracting method, it is characterized in that,

1, (x y) with the gaussian kernel convolution of differential form, obtains r respectively with image z _x, r _y, r _Xx, r _Xy, r _Yy, suc as formula [1];

$\left\{\begin{array}{c}{r}_x=(\∂g(x,y)/\∂x)\⊗z(x,y)\\ r_y=(\∂g(x,y)/\∂y)\⊗z(x,y)\\ r_{\mathrm{xx}}=({\∂}^{2}g(x,y)/\∂x^2)\⊗z(x,y)\\ r_{\mathrm{yy}}=({\∂}^{2}g(x,y)/\∂y^2)\⊗z(x,y)\\ r_{\mathrm{xy}}=({\∂}^{2}g(x,y)/\∂x\∂y)\⊗z(x,y)\end{array}\right.---\left[1\right]$

1.1, utilize the separability of Gaussian function, will be converted into the one dimension convolution to the two-dimensional convolution of image; To image z (x, two-dimentional Gaussian convolution equivalence y) is Gauss row convolution and Gauss's row convolution, is two-dimentional Gauss's template of n * n for a size, the operand of the two-dimensional convolution shown in the formula [1] is 5n ²Inferior taking advantage of adds, and the operand of one dimension convolution is to take advantage of for 10n time to add, and therefore, the two-dimensional convolution shown in the formula [1] is converted into twice one dimension convolution shown in the formula [2];

$\left\{\begin{array}{c}{r}_x=g\left(y\right)\⊗((\mathrm{dg}\left(x\right)/\mathrm{dx})\⊗z(x,y))\\ r_y=(\mathrm{dg}\left(y\right)/\mathrm{dy})\⊗(g\left(x\right)\⊗z(x,y))\\ r_{\mathrm{xx}}=g\left(y\right)\⊗((d^{2}g\left(x\right)/d{x}^2)\⊗z(x,y))\\ r_{\mathrm{yy}}=(d^{2}g\left(y\right)/d{y}^2)\⊗(g\left(x\right)\⊗z(x,y))\\ r_{\mathrm{xy}}(\mathrm{dg}\left(y\right)/\mathrm{dy})\⊗((\mathrm{dg}\left(x\right)/\mathrm{dx})\⊗z(x,y))\end{array}\right.---\left[2\right]$

1.2, utilize recursion method to realize Gauss's one dimension convolution, reduce the redundant computation amount in the calculating process, the process of Recursive Implementation is divided into forward recursive and two parts of backward recursive, the result who is input as forward recursive of backward recursive; Suppose certain delegation or a certain I of classifying as (n) of input picture, the output of the forward recursive of the Gaussian convolution of the Gaussian convolution of image, single order differential and second-order differential is respectively T (n), T ' (n) and T " (n), backward recursive is exported and is respectively O (n); O ' (n) and O " (n), then have: $\left\{\begin{array}{c}T\left(n\right)=\mathrm{BI}\left(n\right)+\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{c}_{i}T(n-i)\\ O\left(n\right)=\mathrm{BT}\left(n\right)+\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{c}_{i}O(n+i)\\ T^{\′}\left(n\right)=B(I(n+1)-I(n-1))/2+\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{c}_i{T}^{\′}(n-i)\\ O^{\′}\left(n\right)=B{T}^{\′}\left(n\right)+\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{c}_i{O}^{\′}(n+i)\\ T^{\′\′}\left(n\right)=B(I\left(n\right)-I(n-1))+\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{c}_i{T}^{\′\′}(n-i)\\ O^{\′\′}\left(n\right)=B(T^{\′\′}(n+1)-T^{\′\′}\left(n\right))+\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{c}_i{O}^{\′\′}(n+i)\end{array}\right.---\left[3\right]$

Coefficient c in the formula ₁, c ₂, c ₃, B is:

$q=\left\{\begin{array}{cc}0.98711\mathrm{\σ}-0.96330& ,\mathrm{\σ}>2.5\\ 3.97156-4.14554\sqrt{1-0.26891\mathrm{\σ}}& ,0.5\≤\mathrm{\σ}\≤2.5\end{array}\right.$

c ₀＝1.57825+2.44413q+1.4281q ²+0.422205q ³

c ₁＝(2.44413q+2.85619q ²+1.26661q ³)/c ₀

c ₂＝-(1.4281q ²+1.26661q ³)/c ₀

c ₃＝0.422205q ³/c ₀

B＝1-(c ₁+c ₂+c ₃)；

2, find the solution the eigenwert and the proper vector of Hessian matrix, obtain the normal direction (n of lines _x, n _y); The expression formula H of Hessian matrix (x, y) suc as formula shown in [4], normal direction (n _x, n _y) by image z (x, the pairing proper vector of Hessian matrix eigenvalue of maximum absolute value y) provides;

$H(x,y)=\left(\begin{array}{cc}\frac{{\∂}^{2}g(x,y)}{\∂x^2}& \frac{{\∂}^{2}g(x,y)}{\∂x\∂y}\\ \frac{{\∂}^{2}g(x,y)}{\∂x\∂y}& \frac{{\∂}^{2}g(x,y)}{\∂y^2}\end{array}\right)\⊗z(x,y)---\left[4\right]$

$=\left(\begin{array}{cc}{r}_{\mathrm{xx}}& r_{\mathrm{xy}}\\ r_{\mathrm{xy}}& r_{\mathrm{yy}}\end{array}\right)$

3, find the solution the sub-pix coordinate at striations center according to Taylor expansion; The vector of unit length of supposing the striation normal direction of being tried to achieve according to the Hessian matrix is (n _x, n _y), with current point (x ₀, y ₀) be basic point, the intensity profile function on the structural light stripes xsect is carried out the second order Taylor expansion, then point (the x on the striped xsect ₀+ tn _x, y ₀+ tn _y) gray scale can be expressed as:

z(x ₀+tn _x，y ₀+tn _y)＝Z(x ₀，y ₀)+N(r _x r _y) ^T+NH(x，y)N ^T/2

N=(tn wherein _xTn _y), by _ Z/_t=0, can obtain:

$t=-\frac{n_x{r}_x+n_y{r}_y}{n_x^2{r}_{\mathrm{xx}}+2n_x{n}_y{r}_{\mathrm{xy}}+n_y^2{r}_{\mathrm{yy}}}$ Then the exact position of striation central point is (x ₀+ tn _x, y ₀+ tn _y).

Advantage of the present invention is: the convolution recurrence fast algorithm that the present invention proposes is under the precondition of not sacrificing precision and robustness, reduced the operand of algorithm widely, realized the rapid extraction of structural light stripes center line, for the real-time application of algorithm is laid a good foundation.

Description of drawings

Fig. 1 is the operand contrast of three kinds of algorithms of different.Among the figure, top dotted line is the convolution algorithm amount that adopts true two-dimentional Gaussian convolution implementation algorithm; Following dotted line is that part employing the inventive method is the convolution algorithm amount that convolution is separated implementation algorithm; Following solid line is the convolution algorithm amount that comprehensively adopts convolution Recursive Implementation algorithm of the present invention.

Fig. 2 is that the effect that adopts convolution separation method and convolution recursion method to handle same width of cloth structured light print image compares, and Fig. 2 a is a raw image, and Fig. 2 b is the result who adopts the convolution separation method to obtain, and Fig. 2 c is the result who adopts the inventive method to obtain.

Fig. 3 is that process flow diagram is extracted at the structural light stripes center that the present invention proposes.

Embodiment

Below the present invention is described in further details.At first, briefly introduce ultimate principle based on the structural light stripes center extracting method of Hessian matrix.

Basic ideas based on the sub-pixel precision structural light stripes center extraction algorithm of Hessian matrix are: at first utilize the Hessian matrix to determine the normal direction of lines, utilize Taylor expansion to obtain the sub-pixel location at striations center then on its normal direction.

The normal direction of lines be exactly image z (x, y) second order directional derivative absolute value is got the direction of maximum value in (wherein x, y is respectively horizontal stroke, the ordinate of image), this direction can be determined by eigenwert and the proper vector of calculating the Hessian matrix.The Hessian matrix can be expressed as:

$H(x,y)=\left(\begin{array}{cc}\frac{{\∂}^{2}g(x,y)}{\∂x^2}& \frac{{\∂}^{2}g(x,y)}{\∂x\∂y}\\ \frac{{\∂}^{2}g(x,y)}{\∂x\∂y}& \frac{{\∂}^{2}g(x,y)}{\∂y^2}\end{array}\right)\⊗z(x,y)$ First

$=\left(\begin{array}{cc}{r}_{\mathrm{xx}}& r_{\mathrm{xy}}\\ r_{\mathrm{xy}}& r_{\mathrm{yy}}\end{array}\right)$

Wherein (x y) is two-dimensional Gaussian function to g, _ expression convolution algorithm.Point (x ₀, y ₀) normal direction (x y) is provided by the characteristic of correspondence vector at the Hessian of this some matrix eigenvalue of maximum absolute value by image z.

The vector of unit length of supposing the striation normal direction of being tried to achieve according to the Hessian matrix is (n _x, n _y), with point (x ₀, y ₀) be basic point, the intensity profile function on the structural light stripes xsect is carried out the second order Taylor expansion, then point (the x on the striped xsect ₀+ tn _x, y ₀+ tn _y) gray scale can be expressed as:

Z (x ₀+ tn _x, y ₀+ tn _y)=Z (x ₀, y ₀)+N (r _xr _y) ^T+ NH (x, y) N ^T/ 2 second

N=(tn wherein _xTn _y), r _x, r _y(x y) obtains with the gaussian kernel convolution of corresponding differential form respectively, promptly by image z

$\left\{\begin{array}{c}{r}_x=(\∂g(x,y)/\∂x)\⊗z(x,y)\\ r_y=(\∂g(x,y)/\∂y)\⊗z(x,y)\end{array}\right.$ Third

By _ Z/_t=0, obtain according to formula second:

$t=-\frac{n_x{r}_x+n_y{r}_y}{n_x^2{r}_{\mathrm{xx}}+2n_x{n}_y{r}_{\mathrm{xy}}+n_y^2{r}_{\mathrm{yy}}}$ Fourth

Then the exact position of striation central point is (x ₀+ tn _x, y ₀+ tn _y).

By top narration as can be seen, owing to will carry out the two-dimentional Gaussian convolution of at least 5 large forms to every of entire image in the process of asking the Hessian matrix, this causes the operand of algorithm very big, is difficult to the extract real-time at implementation structure striations center.Therefore, need under the precondition that guarantees the extraction precision, reduce the operand of algorithm, the realization that improves algorithm as far as possible.

According to the separability (see: Jia Yun gets, " machine vision ", Beijing: Science Press, 2000.) of Gaussian function, (x, two-dimentional Gaussian convolution y) can equivalence be Gauss's row convolution and Gauss's row convolution to image z.For a size is two-dimentional Gauss's template of n * n, and the operand of a two-dimensional convolution is n ²Inferior taking advantage of adds, and the operand of quadratic one-dimensional convolution is to take advantage of for 2n time to add.Obviously, the separability of Gaussian convolution can reduce the operand of convolution.The Gaussian convolution nuclear of differential form also satisfies this character.Utilize the separability of Gaussian convolution, 5 two-dimensional convolutions to image in the algorithm are converted into the one dimension convolution 10 times, it is identical that 2 one dimension convolution are wherein arranged, and rationally arranges can be reduced to the one dimension convolution 8 times after the computation sequence of convolution.The convolution algorithm amount of a picture point is by the 5n of the two-dimensional convolution of direct calculating in the image ²Inferior take advantage of to add to be reduced to take advantage of for 8n time add.

The inventive method can be described as " convolution recurrence fast algorithm " again.In fact, in every the two-dimentional Gaussian convolution process, same template covering lap is n (n-2) size between adjacent 2, therefore exists bulk redundancy to calculate in computed image.Above-mentioned convolution decouples computation method can not fundamentally reduce the operand of algorithm, and especially for the Gaussian convolution computing of large form, so the present invention introduces the disposal route of recurrence.

Operator f (k) to the convolution of piece image is:

$y\left(i\right)=\underset{k=0}{\overset{N-1}{\mathrm{\Σ}}}f\left(k\right)x(i-k)$ Penta

Its transport function is: $F\left(z\right)=\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}f\left(n\right)z^{-n},$ The sequence number of picture point in the i presentation video, z ^-1Be the transform operator.

Formula penta is carried out transform can be got: Y (z)=F (z) X (z), F (z)=Y (z)/X (z).F (z) is N rank functions, then has

$F\left(z\right)=\underset{i=0}{\overset{n-1}{\mathrm{\Σ}}}{a}_i{z}^{-i}/(1+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{b}_i{z}^{-i})=\frac{Y\left(z\right)}{X\left(z\right)}$

$Y\left(z\right)(1+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{b}_i{z}^{-i})=X\left(z\right)\underset{i=0}{\overset{n-1}{\mathrm{\Σ}}}{a}_i{z}^{-i}$ Heptan

Formula is carried out the Z inverse transformation heptan to be obtained:

$y\left(i\right)=\underset{j=0}{\overset{n-1}{\mathrm{\Σ}}}{a}_{j}x(i-j)-\underset{k=0}{\overset{n}{\mathrm{\Σ}}}{b}_{k}y(i-k)$ Hot

Suppose that input picture is I (n), the output of the forward recursive of the Gaussian convolution of the Gaussian convolution of image, single order differential and second-order differential is respectively T (n), T ' (n) and T " (n), backward recursive is exported and is respectively O (n), O ' (n) and O " (n), then have:

$\left\{\begin{array}{c}T\left(n\right)=\mathrm{BI}\left(n\right)+\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{c}_{i}T(n-i)\\ O\left(n\right)=\mathrm{BI}\left(n\right)+\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{c}_{i}O(n+i)\\ T^{\′}\left(n\right)=B(I(n+1)-I(n-1))/2+\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{c}_i{T}^{\′}(n-i)\\ O^{\′}\left(n\right)=B{T}^{\′}\left(n\right)+\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{c}_i{O}^{\′}(n+i)\\ T^{\′\′}\left(n\right)=B(I\left(n\right)-I(n-1))+\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{c}_i{T}^{\′\′}(n-i)\\ O^{\′\′}\left(n\right)=B(T^{\′\′}(n+1)-T^{\′\′}\left(n\right))+\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{c}_i{O}^{\′\′}(n+i)\end{array}\right.---\left[3\right]$

Coefficient c in the formula ₁, c ₂, c ₃, B is

$q=\left\{\begin{array}{cc}0.98711\mathrm{\σ}-0.96330& ,\mathrm{\σ}>2.5\\ 3.97156-4.14554\sqrt{1-0.26891\mathrm{\σ}}& ,0.5\≤\mathrm{\σ}\≤2.5\end{array}\right.$

c ₀＝1.57825+2.44413q+1.4281q ²+0.422205q ³

c ₁＝(2.44413q+2.85619q ²+1.26661q ³)/c ₀

c ₂＝-(1.4281q ²+1.26661q ³)/c ₀

c ₃＝0.422205q ³/c ₀

B＝1-(c ₁+c ₂+c ₃)

According to the separability of Gaussian function, can be successively image be carried out recursive convolution on line direction and the column direction, the result who obtains is with directly image to be carried out two-dimensional convolution consistent.Therefore, structural light stripes of the present invention center convolution recurrence Fast Extraction is summarized as follows:

1, (x y) with the gaussian kernel convolution of differential form, obtains r respectively with image z _x, r _y, r _Xx, r _Xy, r _Yy, suc as formula [1];

$\left\{\begin{array}{c}{r}_x=(\∂g(x,y)/\∂x)\⊗z(x,y)\\ r_y=(\∂g(x,y)/\∂y)\⊗z(x,y)\\ r_{\mathrm{xx}}=({\∂}^{2}g(x,y)/\∂x^2)\⊗z(x,y)\\ r_{\mathrm{yy}}=({\∂}^{2}g(x,y)/\∂y^2)\⊗z(x,y)\\ r_{\mathrm{xy}}=({\∂}^{2}g(x,y)/\∂x\∂y)\⊗z(x,y)\end{array}\right.---\left[1\right]$

1.1, utilize the separability of Gaussian function, will be converted into the one dimension convolution to the two-dimensional convolution of image; To image z (x, two-dimentional Gaussian convolution equivalence y) is Gauss row convolution and Gauss's row convolution, is two-dimentional Gauss's template of n * n for a size, the operand of the two-dimensional convolution shown in the formula [1] is 5n ²Inferior taking advantage of adds, and the operand of one dimension convolution is to take advantage of for 10n time to add, and therefore, the two-dimensional convolution shown in the formula [1] is converted into twice one dimension convolution shown in the formula [2];

$\left\{\begin{array}{c}{r}_x=g\left(y\right)\⊗((\mathrm{dg}\left(x\right)/\mathrm{dx})\⊗z(x,y))\\ r_y=(\mathrm{dg}\left(y\right)/\mathrm{dy})\⊗(g\left(x\right)\⊗z(x,y))\\ r_{\mathrm{xx}}=g\left(y\right)\⊗((d^{2}g\left(x\right)/d{x}^2)\⊗z(x,y))\\ r_{\mathrm{yy}}=(d^{2}g\left(y\right)/d{y}^2)\⊗(g\left(x\right)\⊗z(x,y))\\ r_{\mathrm{xy}}(\mathrm{dg}\left(y\right)/\mathrm{dy})\⊗((\mathrm{dg}\left(x\right)/\mathrm{dx})\⊗z(x,y))\end{array}\right.---\left[2\right]$

1.2, utilize recursion method to realize Gauss's one dimension convolution, reduce the redundant computation amount in the calculating process, the process of Recursive Implementation is divided into forward recursive and two parts of backward recursive, the result who is input as forward recursive of backward recursive; Suppose certain delegation or a certain I of classifying as (n) of input picture, the output of the forward recursive of the Gaussian convolution of the Gaussian convolution of image, single order differential and second-order differential is respectively T (n), T ' (n) and T " (n), backward recursive is exported and is respectively O (n); O ' (n) and O " (n), then have:

$\left\{\begin{array}{c}T\left(n\right)=\mathrm{BI}\left(n\right)+\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{c}_{i}T(n-i)\\ O\left(n\right)=\mathrm{BI}\left(n\right)+\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{c}_{i}O(n+i)\\ T^{\′}\left(n\right)=B(I(n+1)-I(n-1))/2+\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{c}_i{T}^{\′}(n-i)\\ O^{\′}\left(n\right)=B{T}^{\′}\left(n\right)+\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{c}_i{O}^{\′}(n+i)\\ T^{\′\′}\left(n\right)=B(I\left(n\right)-I(n-1))+\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{c}_i{T}^{\′\′}(n-i)\\ O^{\′\′}\left(n\right)=B(T^{\′\′}(n+1)-T^{\′\′}\left(n\right))+\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{c}_i{O}^{\′\′}(n+i)\end{array}\right.---\left[3\right]$

Coefficient c in the formula ₁, c ₂, c ₃, B is:

$q=\left\{\begin{array}{cc}0.98711\mathrm{\σ}-0.96330& ,\mathrm{\σ}>2.5\\ 3.97156-4.14554\sqrt{1-0.26891\mathrm{\σ}}& ,0.5\≤\mathrm{\σ}\≤2.5\end{array}\right.$

c ₀＝1.57825+2.44413q+1.4281q ²+0.422205q ³

c ₁＝(2.44413q+2.85619q ²+1.26661q ³)/c ₀

c ₂＝-(1.4281q ²+1.26661q ³)/c ₀

c ₃＝0.422205q ³/c ₀

B＝1-(c ₁+c ₂+c ₃)；

2, find the solution the eigenwert and the proper vector of Hessian matrix, obtain the normal direction (n of lines _x, n _y); The expression formula H of Hessian matrix (x, y) suc as formula shown in [4], normal direction (n _x, n _y) by image z (x, the pairing proper vector of Hessian matrix eigenvalue of maximum absolute value y) provides;

$H(x,y)=\left(\begin{array}{cc}\frac{{\&PartialD;}^{2}g(x,y)}{\&PartialD;x^2}& \frac{{\&PartialD;}^{2}g(x,y)}{\&PartialD;x\&PartialD;y}\\ \frac{{\&PartialD;}^{2}g(x,y)}{\&PartialD;x\&PartialD;y}& \frac{{\&PartialD;}^{2}g(x,y)}{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="A20051012372400131.png"\; state="\{\{state\}\}">y</figure-callout>}}^2}\end{array}\right)\&CircleTimes;z(x,y)---\left[4\right]$

$=\left(\begin{array}{cc}{r}_{\mathrm{xx}}& r_{\mathrm{xy}}\\ r_{\mathrm{xy}}& r_{\mathrm{yy}}\end{array}\right)$

3, find the solution the sub-pix coordinate at striations center according to Taylor expansion; The vector of unit length of supposing the striation normal direction of being tried to achieve according to the Hessian matrix is (n _x, n _y), with current point (x ₀, y ₀) be basic point, the intensity profile function on the structural light stripes xsect is carried out the second order Taylor expansion, then point (the x on the striped xsect ₀+ tn _x, y ₀+ tn _y) gray scale can be expressed as:

z(x ₀+tn _x，y ₀+tn _y)＝Z(x ₀，y ₀)+N(r _x r _y) ^T+NH(x，y)N ^T/2

N=(tn wherein _xTn _y), by _ Z/_t=0, can obtain:

$t=-\frac{n_x{r}_x+n_y{r}_y}{n_x^2{r}_{\mathrm{xx}}+2n_x{n}_y{r}_{\mathrm{xy}}+n_y^2{r}_{\mathrm{yy}}}$

Then the exact position of striation central point is (x ₀+ tn _x, y ₀+ tn _y).

Embodiment

By experiment, from operand, extract precision, three aspects of robustness have compared the performance of former algorithm and fast algorithm.

Operand relatively.

Referring to Fig. 1, this is the not operand of three kinds of implementation methods contrast simultaneously of template size.Suppose that the image size that a width of cloth has a structural light stripes is 768 * 576, choose Gauss's parameter σ=2.5, the size of Gaussian convolution template is got n=[8 σ]+1.When σ=2.5, n=21.The convolution algorithm amount that adopts true two-dimentional Gaussian convolution implementation algorithm is 5n ²Take advantage of for * 768 * 576=975421440 time and add; The convolution algorithm amount that adopts convolution to separate implementation algorithm is that 8n * 768 * 576=74317824 time takes advantage of and adds; The convolution algorithm amount that adopts the quick implementation algorithm of convolution recurrence is to take advantage of for 8 * 8 * 768 * 576=28311552 time to add.Obviously, the operand of convolution recurrence Fast Extraction reduces greatly, and the operand of algorithm and Gauss's parameter choose irrelevant.

On the PC of dominant frequency Pentium 2.4G, utilize VISUAL C++6.0 respectively convolution separation algorithm and convolution recursive algorithm, handle same width of cloth size and be 768 * 576 image, get σ=4 and handle required times and be respectively 650ms and 200ms.Hence one can see that, compares with the convolution separation algorithm, and convolution recurrence fast algorithm of the present invention has reduced calculated amount greatly, has improved the speed of algorithm significantly.

Algorithm extracts ratio of precision.

Adopted true picture, the extraction precision of convolution separation algorithm and convolution recurrence fast algorithm of the present invention is compared, the result is as shown in table 1.

The extraction result of two kinds of algorithms of table 1 relatively

Rounded coordinate		The convolution separation algorithm		Convolution recurrence fast algorithm		Error			The RMS error
										x/pixels	y/pixels	x/pixels	y/pixels	x/pixels	y/pixels	x/pixels	y/pixels	Distance error
275	120	274.93	119.78	274.86	119.81	0.07	0.03	0.076											0.113
									275	121	275.02	121.07	275.06	121.08	0.04	0.01	0.041
274	122	273.82	121.46	273.65	121.51	0.17	0.05	0.177
									275	122	275.12	122.37	275.25	122.36	0.13	0.01	0.130
274	123	273.92	122.76	273.85	122.79	0.07	0.03	0.076
									274	124	274.02	124.05	274.04	124.06	0.02	0.01	0.022
273	125	272.82	124.44	272.62	124.47	0.20	0.03	0.202
									274	125	274.11	125.35	274.23	125.33	0.12	0.02	0.122
273	126	272.91	125.73	272.81	125.73	0.10	0.00	0.100
									273	127	273.01	127.01	272.98	126.99	0.03	0.02	0.036

Error between convolution recurrence fast algorithm of the present invention as can be seen from Table 1 and the convolution partition method is about 0.113 pixel, show thus, convolution recurrence fast algorithm has improved speed in extracting the process of striation, but still has obtained the extraction precision with the convolution partition method.

The algorithm robustness relatively.

Referring to Fig. 2, Fig. 2 a is a raw image, and Fig. 2 b is the result who adopts the convolution separation method to obtain, and Fig. 2 c is the result who adopts the inventive method to obtain.By comparing the effect of the two kinds of same width of cloth structured light of algorithm process print images, these two kinds of methods all have good robustness.

Claims (1)

1, a kind of structural light stripes center rapid extracting method is characterized in that,

1.1, (x y) with the gaussian kernel convolution of differential form, obtains r respectively with image z _x, r _y, r _Xx, r _Xy, r _Yy, suc as formula [1];

$\left\{\begin{array}{c}{r}_x=(\&PartialD;g(x,y)/\&PartialD;x)\&CircleTimes;z(x,y)\\ r_y=(\&PartialD;g(x,y)/\&PartialD;y)\&CircleTimes;z(x,y)\\ r_{\mathrm{xx}}=({\&PartialD;}^{2}g(x,y)/\&PartialD;x^2)\&CircleTimes;z(x,y)\\ r_{\mathrm{yy}}=({\&PartialD;}^{2}g(x,y)/\&PartialD;y^2)\&CircleTimes;z(x,y)\\ r_{\mathrm{xy}}=({\&PartialD;}^{2}g(x,y)/\&PartialD;x\&PartialD;y)\&CircleTimes;z(x,y)\end{array}\right.---\left[1\right]$

1.1.1, utilize the separability of Gaussian function, will be converted into the one dimension convolution to the two-dimensional convolution of image; To image z (x, two-dimentional Gaussian convolution equivalence y) is Gauss row convolution and Gauss's row convolution, is two-dimentional Gauss's template of n * n for a size, the operand of the two-dimensional convolution shown in the formula [1] is 5n ²Inferior taking advantage of adds, and the operand of one dimension convolution is to take advantage of for 10n time to add, and therefore, the two-dimensional convolution shown in the formula [1] is converted into twice one dimension convolution shown in the formula [2];

$\left\{\begin{array}{c}{r}_x=g\left(y\right)\&CircleTimes;((\mathrm{dg}\left(x\right)/\mathrm{dx})\&CircleTimes;z(x,y))\\ r_y=(\mathrm{dg}\left(y\right)/\mathrm{dy})\&CircleTimes;(g\left(x\right)\&CircleTimes;z(x,y))\\ r_{\mathrm{xx}}=g\left(y\right)\&CircleTimes;((d^{2}g\left(x\right)/d{x}^2)\&CircleTimes;z(x,y))\\ r_{\mathrm{yy}}=(d^{2}g\left(y\right)/d{y}^2)\&CircleTimes;(g\left(x\right)\&CircleTimes;z(x,y))\\ r_{\mathrm{xy}}=(\mathrm{dg}\left(y\right)/\mathrm{dy})\&CircleTimes;((\mathrm{dg}\left(x\right)/\mathrm{dx})\&CircleTimes;z(x,y))\end{array}\right.---\left[2\right]$

1.1.2, utilize recursion method to realize Gauss's one dimension convolution, reduce the redundant computation amount in the calculating process, the process of Recursive Implementation is divided into forward recursive and two parts of backward recursive, the result who is input as forward recursive of backward recursive; Suppose certain delegation or a certain I of classifying as (n) of input picture, the output of the forward recursive of the Gaussian convolution of the Gaussian convolution of image, single order differential and second-order differential is respectively T (n), T ' (n) and T " (n), backward recursive is exported and is respectively O (n); O ' (n) and O " (n), then have:

$\left\{\begin{array}{c}T\left(n\right)=\mathrm{BI}\left(n\right)+\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{c}_{i}T(n-i)\\ O\left(n\right)=\mathrm{BT}\left(n\right)+\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{c}_{i}O(n+i)\\ T\left(n\right)=B(I(n+1)-I(n-1))/2+\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{c}_i{T}^{\&prime;}(n-i)\\ O^{\&prime;}\left(n\right)={\mathrm{BT}}^{\&prime;}\left(n\right)+\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{c}_i{O}^{\&prime;}(n+i)\\ T^{\&prime;\&prime;}\left(n\right)=B(I\left(n\right)-I(n-1))+\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{c}_i{T}^{\&prime;\&prime;}(n-i)\\ O^{\&prime;\&prime;}\left(n\right)=B(T^{\&prime;\&prime;}(n+1)-T^{\&prime;\&prime;}\left(N\right))+\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{c}_i{O}^{\&prime;\&prime;}(n+i)\end{array}\right.---\left[3\right]$

Coefficient c in the formula ₁, c ₂, c ₃, B is:

$q=\left\{\begin{array}{cc}0.98711\mathrm{\&sigma;}-0.96330& ,\mathrm{\&sigma;}>2.5\\ 3.97156-4.14554\sqrt{1-0.26891\mathrm{\&sigma;}}& ,0.5\&le;\mathrm{\&sigma;}\&le;2.5\end{array}\right.$

c ₀＝1.57825+2.44413q+1.4281q ²+0.422205q ³

c ₁＝(2.44413q+2.85619q ²+1.26661q ³)/c ₀

c ₂＝-(1.4281q ²+1.26661q ³)/c ₀

c ₃＝0.422205q ³/c ₀

B＝1-(c ₁+c ₂+c ₃)；

1.2, find the solution the eigenwert and the proper vector of Hessian matrix, obtain the normal direction (n of lines _x, n _y); The expression formula H of Hessian matrix (x, y) suc as formula shown in [4], normal direction (n _x, n _y) by image z (x, the pairing proper vector of Hessian matrix eigenvalue of maximum absolute value y) provides;

$H(x,y)=\left(\begin{array}{cc}\frac{{\&PartialD;}^{2}g(x,y)}{\&PartialD;x^2}& \frac{{\&PartialD;}^{2}g(x,y)}{\&PartialD;x\&PartialD;y}\\ \frac{{\&PartialD;}^{2}g(x,y)}{\&PartialD;x\&PartialD;y}& \frac{{\&PartialD;}^{2}g(x,y)}{\&PartialD;y^2}\end{array}\right)\&CircleTimes;z(x,y)---\left[4\right]$

$=\left(\begin{array}{cc}{r}_{\mathrm{xx}}& r_{\mathrm{xy}}\\ r_{\mathrm{xy}}& r_{\mathrm{yy}}\end{array}\right)$

1.3, find the solution the sub-pix coordinate at striations center according to Taylor expansion; The vector of unit length of supposing the striation normal direction of being tried to achieve according to the Hessian matrix is (n _x, n _y), with current point (x ₀, y ₀) be basic point, the intensity profile function on the structural light stripes xsect is carried out the second order Taylor expansion, then point (the x on the striped xsect ₀+ tn _x, y ₀+ tn _y) gray scale can be expressed as:

z(x ₀+tn _x，y ₀+tn _y)＝Z(x ₀，y ₀)+N(r _x r _y) ^T+NH(x，y)N ^T/2

N=(tn wherein _xTn _y), by _ Z/_t=0, can obtain:

$t=-\frac{n_x{r}_x+n_y{r}_y}{n_x^2{r}_{\mathrm{xx}}+2n_x{n}_y{r}_{\mathrm{xy}}+n_y^2{r}_{\mathrm{yy}}}$

Then the exact position of striation central point is (x ₀+ tn _x, y ₀+ tn _y).

Images