CN101408985A - Method and apparatus for extracting circular luminous spot second-pixel center - Google Patents

Method and apparatus for extracting circular luminous spot second-pixel center Download PDF

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CN101408985A
CN101408985A CNA2008102226666A CN200810222666A CN101408985A CN 101408985 A CN101408985 A CN 101408985A CN A2008102226666 A CNA2008102226666 A CN A2008102226666A CN 200810222666 A CN200810222666 A CN 200810222666A CN 101408985 A CN101408985 A CN 101408985A
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center
light spot
pixel
pixels
circular light
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CN101408985B (en
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张广军
杨珍
孙军华
刘谦哲
吴子彦
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Beihang University
Beijing University of Aeronautics and Astronautics
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Abstract

The invention discloses a method for extracting circular facula sub-pel center and a device thereof. In the proposal of the invention, firstly, the initial position of the circular facula center is determined by utilizing a center of mass method; then, the pel position of the circular facula center is determined in a window by taking the initial position as a center according to the characteristic value of Hessian matrix; finally, image gradation function which is continuously distributed in a neighborhood of the pel position of the circular facula center is determined by using second order taylor expansion, and the position of extreme point of the image gradation function is the sub-pel position of the circular facula center. The searching range of the circular facula center is narrowed to a smaller area fast by the proposal of the invention, thus leading the follow-up operation such as gauss convolution, the calculation of S and the searching of the extremum to be carried out in the smaller area, and the calculated amount is small and the extracting speed is rapid. Therefore, the sub-pel position of the circular facula center is determined by the taylor expansion and the extracting precision of the circular facula center is ensured.

Description

A kind of circular facula sub-pel center extracting method and device
Technical field
The present invention relates to image processing techniques, be meant a kind of circular facula sub-pel center extracting method and device especially.
Background technology
The hot spot extraction is the important step in demarcation of 3D vision detection system and the measuring process, and in order to guarantee accuracy of measurement system and stability, the extraction precision that requires hot spot is at sub-pixel.Circular light spot widely uses in extraction, because the round-shaped of its uniqueness is easy to identification and extraction, and it is higher to extract ratio of precision.Traditional circular luminous spot second-pixel extracting method mainly comprises: edge fitting method and Gauss's surface fitting method.
A kind of implementation of edge fitting method is to utilize the edge of Canny operator extraction circular light spot, to the edge of circular light spot carrying out the center that the least square ellipse fitting obtains circular light spot; Another kind of implementation is to utilize the morphology principle to extract the circular light spot edge, and match obtains the circular light spot center.The computation process of edge fitting method is simple, but less when circular light spot shared pixel in image, or picture noise is when big, and the circular light spot edge can be irregular, makes that to extract precision lower.
Gauss's surface fitting method is carried out Gauss's surface fitting near the gray scale of the pixel circular light spot, and the center of match gained Gauss curved surface is the circular light spot center.Though it is higher that Gauss's surface fitting method is extracted precision, but, before pixel grey scale is carried out Gauss's surface fitting, usually need carry out Gaussian convolution to the big neighborhood scope of circular light spot, eliminate of the influence of circular light spot out-of-shape with this to Gauss's surface fitting, therefore calculated amount is bigger, and extraction time is long.
In sum, how high precision, realizing that circular light spot extracts becomes the problem that presses for solution fast.
Summary of the invention
In view of this, fundamental purpose of the present invention is to provide a kind of circular facula sub-pel center extracting method and device, and extraction rate is fast, and extracts the precision height.
For achieving the above object, technical scheme of the present invention is achieved in that
A kind of circular facula sub-pel center extracting method, this method comprises:
A, utilize centroid method to determine the initial position at circular light spot center;
B, be in the window at center with described initial position, determining the location of pixels at circular light spot center according to the eigenwert of the gloomy Hessian matrix in sea;
C, utilize the second order Taylor expansion to determine the gradation of image function of continuous distribution in the location of pixels neighborhood at described circular light spot center, the extreme point position of this gradation of image function is the sub-pixel location at circular light spot center.
Initial position described in the steps A is: (x i, y i), wherein, x i = round ( Σ x Σ y I ( x , y ) · x Σ x Σ y I ( x , y ) ) , y i = round ( Σ x Σ y I ( x , y ) · y Σ x Σ y I ( x , y ) ) , Wherein, round () is the computing that rounds up, and (x is that image is at pixel (x, the gray-scale value of y) locating y) to I.
Described step B comprises: the expression formula of Hessian matrix is: H ( x , y ) = f xx f xy f xy f yy , Wherein, f Xx, f XyAnd f YyBe respectively the second-order partial differential coefficient of gradation of image function with respect to x, y; λ 1, λ 2Be two eigenwerts of described Hessian matrix, the second derivative that is used for presentation video gray scale function pixel (x, maximum value of y) locating and minimal value, S = λ 1 · λ 2 x = f x f yy - f xy 2 ; With pixel (x i, y i) be in the window at center, calculate the S value of each pixel, make the pixel (x that the S value is maximum 0, y 0) be the location of pixels at circular light spot center.
Described step C comprises: utilize the second order Taylor expansion to obtain the gradation of image function at pixel (x 0, y 0) (x more arbitrarily in the neighborhood 0+ u, y 0The expression formula of+the gray-scale value v) located is r ( x 0 + u , y 0 + v ) = r 0 + u v f x ( x 0 , y 0 ) f y ( x 0 , y 0 ) + 1 2 u v f xx ( x 0 , y 0 ) f xy ( x 0 , y 0 ) f xy ( x 0 , y 0 ) f yy ( x 0 , y 0 ) u v , Wherein, r 0For image at pixel (x 0, y 0) gray-scale value located, u, v are respectively pixel (x 0, y 0) in the neighborhood arbitrarily a bit with respect to x 0, y 0Side-play amount, f x(x 0, y 0), f y(x 0, y 0), f Xx(x 0, y 0), f Xy(x 0, y 0) and f Yy(x 0, y 0) be respectively the gradation of image function at pixel (x 0, y 0) locate with respect to x, y one, second-order partial differential coefficient; According to extreme point x, y directional derivative is 0, obtains system of linear equations on the basis of described expression formula: f xx ( x 0 , y 0 ) u + f xy ( x 0 , y 0 ) v + f x ( x 0 , y 0 ) = 0 f xy ( x 0 , y 0 ) u + f yy ( x 0 , y 0 ) v + f y ( x 0 , y 0 ) = 0 , According to this system of linear equations, determine the sub-pixel location (x at circular light spot center 0+ u s, y 0+ v s), wherein, u s = f y ( x 0 , y 0 ) f xy ( x 0 , y 0 ) - f x ( x 0 , y 0 ) f yy ( x 0 , y 0 ) f xx ( x 0 , y 0 ) f yy ( x 0 , y 0 ) - f xy 2 ( x 0 , y 0 ) , v s = f x ( x 0 , y 0 ) f xy ( x 0 , y 0 ) - f y ( x 0 , y 0 ) f xx ( x 0 , y 0 ) f xx ( x 0 , y 0 ) f yy ( x 0 , y 0 ) - f xy 2 ( x 0 , y 0 ) , u s, v sAll determine according to described system of linear equations.
The size of described window is that 3 pixels * 3 pixels are to 5 pixels * 5 pixels.
Described window is square window or circular window.
A kind of circular facula sub-pel center extraction element, this device comprises: initial position determining unit, center determining unit and sub-pixel location determining unit, wherein, the initial position determining unit is used to utilize centroid method to determine the initial position at circular light spot center; The center determining unit is used for determining the location of pixels at circular light spot center according to the eigenwert of Hessian matrix being in the window at center with described initial position; The gradation of image function of continuous distribution in the location of pixels neighborhood that the sub-pixel location determining unit is used to utilize the second order Taylor expansion to determine described circular light spot center, the extreme point position of this gradation of image function is the sub-pixel location at circular light spot center.
The size of described window is that 3 pixels * 3 pixels are to 5 pixels * 5 pixels.
Described window is square window or circular window.
In the scheme provided by the invention, at first utilize centroid method to determine the initial position at circular light spot center, the scope of circular light spot center search is contracted to a less zone rapidly, makes the calculating of subsequent operation such as Gaussian convolution, S value and the search of S value extreme value only need in a less zone, to carry out; In a window that with this initial position is the center, determine the location of pixels at circular light spot center according to the eigenwert of Hessian matrix then; Utilize the second order Taylor expansion to determine the gradation of image function of continuous distribution in the location of pixels neighborhood at circular light spot center at last, the extreme point position of this gradation of image function is the sub-pixel location at circular light spot center.
Extract the scheme at circular light spot center with respect to Gauss's surface fitting method, scheme provided by the invention is carried out Gaussian convolution to the circular light spot image in need not on a large scale, and calculated amount is less, and extraction rate is fast.Can determine the sub-pix center at circular light spot center at last by Taylor expansion, guarantee the extraction precision at circular light spot center.
Extract the scheme at circular light spot center with respect to the edge fitting method, when scheme provided by the invention is finally determined the circular facula sub-pel center position, just utilized the contiguous gradation of image in circular light spot center, be not subjected to therefore that the circular light spot edge is irregular influences, it is higher to extract precision; Utilize the smoothing effect of Gaussian convolution simultaneously, reduced the influence when noise extracts the circular light spot center, under the bigger situation of noise, still have higher extraction precision image.
Description of drawings
Fig. 1 extracts process flow diagram for circular facula sub-pel center among the present invention;
Fig. 2 is typical circular light spot gradation of image synoptic diagram;
Fig. 3 is the S value distribution schematic diagram in the circular light spot field;
Fig. 4 is the gradation of image function synoptic diagram of continuous distribution in the circular light spot pixel center neighborhood that is obtained by Taylor expansion;
Fig. 5 is the structural representation of circular facula sub-pel center extraction element among the present invention.
Embodiment
In the scheme provided by the invention, at first utilize centroid method to determine the initial position at circular light spot center; In a window that with this initial position is the center, determine the location of pixels at circular light spot center according to the eigenwert of Hai Sen (Hessian) matrix then; Utilize the second order Taylor expansion to determine the gradation of image function of continuous distribution in the location of pixels neighborhood at circular light spot center at last, the extreme point position of this gradation of image function is the sub-pixel location at circular light spot center.
Fig. 1 extracts process flow diagram for circular facula sub-pel center among the present invention, and as shown in Figure 1, the leaching process of circular facula sub-pel center may further comprise the steps:
Step 101: utilize centroid method to determine the initial position (x at circular light spot center i, y i), x i = round ( Σ x Σ y I ( x , y ) · x Σ x Σ y I ( x , y ) ) , y i = round ( Σ x Σ y I ( x , y ) · y Σ x Σ y I ( x , y ) ) , Round () is the computing that rounds up, and wherein, (x is that image is at pixel (x, the gray-scale value of y) locating y) to I.
Step 102: with initial position (x i, y i) be in the window at center, determine the location of pixels at circular light spot center according to the eigenwert of Hessian matrix.The size of window is about 3 pixels * 3 pixels to 5 pixels * 5 pixels, and this window can be square window or circular window.
The expression formula of Hessian matrix is: H ( x , y ) = f xx f xy f xy f yy , Wherein, f Xx, f XyAnd f YyBe respectively the second-order partial differential coefficient of gradation of image function, can obtain with the Gauss operator convolution of corresponding differential form by the gradation of image function with respect to x, y.
Because S = λ 1 · λ 2 x = f x f yy - f xy 2 , Wherein, λ 1, λ 2Be two eigenwerts of Hessian matrix, the second derivative that is used for presentation video gray scale function is in pixel (x, maximum value of y) locating and minimal value.According to the intensity profile characteristics of circular light spot, as shown in Figure 2, λ 1, λ 2Pixel will reach the negative pole value at place, circular light spot center, and therefore, S will reach positive extreme value.Like this, with pixel (x i, y i) be in the square window at center, calculate the S value of each pixel, the S value in this square window distributes as shown in Figure 3, makes the pixel (x of S value maximum 0, y 0) be the location of pixels at circular light spot center.
Step 103: utilize the second order Taylor expansion to describe the gradation of image function of continuous distribution in this circular light spot center pixel position neighborhood, the extreme point position of this gradation of image function is the sub-pixel location at circular light spot center.
After determining the location of pixels at circular light spot center, can utilize the second order Taylor expansion to describe in this vertex neighborhood, the gradation of image function is at (x more arbitrarily 0+ u, y 0The expression formula of+the gray-scale value v) located is:
r ( x 0 + u , y 0 + v ) = r 0 + u v f x ( x 0 , y 0 ) f y ( x 0 , y 0 ) + 1 2 u v f xx ( x 0 , y 0 ) f xy ( x 0 , y 0 ) f xy ( x 0 , y 0 ) f yy ( x 0 , y 0 ) u v - - - ( 1 )
Wherein, r 0Image is at pixel (x 0, y 0) gray-scale value located; U, v are respectively pixel (x 0, y 0) in the neighborhood arbitrarily a bit with respect to x 0, y 0Side-play amount; f x(x 0, y 0), f y(x 0, y 0), f Xx(x 0, y 0), f Xy(x 0, y 0) and f Yy(x 0, y 0) be respectively the gradation of image function at pixel (x 0, y 0) locate with respect to x, y one, second-order partial differential coefficient.
Fig. 4 is the gradation of image function in the circular light spot center neighborhood that is obtained by Taylor expansion, and this gradation of image function is the quadric surface of a hat, and its extreme point is the sub-pixel location at circular light spot center.Should be 0 according to extreme point x, y directional derivative, on the basis of formula (1), can obtain system of linear equations f xx ( x 0 , y 0 ) u + f xy ( x 0 , y 0 ) v + f x ( x 0 , y 0 ) = 0 f xy ( x 0 , y 0 ) u + f yy ( x 0 , y 0 ) v + f y ( x 0 , y 0 ) = 0 , According to this system of linear equations, determine the sub-pixel location (x at circular light spot center 0+ u s, y 0+ v s), wherein, u s = f y ( x 0 , y 0 ) f xy ( x 0 , y 0 ) - f x ( x 0 , y 0 ) f yy ( x 0 , y 0 ) f xx ( x 0 , y 0 ) f yy ( x 0 , y 0 ) - f xy 2 ( x 0 , y 0 ) , v s = f x ( x 0 , y 0 ) f xy ( x 0 , y 0 ) - f y ( x 0 , y 0 ) f xx ( x 0 , y 0 ) f xx ( x 0 , y 0 ) f yy ( x 0 , y 0 ) - f xy 2 ( x 0 , y 0 ) , u s, v sAll determine according to system of linear equations.
Come performing step of the present invention is further specified below by simulation example.Generate the circular light spot image by computing machine, the detailed process that this circular light spot image is extracted is as follows:
Step 201: utilize centroid method to calculate the initial position at circular light spot center.
Step 202: in the window of one 5 pixel * 5 pixels that with the initial position is the center, to each pixel in the circular light spot image, by with the gray scale of each pixel of Gauss operator convolutional calculation of corresponding differential form second-order partial differential coefficient f with respect to x, y Xx, f XyAnd f Yy
Step 203: the S value of each pixel in the calculation window, determine the location of pixels at circular light spot center by the extreme value of S.
Step 204:, determine the sub-pixel location at circular light spot center according to formula (1) to the circular light spot center pixel position of determining in the step 203.
Fig. 5 is the structural representation of circular facula sub-pel center extraction element among the present invention, as shown in Figure 5, this device comprises initial position determining unit, center determining unit and sub-pixel location determining unit, wherein, the initial position determining unit is used to utilize centroid method to determine the initial position at circular light spot center, and this initial position is offered the center determining unit; The center determining unit is used in a window that with the initial position is the center, determines the location of pixels at circular light spot center according to the eigenwert of Hessian matrix, and the location of pixels at this circular light spot center is offered the sub-pixel location determining unit; The gradation of image function of continuous distribution in the location of pixels neighborhood that the sub-pixel location determining unit is used to utilize the second order Taylor expansion to determine the circular light spot center, the extreme point position of this gradation of image function is the sub-pixel location at circular light spot center.
Adding noise variance on the circular light spot gradation of image is the Gaussian noise of s, and s gets 10 from 1.Table 1 is traditional Gauss curve fitting circular light spot center extraction scheme and the extraction precision contrast of circular light spot of the present invention center extraction scheme under different noise levels, and by table 1 as seen, scheme provided by the invention slightly is better than traditional Gauss curve fitting scheme on the extraction precision.
Figure A20081022266600101
Two kinds of schemes of table 1 are extracted the precision contrast
Table 2 is to extract the existing Gauss curve fitting scheme of single spot center and the contrast of scheme provided by the invention used averaging time, and the extraction rate of scheme provided by the invention will be obviously faster than existing Gauss curve fitting scheme.
Average extraction time (unit: second)
Existing Gauss curve fitting scheme 2.79
The present invention program 1.35
The extraction time contrast of two kinds of schemes of table 2
The above is preferred embodiment of the present invention only, is not to be used to limit protection scope of the present invention.

Claims (9)

1, a kind of circular facula sub-pel center extracting method is characterized in that, this method comprises:
A, utilize centroid method to determine the initial position at circular light spot center;
B, be in the window at center with described initial position, determining the location of pixels at circular light spot center according to the eigenwert of the gloomy Hessian matrix in sea;
C, utilize the second order Taylor expansion to determine the gradation of image function of continuous distribution in the location of pixels neighborhood at described circular light spot center, the extreme point position of this gradation of image function is the sub-pixel location at circular light spot center.
2, method according to claim 1 is characterized in that, initial position described in the steps A is: (x i, y i), wherein, x i = round ( Σ x Σ y I ( x , y ) · x Σ x Σ y I ( x , y ) ) , y i = round ( Σ x Σ y I ( x , y ) · y Σ x Σ y I ( x , y ) ) , Wherein, round () is the computing that rounds up, and (x is that image is at pixel (x, the gray-scale value of y) locating y) to I.
3, method according to claim 2 is characterized in that, described step B comprises:
The expression formula of Hessian matrix is: H ( x , y ) = f xx f xy f xy f yy , Wherein, f Xx, f XyAnd f YyBe respectively the second-order partial differential coefficient of gradation of image function with respect to x, y;
λ 1, λ 2Be two eigenwerts of described Hessian matrix, the second derivative that is used for presentation video gray scale function pixel (x, maximum value of y) locating and minimal value, S = λ 1 · λ 2 x = f x f yy - f xy 2 ;
With pixel (x i, y i) be in the window at center, calculate the S value of each pixel, make the pixel (x that the S value is maximum 0, y 0) be the location of pixels at circular light spot center.
4, method according to claim 3 is characterized in that, described step C comprises:
Utilize the second order Taylor expansion to obtain the gradation of image function at pixel (x 0, y 0) (x more arbitrarily in the neighborhood 0+ u, y 0The expression formula of+the gray-scale value v) located is r ( x 0 + u , y 0 + v ) = r 0 + u v f x ( x 0 , y 0 ) f y ( x 0 , y 0 ) + 1 2 u v f xx ( x 0 , y 0 ) f xy ( x 0 , y 0 ) f xy ( x 0 , y 0 ) f yy ( x 0 , y 0 ) u v , Wherein, r 0For image at pixel (x 0, y 0) gray-scale value located, u, v are respectively pixel (x 0, y 0) in the neighborhood arbitrarily a bit with respect to x 0, y 0Side-play amount, f x(x 0, y 0), f y(x 0, y 0), f Xx(x 0, y 0), f Xy(x 0, y 0) and f Yy(x 0, y 0) be respectively the gradation of image function at pixel (x 0, y 0) locate with respect to x, y one, second-order partial differential coefficient;
According to extreme point x, y directional derivative is 0, obtains system of linear equations on the basis of described expression formula: f xx ( x 0 , y 0 ) u + f xy ( x 0 , y 0 ) v + f x ( x 0 , y 0 ) = 0 f xy ( x 0 , y 0 ) u + f yy ( x 0 , y 0 ) v + f y ( x 0 , y 0 ) = 0 , According to this system of linear equations, determine the sub-pixel location (x at circular light spot center 0+ u s, y 0+ v 0), wherein, u s = f y ( x 0 , y 0 ) f xy ( x 0 , y 0 ) - f x ( x 0 , y 0 ) f yy ( x 0 , y 0 ) f xx ( x 0 , y 0 ) f yy ( x 0 , y 0 ) - f xy 2 ( x 0 , y 0 ) , v s = f x ( x 0 , y 0 ) f xy ( x 0 , y 0 ) - f y ( x 0 , y 0 ) f xx ( x 0 , y 0 ) f xx ( x 0 , y 0 ) f yy ( x 0 , y 0 ) - f xy 2 ( x 0 , y 0 ) , u s, v sAll determine according to described system of linear equations.
According to the arbitrary described method of claim 1 to 4, it is characterized in that 5, the size of described window is that 3 pixels * 3 pixels are to 5 pixels * 5 pixels.
6, method according to claim 5 is characterized in that, described window is square window or circular window.
7, a kind of circular facula sub-pel center extraction element is characterized in that, this device comprises: initial position determining unit, center determining unit and sub-pixel location determining unit, wherein,
The initial position determining unit is used to utilize centroid method to determine the initial position at circular light spot center;
The center determining unit is used for determining the location of pixels at circular light spot center according to the eigenwert of Hessian matrix being in the window at center with described initial position;
The gradation of image function of continuous distribution in the location of pixels neighborhood that the sub-pixel location determining unit is used to utilize the second order Taylor expansion to determine described circular light spot center, the extreme point position of this gradation of image function is the sub-pixel location at circular light spot center.
8, device according to claim 7 is characterized in that, the size of described window is that 3 pixels * 3 pixels are to 5 pixels * 5 pixels.
According to claim 7 or 8 described devices, it is characterized in that 9, described window is square window or circular window.
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