Lens center point extraction method for lens center deviation measurement equipment

Abstract

The present invention relates to a lens center point extraction method for a lens center deviation measuring device, the method is as follows: filtering the collected image; using the canny operator to perform edge detection to obtain the pixel value of each pixel point; taking the pixel points with pixel values ​​of each row and each column equal to 255 as feature points; fitting the feature points to obtain four straight lines and obtaining the coordinates of the center point of the crosshair target image according to the intersection of the four straight lines; rotating the rotating table to obtain a fitting circle of the center points of multiple crosshair target images, adjusting the placement angle of the measured lens to move the center point of the crosshair target image to the center position of the fitting circle until the fitting circle cannot be reduced, and taking the center point of the crosshair target image at this time as the center of the measured lens. The present invention improves the measurement accuracy of the lens center deviation.

Description

Technical Field

[0001] The invention belongs to the technical field of lens center deviation measurement, and relates to a lens center point extraction method of a lens center deviation measurement device. Background Art

[0002] As the last link in the production, the adjustment of optical lenses is one of the keys to ensure the performance of optical lenses by strictly controlling the center deviation and mirror spacing of optical lenses. In addition, the detection and verification of the center deviation of each lens in the assembled optical lens group is also a problem often encountered by optical personnel. The non-contact lens center deviation measuring instrument is based on the reflective measurement method. The light source illuminates the crosshair target, which passes through the dichroic prism and the measuring lens group to form a converging beam or a diverging beam. The converging beam has a convergence point, and the reverse extension line of the diverging beam will also converge at a point, which we call the convergence point here. The convergence point of the crosshair target is made to coincide with the vertex of the current measured mirror surface. At this time, the light beam incident on the measured mirror surface is partially reflected on the surface of the measured lens. The reflected light beam returns to the self-collimation measuring lens group along the original path, passes through the dichroic prism, and is focused on the target surface of the imaging detector to form a clear crosshair target image. The accurate extraction of the center point of the crosshair target image plays a vital role in the result of the lens center deviation measurement.

[0003] At present, in the measurement of lens center deviation, the crosshair target image is extracted using the Hough transform method. This method is susceptible to noise interference and has low accuracy due to inaccurate threshold setting. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a lens center point extraction method for a lens center deviation measuring device, which can effectively prevent noise from affecting the accuracy of extracting the center point of a crosshair target image under noise interference, thereby improving the measurement accuracy of the lens center deviation.

[0005] In order to solve the above technical problems, the lens center point extraction method of the lens center deviation measurement device of the present invention is as follows:

[0006] Each frame of the image collected by the imaging detector is filtered; the edge of the filtered image is detected using the Canny operator to obtain the pixel value of each pixel point of the image after edge detection;

[0007] Find all pixel points with a pixel value of 255 in each row, take the first pixel point with a pixel value of 255 in each row as the A feature point, store its coordinates in the set XL (Lcount), and store all subsequent pixel points with a pixel value of 255 as the B feature points in the set XR (Rcount); find all pixel points with a pixel grayscale value of 255 in each column, store the first pixel point with a pixel value of 255 in each column as the C feature point in the set YUp (upcount), and store all subsequent pixel points with a pixel grayscale value of 255 as the D feature points in the set Yd (dcount);

[0008] Perform straight line fitting on feature points A, B, C and D to obtain four straight lines; calculate the center point coordinates of the crosshair target image based on the four intersection points of the four straight lines;

[0009] Continuously rotate the rotating table of the lens center deviation measuring device, obtain the center point coordinates of multiple crosshair target images during the rotation of the rotating table, fit the center points of the multiple crosshair target images to obtain a fitting circle, adjust the placement angle of the measured lens, so that the center point of the crosshair target image calculated in real time moves to the center position of the fitting circle; similarly continue to rotate the turntable, adjust the placement angle of the measured lens, and obtain the fitting circle formed by fitting the center points of the multiple crosshair target images; until the fitting circle formed by fitting the center points of the multiple crosshair target images cannot be reduced, the center point of the crosshair target image at this time is used as the center of the measured lens.

[0010] Furthermore, the present invention preferably uses median filtering to perform impulse noise processing on each frame of image, and then uses Gaussian filtering to perform Gaussian noise suppression processing on the image after median filtering.

[0011] The median filter uses a two-dimensional template to sort the pixels in the two-dimensional template according to the size of the pixel value, generate a monotonically rising or falling two-dimensional data sequence, and use the following formula to calculate the pixel value of each pixel of the image after the median filter processing:

[0012] g(i, j)=med{f(im, jn), (m, n∈w)}

[0013] Among them, f(i, j) represents the pixel value of any pixel point I(i, j) in the original image, g(i, j) represents the pixel value of the pixel point I(i, j) in the image after median filtering, (i, j) is the coordinate of the pixel point I(i, j); w is a two-dimensional template.

[0014] The two-dimensional template filtering window is 3×3, m=1,2,3, n=1,2,3.

[0015] The Gaussian filter is processed using a 3×3 mask, and the pixel value of each pixel point I (i, j) of the image after Gaussian filtering is calculated using the following formula:

[0016] G(i,j)={g(i-1,j-1)+g(i-1,j+1)+g(i+1,j-1)+g(i+1,j+1)+[g(i-1,j)+g(i,j-1)+g(i+1,j)+g(i,j+1)]} / 16;

[0017] G(i, j) is the pixel value of the image pixel point I(i, j) after Gaussian filtering, and g(i, j) is the pixel value of the image pixel point I(i, j) after median filtering.

[0018] The method of using the canny operator to perform edge detection on the filtered image G(i, j) is as follows:

[0019] Starting from the pixel points with pixel values ​​higher than the high threshold T1, all the pixel points with pixel values ​​greater than the low threshold T2 and connected to each other are retained; T1, T2∈MAX, the maximum pixel value MAX of the pixel point is 255; the high threshold T1 is (0.5, 1)×MAX, and the low threshold T2 is (0, 0.5)×MAX; the pixel value of each pixel point in the image after edge detection is calculated according to the following formula:

[0020] F(i,j)=canny{G(i,j),T2,T1};

[0021] F(i, j) is the pixel value of the image pixel I(i, j) after edge detection;

[0022] In the present invention, the upper threshold T1 is preferably 0.5×MAX, and the lower threshold T2 is preferably 0.3×MAX.

[0023] Use the least squares method to fit a straight line:

[0024] Substitute the coordinates of feature points A, B, C, and D into the formula y i =α0+α1x i Four straight lines are obtained by linear fitting, α0 represents the intercept, and α1 represents the slope;

[0025]

[0026]

[0027] (x i ,y i ) is the coordinate of any feature point.

[0028] The coordinates of the center point of the crosshair target image are (centx, centy) and the calculation method is as follows: suppose one of the straight lines is Lxl (a, b), a and b are the two end points of the straight line respectively; the other straight line is Lxr (c, d), c and d are the two end points of the straight line; according to the following formula, determine whether the two straight lines Lxl (a, b) and Lxr (c, d) have an intersection;

[0029] denominator=(by-ay)×(dx-cx)-(ax-bx)×(cy-dy)

[0030] Where denominator is the denominator judgment value; by is the y coordinate of endpoint b, ay is the y coordinate of endpoint a, dx is the x coordinate of endpoint d, cx is the x coordinate of endpoint c, ax is the x coordinate of endpoint a, bx is the x coordinate of endpoint b, cy is the y coordinate of endpoint c, and dy is the y coordinate of endpoint d; if the denominator judgment value denominator is 0, it means that the two lines are parallel; if the denominator judgment value denominator is not 0, the intersection of the two straight lines is calculated according to the following formula:

[0031]

[0032]

[0033] According to the above formula, we can obtain the coordinates of the four intersection points of the four straight lines as (cx1, cy1), (cx2, cy2), (cx2, cy2), (cx2, cy2), and the coordinates of the center point of the crosshair target image as (centx, centy) according to the following formula;

[0034] centx=(cx1+cx2+cx3+cx4) / 4

[0035] centy=(cy1+cy2+cy3+cy4) / 4

[0036] Beneficial effects of the present invention: The present invention can filter out the noise on the image and accurately extract the center point of the cross in the presence of noise, which plays an important role in the calculation results of the subsequent center deviation measurement. Thus, the center point of the cross target in the detector imaging can be accurately found, and the accuracy of the lens center deviation measurement is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0038] Figure 1 This is the schematic diagram of the mirror center deviation measurement.

[0039] Figure 2 It is a flow chart of the present invention.

[0040] Figure 3 This is the trajectory diagram of the crosshair target image.

[0041] Figure 4 Crosshair target image acquired by the imaging detector.

[0042] Figure 5 It is the crosshair edge image after edge detection.

[0043] Figure 6 Crosshair edge image to find the center point. DETAILED DESCRIPTION

[0044] like Figure 1 As shown, the measuring head of the lens center deviation measuring device includes a light source 1, a beam splitter 2, an autocollimation measuring lens group 3, and an imaging detector 4. The light beam generated by the illumination of the light source 1 passes through the beam splitter 2 and the autocollimation measuring lens group 3 to form a converging light beam or a diverging light beam. There is no restriction on the form of the beam splitter 2 here, and a beam splitter prism or a semi-transparent and semi-reflective beam splitter can be used. The converging light beam has a convergence point, and the reverse extension line of the diverging light beam will also converge at a point, which is called the convergence point here. During the measurement process, the vertical guide rail of the lens center deviation measuring device drives the measuring head to move up and down, so that the convergence point of the crosshair target of the light source 1 coincides with the vertex of the current lens to be measured in the measured lens 5. At this time, the light beam incident on the measured lens is partially reflected on the surface of the measured lens, and the reflected light beam returns to the autocollimation measuring lens group along the original path, and is focused on the target surface of the imaging detector 4 through the beam splitter to form a clear crosshair target image. The lens 5 to be tested is placed at the center of the turntable 6. During the measurement process, the lens to be tested rotates around the central axis 61 of the turntable 6. The central axis 61 is the reference axis in the process of measuring the center deviation. If the vertex of the lens to be tested deviates from the central axis, the crosshair target image will draw a circular track on the target surface of the imaging detector. The circular track of the crosshair target image is as follows: Figure 3 The processor in the lens center deviation measuring device can extract the center point of the crosshair target image, and calculate the center deviation of the vertex of the measured mirror relative to the reference axis according to the diameter of the circular trajectory of the center point of the crosshair target image and the magnification of the autocollimation measuring lens group. By using this method, the center deviation of the vertex of all lenses to be measured relative to the reference axis can be obtained.

[0045] like Figure 2 As shown, the lens center point extraction method of the lens center deviation measurement device of the present invention specifically includes the following steps:

[0046] Step 1: Filter each frame of image collected by the imaging detector; the methods that can be used for image filtering in the present invention include mean filtering, median filtering, maximum and minimum filtering, bilateral filtering, guided filtering, etc. Among them, median filtering is a nonlinear spatial filter, which is suitable for processing impulse noise; Gaussian filtering is a linear filter, which is very suitable for removing Gaussian noise; therefore, the present invention firstly preferably uses median filtering to process impulse noise for each frame of image, and then uses Gaussian filtering to suppress Gaussian noise for the image after median filtering.

[0047] Median filtering uses a median filter and a two-dimensional template method to sort the pixels in the two-dimensional template according to the size of the pixel value, generate a monotonically increasing (or decreasing) two-dimensional data sequence, and use the following formula to calculate the pixel value of each pixel in the image after median filtering:

[0048] g(i, j)=med{f(im, jn), (m, n∈w)}

[0049] Among them, f(i, j) represents the pixel value of any pixel point I(i, j) of the original image, and g(i, j) represents the pixel value of the pixel point I(i, j) of the image after median filtering, (i, j) is the coordinate of the pixel point I(i, j); w is a two-dimensional template, and the filter window to be selected is usually 3×3, 5×5, 7×7 area. The present invention prefers a 3×3 filter window, m=1, 2, 3, n=1, 2, 3.

[0050] Gaussian filtering uses a 3×3 mask for processing, and the pixel value of each pixel I (i, j) of the image after Gaussian filtering is calculated using the following formula:

[0051] G(i,j)={g(i-1,j-1)+g(i-1,j+1)+g(i+1,j-1)+g(i+1,j+1)+[g(i-1,j)+g(i,j-1)+g(i+1,j)+g(i,j+1)]} / 16;

[0052] G(i, j) is the pixel value of the image pixel point I(i, j) after Gaussian filtering, and g(i, j) is the pixel value of the image pixel point I(i, j) after median filtering.

[0053] Step 2: Use the canny operator method to perform edge detection on the Gaussian filtered image G(i, j); canny edge detection requires setting two thresholds, the high threshold T1 and the low threshold T2. All values ​​higher than the high threshold T1 are retained, and all values ​​less than the low threshold T2 are discarded. Starting from the pixel points whose pixel values ​​are higher than the high threshold T1, all pixel points whose pixel values ​​are greater than the low threshold T2 and are interconnected are retained. T1, T2∈MAX, usually the maximum pixel value MAX of the pixel point is 255; the high threshold T1 is (0.5, 1)×MAX, and the low threshold T2 is (0, 0.5)×MAX; the present invention preferably takes the high threshold T1 as 0.5×MAX and the low threshold T2 as 0.3×MAX. The pixel value of each pixel point in the image after edge detection is calculated according to the following formula:

[0054] F(i,j)=canny{G(i,j),T2,T1};

[0055] F(i, j) is the pixel value of the image pixel I(i, j) after edge detection;

[0056] Step 3: edge detection feature point extraction; suppose the image captured by the imaging detector is H×W, H represents the number of rows of image pixels, and W represents the number of columns of image pixels; the original image size used in the present invention is H=2048, W=1024. First, starting from the X-axis direction, starting from the pixel point of the first row and first column of the image after edge detection, find all the pixel points with a pixel value of 255 in each row, and take the first pixel point with a pixel value of 255 in each row as the A feature point, and store its coordinates in the set XL (Lcount). For each additional A feature point, the count value Lcount increases by 1; all subsequent pixel points with a pixel value of 255 are stored in the set XR (Rcount) as B feature points, and the count value Rcount increases by 1 for each additional B feature point; secondly, starting from the Y-axis direction, starting from the first row of the first column of the image after edge detection, find all the pixel points with a grayscale value of 255 in each column, and store the first pixel point with a pixel value of 255 in each column as the C feature point in the set YUp (upcount). For each additional C feature point, the count value upcount increases by 1; all subsequent pixel points with a grayscale value of 255 are stored in the set Yd (dcount) as D feature points, and the count value dcount increases by 1 for each additional D feature point.

[0057] This step is not limited to the above method. Along the X-axis direction, the pixel point in the last column of the first row can also be used as the starting point, or the pixel point in the first column of the last row can be used as the starting point, or the pixel point in the last row and the last column can be used as the starting point; along the Y-axis direction, the pixel point in the first row of the last column can also be used as the starting point, or the pixel point in the last row of the first column can be used as the starting point, or the pixel point in the last row of the last column can be used as the starting point.

[0058] Step 4: Fit the feature points A, B, C, and D with straight lines; the feature point A in the set XL (Lcount) is recorded as xl n , the number of feature points A is equal to the final count value of Lcount, and the feature points B in the set xR(Rcount) are denoted by xr m , the number of B feature points is equal to the final count value of Rcount, and the C feature points in the set YUp (upcount) are denoted as yup p , the number of C feature points is equal to the final count value of upcount, and the D feature points in the set Yd(dcount) are denoted as yd k , the number of feature points D is equal to the final count value of dcount. n , B feature point xr m , C feature point yup p , D feature point yd k Four straight lines are fitted respectively. The fitting method is as follows:

[0059] Line fitting: For any straight line, assume that the functional relationship between the coordinates x and y of the pixel points on the straight line is given by the straight line equation y i =α0+a1x i Given, there are two unknown parameters in the formula, a0 represents the intercept and α1 represents the slope. For the M groups of data (x i ,y i ), i = 1, 2, ..., M. x i The value is considered to be accurate, and any errors are related only to y i ; M is the number of A feature points, B feature points, C feature points or D feature points.

[0060] Next, we use the least squares method to fit the M groups of data into a straight line. The sum of squares of the residuals S is required to be the smallest;

[0061]

[0062] due

[0063]

[0064]

[0065] Arranged

[0066]

[0067] Solve the process, and we get

[0068]

[0069]

[0070] A feature point xl n , B feature point xr m , C feature point yup p , D feature point yd k Substitute into the formula y i =a0+a1x i In the

[0071] Four straight lines; let one of the straight lines be Lxl(a, b), a and b are the two endpoints of the straight line; let the other straight line be Lxr(c, d), c and d are the two endpoints of the straight line; according to the following formula, determine whether the two straight lines Lxl(a, b) and Lxr(c, d) have an intersection;

[0072] denominator=(by-ay)×(dx-cx)-(ax-bx)×(cy-dy)

[0073] Where denominator is the denominator judgment value; by is the y coordinate of endpoint b, ay is the y coordinate of endpoint a, dx is the x coordinate of endpoint d, cx is the x coordinate of endpoint c, ax is the x coordinate of endpoint a, bx is the x coordinate of endpoint b, cy is the y coordinate of endpoint c, and dy is the y coordinate of endpoint d; if the denominator judgment value denominator is 0, it means that the two lines are parallel; if the denominator judgment value denominator is not 0, the intersection of the two straight lines is calculated according to the following formula:

[0074]

[0075]

[0076] According to the above formula, we can obtain the coordinates of the four intersection points of the four straight lines as (cx1, cy1), (cx2, cy2), (cx3, cy3), (cx4, cy4), and finally the coordinates of the center point of the crosshair target image can be calculated as (centx, centy) according to the following formula;

[0077] centx=(cx1+cx2+cx3+cx4) / 4

[0078] centy=(cy1+cy2+cy3+cy4) / 4

[0079] Step 5: Continuously rotate the turntable, obtain the center point coordinates of multiple crosshair target images during the rotation of the turntable, fit the center points of the multiple crosshair target images to obtain a fitting circle, and adjust the placement angle of the lens to be tested so that the center point of the crosshair target image calculated in real time moves to the center position of the fitting circle; after adjustment, continue to rotate the turntable to obtain the fitting circle formed by the center points of the multiple crosshair target images; observe the size of the fitting circle, if the fitting circle is within the adjustable range, continue to adjust the angle of the lens to be tested until the fitting circle formed by the center points of the multiple crosshair target images cannot be reduced, and use the center point of the crosshair target image at this time as the center of the lens to be tested.

[0080] The results show that the extraction accuracy of the center of the cross target using the existing technology can only reach ±0.5μm, while the present invention can reach ±0.2μm.

[0081] The extraction accuracy of the center of the cross target will affect the final lens center point detection result. The present invention improves the extraction accuracy of the cross target center, thereby improving the accuracy of the lens center point detection result.

[0082] The inventors have also used the Hough transform edge detection method combined with the image binarization method to extract the center of the cross target, but the extraction result was unstable and the accuracy was only 1 μm; the least squares fitting iterative method was used to automatically extract the center of the cross target, but the extraction time was long and real-time detection could not be achieved; the template matching method was used to extract the center of the cross target, but the result of the threshold set by this method had holes or edge errors, and the extracted cross center result was unstable.

Claims

1. A method for extracting the center point of a lens of a lens center deviation measuring device, characterized in that The method is as follows: Each frame of the image collected by the imaging detector is filtered; the edge of the filtered image is detected using the Canny operator to obtain the pixel value of each pixel point of the image after edge detection; Find all the pixels with a pixel value of 255 in each row, take the first pixel with a pixel value of 255 in each row as the A feature point, store its coordinates in the set XL, and store all subsequent pixel points with a pixel value of 255 as the B feature points in the set XR; find all the pixels with a pixel value of 255 in each column, store the first pixel with a pixel value of 255 in each column as the C feature point in the set YUp, and store all subsequent pixel points with a pixel value of 255 as the D feature points in the set Yd; Perform straight line fitting on feature points A, B, C and D to obtain four straight lines; calculate the center point coordinates of the crosshair target image based on the four intersection points of the four straight lines; Continuously rotate the rotating table of the lens center deviation measuring device, obtain the center point coordinates of multiple crosshair target images during the rotation of the rotating table, fit the center points of the multiple crosshair target images to obtain a fitting circle, adjust the placement angle of the measured lens, so that the center point of the crosshair target image calculated in real time moves to the center position of the fitting circle; continue to rotate the turntable, repeatedly adjust the placement angle of the measured lens, and obtain the fitting circle fitted by the center points of the multiple crosshair target images; until the fitting circle fitted by the center points of the multiple crosshair target images cannot be reduced, the center point of the crosshair target image at this time is used as the center of the measured lens.

2. The lens center point extraction method of the lens center deviation measuring device according to claim 1, characterized in that The median filter is used to process the impulse noise of each frame of the image, and then the Gaussian filter is used to suppress the Gaussian noise of the median filtered image.

3. The lens center point extraction method of the lens center deviation measuring device according to claim 2, characterized in that The median filter uses a two-dimensional template to sort the pixels in the two-dimensional template according to the size of the pixel value, generate a monotonically rising or falling two-dimensional data sequence, and use the following formula to calculate the pixel value of each pixel of the image after the median filter processing: g(i,j)=med{f(im,jn),(m,n∈w)} Among them, f(i, j) represents the pixel value of any pixel point I(i, j) in the original image, g(i, j) represents the pixel value of the pixel point I(i, j) in the image after median filtering, (i, j) is the coordinate of the pixel point I(i, j); w is a two-dimensional template, and its filtering window is a 3×3, 5×5 or 7×7 area, and m and n are the number of rows and columns of pixels in the two-dimensional template, respectively.

4. The lens center point extraction method of the lens center deviation measuring device according to claim 2, characterized in that The Gaussian filter is processed using a 3×3 mask, and the pixel value of each pixel point I (i, j) of the image after Gaussian filtering is calculated using the following formula: G(i,j)={g(i-1,j-1)+g(i-1,j+1)+g(i+1,j-1)+g(i+1,j+1)+[g(i-1,j)+g(i,j-1)+g(i+1,j)+g(i,j+1)]} / 16; G(i, j) is the pixel value of the image pixel point I(i, j) after Gaussian filtering, and g(i, j) is the pixel value of the image pixel point I(i, j) after median filtering.

5. The lens center point extraction method of the lens center deviation measuring device according to claim 1, characterized in that The method of using the canny operator to perform edge detection on the filtered image G(i, j) is as follows: Starting from the pixel points with pixel values ​​higher than the high threshold T1, all the pixel points with pixel values ​​greater than the low threshold T2 and connected to each other are retained; T1, T2∈MAX, the maximum pixel value MAX of the pixel point is 255; the high threshold T1 is (0.5, 1)×MAX, and the low threshold T2 is (0, 0.5)×MAX; the pixel value of each pixel point in the image after edge detection is calculated according to the following formula: F(i,j)=canny{G(i,j),T2,T1}; F(i, j) is the pixel value of the image pixel point I(i, j) after edge detection.

6. The lens center point extraction method of the lens center deviation measuring device according to claim 5, characterized in that The high threshold T1 is set to 0.5×MAX, and the low threshold T2 is set to 0.3×MAX.

7. The lens center point extraction method of the lens center deviation measuring device according to claim 5, characterized in that The least squares method is used for straight line fitting as follows: Substitute the coordinates of feature points A, B, C, and D into the formula y i =a0+a1x i Four straight lines are obtained by linear fitting, a0 represents the intercept, and a1 represents the slope; (x i ,y i ) is the coordinate of any feature point among feature points A, B, C or D; M is the number of feature points A, B, C or D.

8. The lens center point extraction method of the lens center deviation measuring device according to claim 7, characterized in that The calculation method of the center point coordinates (centx, centy) of the crosshair target image is as follows: suppose one of the straight lines is Lxl (a, b), a and b are the two end points of the straight line respectively; the other straight line is Lxr (c, d), c and d are the two end points of the straight line; determine whether the two straight lines Lxl (a, b) and Lxr (c, d) have an intersection according to the following formula; denominator=(by-ay)×(dx-cx)-(ax-bx)×(cy-dy) Where denominator is the denominator judgment value; by is the y coordinate of endpoint b, ay is the y coordinate of endpoint a, dx is the x coordinate of endpoint d, cx is the x coordinate of endpoint c, ax is the x coordinate of endpoint a, bx is the x coordinate of endpoint b, cy is the y coordinate of endpoint c, and dy is the y coordinate of endpoint d; if the denominator judgment value denominator is 0, it means that the two lines are parallel; if the denominator judgment value denominator is not 0, the intersection of the two straight lines is calculated according to the following formula: Assume that the coordinates of the four intersection points of the four straight lines are (cxl, cyl), (cx2, cy2), (cx3, cy3), (cx4, cy4), and the coordinates of the center point of the crosshair target image are calculated as (centx, centy) according to the following formula; centx=(cx1+cx2+cx3+cx4) / 4 centy=(cy1+cy2+cy3+cy4) / 4.

Images