Marker ball positioning method and its application

Abstract

The present invention discloses a marker ball positioning method and its application, comprising the following steps: (1) installing at least three coplanar and non-colinear actual marker balls at the human lesion site, and collecting an image containing the actual marker balls; (2) extracting all spheres in the image as suspected marker balls and respectively calculating the center of mass of each sphere; (3) selecting the same number of suspected marker balls as the actual marker balls to form a plurality of to-be-matched point sets, and sequentially judging whether they match or not with the actual point sets composed of the actual marker balls; if they match, the to-be-matched point sets are used as candidate point sets; otherwise, they are eliminated, and all candidate point sets are obtained; (4) aligning the obtained candidate point sets with the actual point sets, and selecting the marker ball combination corresponding to the candidate point set with the smallest projection error as the final marker ball combination. The present invention uses non-metallic markers to avoid the alignment errors caused by artifacts brought by metal markers to CT images and the alignment errors caused by manufacturing and measurement errors of steel balls and tracers.

Description

Technical Field

[0001] The invention relates to the field of image processing, and in particular to a marking ball positioning method and application thereof. Background Art

[0002] Lung cancer is one of the most threatening cancers to human life and health. Lung biopsy is the gold standard for diagnosing lung tumors. Lung biopsy surgery requires doctors with rich clinical experience to remove lesions for pathological analysis. The main principle of the surgical navigation system is to align the image coordinate system of the CT image space with the design coordinate system of the human body space, so as to realize the real-time display of surgical instruments in the image space. The alignment of the image coordinate system and the design coordinate system requires the placement of steel balls and tracers on the human body for positioning and alignment. However, there are errors in the processing and measurement of steel structures, and errors will also occur when aligning steel balls and tracers. In addition, steel balls, as metal markers, will bring artifacts to CT images, which will eventually lead to a large alignment error between the image coordinate system and the design coordinate system. Summary of the invention

[0003] Purpose of the invention: In view of the above-mentioned deficiencies, the present invention proposes a marker ball positioning method and its application, which adopts non-metallic markers to replace the steel balls and tracer balls in the prior art to align the design coordinate system and the image coordinate system, thereby avoiding the registration errors caused by artifacts brought by metal markers to the CT images and the registration errors caused by the manufacturing and measurement errors of steel balls and tracers.

[0004] Technical solution:

[0005] The marking ball positioning method comprises the following steps:

[0006] (1) installing at least three coplanar but non-colinear actual marker balls at the lesion site of the human body, and collecting images containing the actual marker balls;

[0007] (2) Extract all spheres in the image as suspected marker spheres and calculate the center of mass of each sphere;

[0008] (3) The actual marker balls constitute the actual point set in the design coordinate system, and the suspected marker balls with the same number as the actual marker balls are selected to constitute a number of to-be-matched point sets. Each of the to-be-matched point sets is judged in turn with the actual point set to see whether it matches or not; if they match, the to-be-matched point set is used as a candidate point set; otherwise, it is eliminated; until the matching judgment between all to-be-matched point sets and the actual point sets is completed, and all candidate point sets are obtained;

[0009] (4) Align the candidate point set obtained in step (3) with the actual point set, and select the marker ball combination corresponding to the candidate point set with the smallest projection error as the final marker ball combination.

[0010] The actual marking ball material is acrylonitrile-butadiene copolymer.

[0011] The diameter of the marking ball is 11-13 mm.

[0012] The step (2) is specifically:

[0013] (21) In the image coordinate system, slices are taken along the cross section parallel to the sphere, and circles in all slices are detected using Hough transform and clustered to obtain several groups of circle combinations, each of which defines a suspected marker sphere;

[0014] (22) Obtain the coordinates of the center of mass of each suspected marker ball.

[0015] The circle clustering of step (21) is as follows: set one of all detected circles as a seed circle, traverse all other detected circles, and calculate the Euclidean distance between the center of each circle and the center of the seed circle. If the Euclidean distance is less than a set threshold, the corresponding circle and the seed circle are classified into one category until the seed circle traverses all circles and obtains a circle combination of a suspected marked ball; repeat the above clustering process to obtain a circle combination of all suspected marked balls.

[0016] The step (22) of obtaining the coordinates of the center of mass of each suspected marker ball is as follows:

[0017] The coordinates of the centers of all circles in each circle combination of the suspected marked sphere obtained by step (21) in the same two-dimensional coordinate system parallel to the cross section satisfy the Gaussian distribution: μ is the mean value of all samples, σ is the standard deviation of all samples; the confidence interval of the normal distribution n~N(μ,σ) is [μ-λσ,μ+λσ], where λ depends on the confidence level; the x and y coordinates of the center of mass of the sphere are obtained as the mean values ​​of the samples in the confidence interval, and the z coordinate is the median value of the z coordinates of all circles in each circle combination obtained by circle clustering.

[0018] In the step (3), the set of points to be matched is formed by randomly selecting the same number of suspected marked balls as the actual marked balls.

[0019] In step (3), the method for selecting the set of points to be matched is: first randomly select a suspected marker ball, and then select other suspected marker balls whose positional relationship with the suspected marker ball is the same as the relative positional relationship between the actual marker balls in the actual point set to form the set of points to be matched.

[0020] In step (3), whether the to-be-matched point set matches the actual point set is determined by the following criteria:

[0021] a. Whether the deviation between the actual Euclidean distance between any two points in the set of matching points and the real Euclidean distance between the corresponding two points in the actual point set is less than the first threshold;

[0022] b. Whether the deviation between the angle between two connecting lines between any three points in the to-be-matched point set and the actual angle between the corresponding two connecting lines in the actual point set is less than a second threshold;

[0023] c. Whether the deviation between the flatness of the plane where the to-be-matched point set is located and the actual flatness of the plane where the actual point set is located is less than a third threshold;

[0024] When the deviations of a, b, and c are all within the corresponding threshold range, the to-be-matched point set is determined to match the actual point set, otherwise it is determined to be mismatched.

[0025] In the step (4), the registration of the candidate point set and the actual point set adopts a rigid body registration method to obtain the rotation transformation matrix R and the translation transformation matrix T of the image coordinate system and the design coordinate system.

[0026] In step (4), the projection error is calculated as follows:

[0027] The centroid of each point in the candidate point set of the image coordinate system is converted to the design coordinate system, and then the root mean square error RMSE between the centroid of each point in the candidate point set and the actual point set is calculated, and a set of candidate point sets with the smallest root mean square error is selected as the final marker ball combination; where:

[0028] Conversion formula: ObPoint = R * matchPoint + T;

[0029] The root mean square error is:

[0030] Among them, ObPoint is the observed point set converted from the candidate point set in the image coordinate system to the design coordinate system, matchPoint is the candidate point set in the image coordinate system, basePoint is the actual point set coordinates in the design coordinate system; i represents the i-th point.

[0031] The method further comprises step (5) of precisely positioning the final marking ball, which comprises:

[0032] (51) extracting, from a plurality of sections parallel to the coronal plane and / or the sagittal plane, the outer contour of the circle in the section where the center of mass of each marker ball in the final marker ball combination is located and in the two sections before and after it;

[0033] (52) fitting the points on the outer contour of the circle in each section to obtain the center of the circle in each section, and taking the center of the circle with the smallest Euclidean distance from the center coordinate O as the new center to obtain the new center of mass coordinates of each marked sphere;

[0034] (53) Calculate the registration matrix and root mean square error between the new centroid in the final marker ball combination and the actual point set. If the root mean square error is less than the previously calculated root mean square error, update the new centroid of each marker ball to the centroid of each marker ball in the final marker ball combination; otherwise, do not update.

[0035] The specific steps of step (52) are as follows: Fit the points on the outer contour of the inner circle of each section obtained in step (51) to obtain the center of the inner circle of each section, and select the center closest to the center of the current marker ball in the current section as the new center, and obtain the latest centroid of the corresponding marker ball.

[0036] Fitting the points on the outer contour of the inner circle of each section obtained in step (51) to obtain the center of the inner circle of each section is more specific as follows: According to the centroid of the marker balls in the final marker ball combination obtained above, obtain the two-dimensional center coordinate O of the marker ball in the current section. Define an ideal circle with the radius of the marker ball, remove the points on the outer contour that are more than the set threshold away from the outer contour of the ideal circle, and perform least squares circle fitting on the remaining outer contour points to obtain the center of the remaining outer contour points.

[0037] It also includes the step of adjusting window level and window width:

[0038] According to the calculated centroid coordinates of the marker balls, calculate the maximum and minimum Hu values of the circular cross-section parallel to the transverse plane of the marker balls. The number of gray levels in the histogram is set to 60. Use the gray level range as the abscissa and the number of pixel points to obtain the histogram hist of the marker balls;

[0039] Starting from the 0 index of the histogram hist, search incrementally. If h[i]<h[i + 1] and h[i + 1]<h[i + 2], where i represents the i-th gray level range and h[i] represents the number of pixel points in the i-th gray level range; then set the current index i of the histogram to i min ; Starting from the maximum index of the histogram, search decrementally. If h[i]<h[i - 1] and h[i - 1]<h[i - 2], then set the current index i of the histogram to i max ;

[0040] At i min and i max Find the maximum index local of the histogram max , set the threshold threshold = h[local max *0.2; Starting from the i min index, search. Between i min and local max find a histogram index i1 whose ordinate is less than the threshold threshold; Starting from local maxIndex starts searching in local max and i max Find a histogram index i2 whose ordinate is less than the threshold threshold;

[0041] Thus, the real window level and window width ww of the tracer ball are obtained and written to the local computer.

[0042] level=(h[i2]-h[i1])*0.5*slope+intercept

[0043] ww(h[i2]-h[i1])*slope

[0044] Slope is the slope of the image tag, and intercept is the intercept of the image tag, which can be obtained from the image.

[0045] An application of the aforementioned marker ball positioning method in surgical navigation.

[0046] Beneficial effects: The present invention adopts non-metallic markers to replace the steel balls and tracer balls in the prior art to align the design coordinate system and the image coordinate system, avoiding the alignment errors caused by artifacts brought by metal markers to the CT images and the alignment errors caused by the manufacturing and measurement errors of the steel balls and tracers. It also avoids the alignment errors caused by the two markers as rigid structures in processing and measurement, greatly simplifies the design of the rigid structure, and provides a robust, efficient and high-precision three-dimensional image marker point automatic positioning algorithm, which is suitable for complex surgical environments and has high accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a schematic diagram of the surgical navigation marker ball positioning method of the present invention.

[0048] Figure 2 It is a schematic diagram of the structure of the registration document of the present invention.

[0049] Figure 3 It is the CT image after the window level and window width are adjusted.

[0050] Figure 4 Schematic diagram of the circle clustering process.

[0051] Among them, 1 is a registration piece, 11 is a marking ball, and 12 is a bracket. DETAILED DESCRIPTION

[0052] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments.

[0053] Figure 1 Schematic diagram of the surgical navigation marker ball positioning method of the present invention, as shown in Figure 1As shown, the marker used in the surgical navigation marker point positioning method of the present invention is a marker ball made of a non-metallic material on the surface, and the surface material is preferably acrylonitrile-butadiene copolymer. Of course, it is not limited to this material, and other non-metallic materials can also be used for manufacturing, with a diameter of 11 to 13 mm. Figure 2 As shown, four marking balls 11 are coplanar but not colinearly mounted on a bracket 12 to form a registration piece 1. The bracket 12 is made of polyetheretherketone. The registration piece 1 is mounted on the surface of the human body close to the lesion.

[0054] In the present invention, the CT value of the marker ball is close to the CT value of the human soft tissue, and no artifacts caused by metal markers on the CT image will be generated, thereby not affecting the doctor's diagnosis. In order to achieve the registration between the design coordinate system and the image coordinate system, it is necessary to accurately locate the center of mass of each marker ball.

[0055] The steps of the positioning method of the marker ball of the present invention are as follows:

[0056] (1) First, read the window position and width of the local file. If the reading is successful, set the window position and width to the local value. Otherwise, the doctor sets the fixed window position and width to the local value. Obtain the original CT image containing the marker ball, convert the original CT image containing the marker ball into Hu value, and normalize it to the grayscale value in the interval [0, 255], that is, Figure 3 , converted by the following formula:

[0057] p v =(h v -h min )*255.0 / (h max -h min )

[0058] h min =(2*W C -W W ) / 2+0.5

[0059] h max =(2*W C +W W ) / 2+0.5

[0060] Among them, p v It represents the normalized gray value of a pixel on the original CT image. v Indicates Hu value, h min Indicates the minimum value of the Hu value of the original CT image, h max Indicates the maximum value of the original CT image Hu value, W C Indicates the window level, W W Indicates the window width; h min and h maxThe final value of is the actual calculated value rounded up to the integer;

[0061] (2) Roughly locate the center of mass of the marker ball;

[0062] Because the marker ball is a sphere, it is sliced ​​along the cross section parallel to the sphere in the image coordinate system. The marker ball is a plane circle in each slice, and the center coordinates of each plane circle of the same marker ball are the same in the same two-dimensional coordinate system parallel to the cross section (i.e., the XY plane coordinate system of the image coordinate system); connect multiple circle centers with the same coordinates in the two-dimensional coordinate system into a straight line segment, then the midpoint of the straight line segment is the center of mass of the sphere, and the center of mass of all spheres is obtained based on this;

[0063] Since the CT value of the marker sphere is similar to that of human tissue, and some parts of human tissue are spheres, these parts will be demarcated as spheres and detected together. Therefore, the number of spheres actually extracted is greater than the number of marker spheres, and all extracted spheres are collectively referred to as suspected marker spheres.

[0064] The rough extraction of the centroid of the sphere includes the following steps:

[0065] (21) Circle clustering: The circle clustering process is as follows Figure 4 As shown, each section image parallel to the cross section of the sphere is traversed, and all circles in all section images are detected using Hough transform. The center of the plane circle of the same sphere in each section has the same coordinate in theory in the same two-dimensional coordinate system parallel to the cross section, and the circles are clustered;

[0066] The specific circle clustering process is as follows:

[0067] One of all the detected circles is set as a seed circle, and the center and radius of the seed circle are represented by vector b. All other detected circles are traversed, and the Euclidean distance between the center of these circles and the center of the seed circle is calculated. If the Euclidean distance is less than the set threshold value of 6mm, the center and radius of the circle are represented by vector a, and it is classified into one category with the seed circle until the seed circle traverses all circles. Finally, all circles with vector b and seed circles with vector a are clustered together to obtain a combination of circles of a suspected marker ball in all sections parallel to the cross section; then another seed circle is selected from other circles outside the circle combination of the suspected marker ball, and the above clustering process is repeated to obtain a combination of circles of all suspected marker balls;

[0068] (22) Find the center of mass and radius of the sphere:

[0069] The coordinates of the centers of all circles in each circle combination of the suspected marker sphere obtained in step (21) in the same two-dimensional coordinate system parallel to the cross section satisfy the Gaussian distribution: μ is the mean value of all samples, σ is the standard deviation of all samples; the confidence interval of the normal distribution n~N(μ,σ) is [μ-λσ,μ+λσ], where λ is determined according to the confidence level;

[0070] The x and y coordinates of the centroid of the sphere are obtained as the average values ​​of the samples in the confidence interval; in the present invention, λ is equal to 3; the z coordinate is the median of the z coordinates of all circles in each circle combination obtained by circle clustering; then the radius of the sphere is the maximum radius of all circles in each circle combination:

[0071] (3) Extract the candidate marker ball combination, which is the candidate point set:

[0072] According to the centroid coordinates of each suspected marker ball obtained in step (22), four of the suspected marker balls are randomly combined to form a to-be-matched point set, thereby obtaining a plurality of to-be-matched point sets in the image coordinate system; the actual relative position relationship of the four actual marker balls constitutes an actual point set in the design coordinate system, and the plurality of to-be-matched point sets are matched one by one with the actual point set in sequence. The specific steps are as follows:

[0073] Take out one of the to-be-matched point sets, and determine whether the relative position relationship between the four points in the to-be-matched point set matches the relative position relationship between the four points in the actual point set. If they match, put the to-be-matched point set into the candidate marker ball combination of the image coordinate system as a candidate point set, and remove the candidate point set from the to-be-matched point set; otherwise, repeat the above process until the matching relationship between all the to-be-matched point sets and the actual point sets is determined;

[0074] In the present invention, a suspected marker ball may be randomly selected first, and then other suspected small balls whose positional relationship with the suspected marker ball is the same as the relative positional relationship between the four point sets in the actual point set are selected to form a point set to be matched, and then matched with the actual point set.

[0075] Of course, the method of selecting the point sets to be matched is not limited to the two methods listed above, as long as all candidate point sets can be randomly and orderly combined into a number of point sets to be matched.

[0076] Among them, whether the relative position relationship of the point set to be matched matches the relative position relationship of the actual point set is judged by the following three points:

[0077] a. Whether the deviation between the Euclidean distance between any two points in the to-be-matched point set and the Euclidean distance between the corresponding two points in the actual point set is less than a first threshold;

[0078] b. Whether the deviation between the angle between two connecting lines between any three points in the to-be-matched point set and the actual angle between the corresponding two connecting lines in the actual point set is less than a second threshold;

[0079] c. Whether the deviation between the flatness of the plane where the four points of the to-be-matched point set are located and the actual flatness of the plane where the four points of the actual point set are located is less than a third threshold;

[0080] When the deviations of a, b, and c are all within the corresponding threshold range, the to-be-matched point set is determined to match the actual point set, otherwise it is determined to be mismatched; wherein the first, second, and third thresholds are set as required;

[0081] (4) Registration, find the final marker ball combination:

[0082] The candidate marker sphere combinations in the candidate point set obtained in step (3) are respectively aligned with the actual point set in the design coordinate system, and the candidate marker sphere combination with the smallest projection error is obtained as the marker sphere combination in the image coordinate system;

[0083] Among them, the registration adopts the rigid body registration method, such as: SVD decomposition method, to find the rotation transformation matrix R and translation transformation matrix T of the image coordinate system and the design coordinate system;

[0084] The projection error is calculated as follows:

[0085] The centroid of the candidate marker ball combination in the image coordinate system is converted to the design coordinate system, and then the root mean square error RMSE between the centroid of the candidate marker ball combination and the centroid of the actual marker ball is calculated, and a set of candidate marker ball combinations with the smallest root mean square error is selected as the final marker ball combination, where:

[0086] Conversion formula: ObPoint = R * matchPoint + T;

[0087] The root mean square error is:

[0088] Wherein, ObPoint is the coordinate of the centroid of the candidate marker ball combination in the image coordinate system converted to the design coordinate system, matchPoint is the coordinate of the centroid of the candidate marker ball combination in the image coordinate system, basePoint is the coordinate of the centroid of the actual marker ball in the design coordinate system; i represents the i-th candidate marker ball combination;

[0089] (5) Precise positioning of the final marker ball combination:

[0090] Since the CT scanning layer is too thick, the marker ball may not be fully scanned. At the same time, the plane circle of the marker ball in the initial section and the end section of the cross section is very likely to be undetectable, which will affect the precise positioning of the center of mass of the marker ball on the Z axis of the image coordinate system. The present invention provides a precise positioning method of the center of mass of the marker ball on the Z axis; the marker ball is also a circle in the slice image parallel to the coronal plane and the sagittal plane (the cross section, the coronal plane, and the sagittal plane are perpendicular to each other), so it can be used to locate the precise coordinates of the center of mass of the marker ball on the Z axis;

[0091] (51) According to the above steps, the three-dimensional coordinates and radius of the centroid of each marker sphere of the final marker sphere combination are obtained. Among several sections parallel to the coronal plane and the sagittal plane, the section where the centroid of each marker sphere of the final marker sphere combination is located and the two sections before and after the section are selected, and the outer contour of the circle in each section is extracted. In the present invention, in the image, the thickness of the section is 1 mm;

[0092] (52) Fitting the points on the outer contour of the circle in each section obtained in step (51), the specific fitting method is as follows:

[0093] a) According to the center of mass of the marker ball in the final marker ball combination obtained above, obtain the two-dimensional center coordinate O of the marker ball in the current section, define an ideal circle with the radius of the marker ball; remove the points on the outer contour whose distance from the outer contour of the ideal circle is greater than a set threshold, where the threshold is set to 6 mm;

[0094] b) performing least squares circle fitting on the remaining outer contour points respectively to obtain the center of the remaining outer contour points, and finally taking the center of the circle with the smallest Euclidean distance from the center coordinate O of the three sections as the new center of the circle to obtain a new center of mass of the marking sphere;

[0095] (53) Repeat steps (51) to (52) to obtain the new center of mass of the four marker balls in the final marker ball combination, and use step (4) to calculate the new alignment matrix and root mean square error. If the new root mean square error is less than the root mean square error calculated previously, the center of mass of the new marker ball is updated to the center of mass of each marker ball in the final marker ball combination, thereby obtaining the precisely positioned center of mass coordinates of each marker ball in the final marker ball combination; otherwise, it is not updated.

[0096] In other embodiments, only the outer contour of the circle in the section parallel to the coronal plane or the sagittal plane may be extracted to precisely locate the coordinates of the center of mass of the marker sphere on the Z axis. The accuracy may be reduced, but it can meet the use requirements.

[0097] In the present invention, a non-metallic marker is used to replace the steel balls and tracer balls in the prior art for registering the design coordinate system and the image coordinate system, avoiding the registration error caused by artifacts in the CT image brought by the metal marker and the registration error caused by the manufacturing and measurement errors of the steel balls and the tracer, and also avoiding the registration error brought by the processing and measurement of the two markers as a rigid body structure. The design of the rigid body structure is greatly simplified, and it is applicable to complex surgical environments with high precision.

[0098] (6) Window level and window width readjustment:

[0099] (61) Calculate the centroid coordinates of the precise positioning of the marker balls obtained according to step (5), calculate the maximum and minimum Hu values of each marker ball in the final marker ball combination on the sectional plane circle parallel to the cross-section, and set the number of gray level ranges of the histogram to 60. In this way, a histogram can be obtained with the gray level range as the abscissa and the number of pixel points as the ordinate;

[0100] (62) Start incrementally searching from the 0 index of the histogram. If h[i] < h[i + 1] and h[i + 1] < h[i + 2], where i represents the i-th gray level range and h[i] represents the number of pixel points in the i-th gray level range; then set the current index i of the histogram to i min ; Start decrementally searching from the maximum index of the histogram. If h[i] < h[i - 1] and h[i - 1] < h[i - 2], then set the current index i of the histogram to i max ;

[0101] (63) According to step (62), search for the local maximum index local min and i max in the histogram. The so-called local maximum index is the maximum value between i max and i min and i max . Set the threshold H = h[local max *0.2; Start searching from the i min index, and search for a histogram index i1 with a vertical coordinate less than the threshold between i min and local max ; Start searching from the local max index, and search for a histogram index i2 with a vertical coordinate less than the threshold between local max and i max . In this way, we can calculate the true window level level and window width Ww of the tracer ball, write them to the local, and use them for the centroid calculation of the next marker ball;

[0102] level = (h[i2] - h[i1]) * 0.5 * slope + intercept

[0103] Ww=(h[i2]-h[i1])*slope

[0104] Among them, slope is the slope of the image tag, and intercept is the intercept of the image tag, which can be obtained from the image.

[0105] The preferred embodiments of the present invention are described in detail above, but the present invention is not limited to the specific details in the above embodiments. Within the technical concept of the present invention, various equivalent transformations (such as quantity, shape, position, etc.) can be made to the technical scheme of the present invention, and these equivalent transformations all belong to the protection scope of the present invention.

Claims

1. A marking ball positioning method, characterized in that: The following steps are involved: (1) installing at least three coplanar and non-colinear non-metallic actual marker balls at the lesion site of the human body, and collecting images containing the aforementioned actual marker balls; (2) Extract all spheres in the image as suspected marker spheres and calculate the center of mass of each sphere; (3) The actual marker balls constitute the actual point set in the design coordinate system, and the suspected marker balls with the same number as the actual marker balls are selected to constitute a number of to-be-matched point sets, and each of the to-be-matched point sets is judged in turn with the actual point set to see whether it matches or not; if they match, the to-be-matched point set is used as a candidate point set; otherwise, it is eliminated; Until the matching judgment between all the point sets to be matched and the actual point sets is completed, all the candidate point sets are obtained; (4) Aligning the candidate point set obtained in step (3) with the actual point set, and selecting the marker sphere combination corresponding to the candidate point set with the smallest projection error as the final marker sphere combination; The projection error is calculated as follows: The centroid of each point in the candidate point set of the image coordinate system is converted to the design coordinate system, and then the root mean square error RMSE between the centroid of each point in the candidate point set and the actual point set is calculated, and a set of candidate point sets with the smallest root mean square error is selected as the final marker ball combination; where: Conversion formula: ObPoint = R*matchPoint+T; The root mean square error is: Among them, ObPoint is the observed point set converted from the candidate point set in the image coordinate system to the design coordinate system, matchPoint is the candidate point set in the image coordinate system, basePoint is the actual point set coordinates in the design coordinate system; i represents the i-th point.

2. The marker ball positioning method according to claim 1, characterized in that: The actual marking ball surface material is acrylonitrile-butadiene copolymer.

3. The marker ball positioning method according to claim 1, characterized in that: The actual marking ball diameter is 11-13 mm.

4. The marker ball positioning method according to claim 1, characterized in that: The step (2) is specifically: (21) In the image coordinate system, slices are taken along the cross section parallel to the sphere, and circles in all slices are detected using Hough transform and clustered to obtain several groups of circle combinations, each of which defines a suspected marker sphere; (22) Obtain the coordinates of the center of mass of each suspected marker ball.

5. The marker ball positioning method according to claim 4, characterized in that: The circle clustering of step (21) is as follows: set one of all detected circles as a seed circle, traverse all other detected circles, and calculate the Euclidean distance between the center of each circle and the center of the seed circle. If the Euclidean distance is less than a set threshold, the corresponding circle and the seed circle are classified into one category until the seed circle traverses all circles and obtains a circle combination of a suspected marked ball; repeat the above clustering process to obtain a circle combination of all suspected marked balls.

6. The marker ball positioning method according to claim 4, characterized in that: The step (22) of obtaining the coordinates of the center of mass of each suspected marker ball is as follows: The coordinates of the centers of all circles in each circle combination of the suspected marked sphere obtained by step (21) in the same two-dimensional coordinate system parallel to the cross section satisfy the Gaussian distribution: μ is the mean value of all samples, σ is the standard deviation of all samples; the confidence interval of the normal distribution n~N(μ,σ) is [μ-λσ,μ+λσ], where λ depends on the confidence level; the x and y coordinates of the center of mass of the sphere are obtained as the mean values ​​of the samples in the confidence interval, and the z coordinate is the median value of the z coordinates of all circles in each circle combination obtained by circle clustering.

7. The marker ball positioning method according to claim 1, characterized in that: In the step (3), the set of points to be matched is formed by randomly selecting the same number of suspected marked balls as the actual marked balls.

8. The marker ball positioning method according to claim 1, characterized in that: In step (3), the method for selecting the set of points to be matched is: first randomly select a suspected marker ball, and then select other suspected marker balls whose positional relationship with the suspected marker ball is the same as the relative positional relationship between the actual marker balls in the actual point set to form the set of points to be matched.

9. The marker ball positioning method according to claim 1, characterized in that: In step (3), whether the to-be-matched point set matches the actual point set is determined by the following criteria: a. Whether the deviation between the actual Euclidean distance between any two points in the set of matching points and the real Euclidean distance between the corresponding two points in the actual point set is less than the first threshold; b. Whether the deviation between the angle between two connecting lines between any three points in the to-be-matched point set and the actual angle between the corresponding two connecting lines in the actual point set is less than a second threshold; c. Whether the deviation between the flatness of the plane where the to-be-matched point set is located and the actual flatness of the plane where the actual point set is located is less than a third threshold; When the deviations of a, b, and c are all within the corresponding threshold range, the to-be-matched point set is determined to match the actual point set, otherwise it is determined to be mismatched.

10. The marker ball positioning method according to claim 1, characterized in that: In the step (4), the registration of the candidate point set and the actual point set adopts a rigid body registration method to obtain the rotation transformation matrix R and the translation transformation matrix T of the image coordinate system and the design coordinate system.

11. The marker ball positioning method according to claim 1, characterized in that: The method further comprises step (5) of precisely positioning the final marking ball, which comprises: (51) extracting, from a plurality of sections parallel to the coronal plane and / or the sagittal plane, the outer contour of the circle in the section where the center of mass of each marker ball in the final marker ball combination is located and in the two sections before and after it; (52) fitting the points on the outer contour of the circle in each section to obtain the center of the circle in each section, and taking the center of the circle with the smallest Euclidean distance from the center coordinate O as the new center to obtain the new center of mass coordinates of each marked sphere; (53) Calculate the registration matrix and root mean square error between the new center of mass in the final marker ball combination and the actual point set. If the root mean square error is less than the root mean square error calculated previously, update the new center of mass of each marker ball to the center of mass of each marker ball in the final marker ball combination; otherwise, do not update.

12. The marker ball positioning method according to claim 11, characterized in that: The step (52) is specifically as follows: fitting the points on the outer contour of the inner circle of each section obtained in step (51) to obtain the center of the inner circle of each section, and selecting the center of the circle that is closest to the center of mass of the current marking sphere on the current section as the new center of the circle, so as to obtain the latest center of mass of the corresponding marking sphere.

13. The marker ball positioning method according to claim 11, characterized in that: The points on the outer contour of the inner circle of each section obtained in step (51) are fitted to obtain the center of the inner circle of each section. More specifically, according to the center of mass of the marker ball in the final marker ball combination obtained above, the two-dimensional center coordinate O of the marker ball in the current section is obtained, an ideal circle is defined with the radius of the marker ball, and the points on the outer contour whose distance from the outer contour of the ideal circle is greater than a set threshold are removed, and the least squares circle fitting is performed on the remaining outer contour points to obtain the center of the remaining outer contour points.

14. The marker ball positioning method according to claim 1, characterized in that: It also includes the steps for adjusting the window position and width: According to the coordinates of the centroid of the marker ball obtained by calculation, the maximum and minimum values ​​of the Hu value of the marker ball on the section circle parallel to the cross section are calculated. The number of grayscale ranges of the histogram is set to 60, and the histogram histogram of the marker ball is obtained with the grayscale range as the abscissa and the number of pixels; Incrementally search starting from the 0 index of histogram hist. If h[i] < h[i + 1] and h[i + 1] < h[i + 2], where i represents the i-th gray level range and h[i] represents the number of pixel points in the i-th gray level range; then set the current index i of the histogram to i min ; Decrementally search starting from the maximum index of the histogram. If h[i] < h[i - 1] and h[i - 1] < h[i - 2], then set the current index i of the histogram to i max ; in i min and i max Find the maximum index of the histogram locally max , set the threshold threshold = h[local max ]*0.2; from i min Index to start searching, at i min and local max Find a histogram index i1 whose ordinate is less than the threshold threshold; From local max Index starts searching in local max and i max Find a histogram index i2 whose ordinate is less than the threshold threshold; Thus, the real window level and window width ww of the tracer ball are obtained and written to the local computer. level=(h[i2]-h[i1])*0.5*slope+intercept ww(h[i2]-h[i1])*slope Slope is the slope of the image tag, and intercept is the intercept of the image tag, which can be obtained from the image.

15. Application of the marker ball positioning method according to any one of claims 1 to 14 in surgical navigation.

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