WO2022110573A1 - 基于刚性上臂模型的功能性肩关节旋转中心定位方法 - Google Patents
基于刚性上臂模型的功能性肩关节旋转中心定位方法 Download PDFInfo
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- 238000006073 displacement reaction Methods 0.000 claims abstract description 12
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Definitions
- the invention relates to the technical field of human motion measurement, in particular to a functional shoulder joint rotation center positioning method based on a rigid upper arm model.
- human motion measurement and posture prediction technology plays an important role in various fields, such as in the field of athlete selection, sports motion capture, computer vision, biomedicine and medical equipment.
- the shoulder joint is the most flexible joint in the upper limbs of the human body, and its positioning is an important part of establishing a digital dynamic model of the human body.
- the shoulder anatomical center (GHAC, glenohumeral anatomical center) is inferred from the position of the humeral head in anatomy; in the field of human motion measurement, the functional shoulder joint rotation center (FRCS, Functional Rotation Center of Shoulder) is defined It is the rotation center of the upper arm in motion, which is positioned by the kinematic parameters of the upper arm of the human body.
- GHAC glenohumeral anatomical center
- FRCS Functional Rotation Center of Shoulder
- the positioning of the rotation center of the shoulder joint drew on the method of positioning the anatomical center of the shoulder joint, that is, according to the scanning results of the human shoulder contour, combined with complex anatomical knowledge, the bone shape of the humerus and scapula was determined.
- the envelope is predicted and digitized to locate the center of rotation of the shoulder joint.
- the located shoulder rotation center is used to establish the digitization of the human body.
- the early FRCS used the cadaver for positioning, and positioned the intersection of the three rotation axes by inserting spikes on the rotation axes of the upper arm of the cadaver with three degrees of freedom, namely FRCS.
- the FRCS determined by this method still has the defect of insufficient precision in establishing the digital dynamic model of the human body.
- the Japan Digital Humanization Research Center proposed a method to measure the FRCS of the human body in motion, which completely abandons the limitation of anatomical knowledge on the FRCS, and uses geometric algorithms to obtain the accurate upper limb reachable domain.
- the advantage of this method is that the FRCS is obtained according to the human body in motion, which is more in line with the motion posture of the human body, and there is a correlation between the position of the human body FRCS in motion and the limb angle, which can be used to establish a more accurate human body. Digitized dynamic models. In the case of losing anatomical knowledge as a geometric limit, the FRCS positioning errors caused by systematic errors, skin deformation, etc. will be transmitted and amplified in the geometric calculation, which will seriously offset the FRCS positioning results.
- the present invention provides a functional shoulder joint rotation center positioning method based on a rigid upper arm model.
- a functional shoulder joint rotation center localization method based on a rigid upper arm model including
- Step 1 Abstract the upper arm of the human body into a cylinder with FRCS as the top center;
- Step 2 Determine the reference axis vector of the cylinder
- Step 3 Determine the axial vector of the cylinder and the displacement from the reference axial vector to the axial vector;
- Step 4 Correct the direction of the central axis of the cylinder
- Step 5 Determine the height compensation of the cylinder, and position the FRCS.
- step 1 the skin surface of the upper arm of the human body is abstracted as the side surface of the cylinder.
- any of the above-mentioned schemes in step 2, take the midpoint of the human body surface humerus medial and lateral epicondyle points (represented by mark MD) as a starting point, and point to the vector of the acromion point (represented by mark MU) is the reference axis vector of the cylinder whose direction is the reference direction of the cylinder.
- the position information of the point A from the start time t 0 to the end time t s is expressed as M A ,
- t s t 0 +k ⁇ t, k ⁇ 3, and ⁇ t is the sampling interval.
- step 3 the reference axis vector is translated along a direction perpendicular to the reference direction The axial vector is obtained, and the axial vector is equidistant from each point on the skin surface of the upper arm.
- the end point of the axial vector is the vertex of the cylinder, that is, the FRCS, and the position information of the FRCS is expressed as
- step 3 comprises:
- Step 31 Determine 3 marking points M1, M2, M3 on the skin surface of the upper arm, and translate the marking points M1, M2, M3 to the vertical vector of the reference axis vector vertical vector vertical vector
- the starting point of each vertical vector is all located at the position of the midpoint MD of the medial and lateral epicondyle points of the humerus at this moment;
- Step 32 Determine the center of the circle where the end point of each vertical vector after translation is located (indicated by mark O), and the displacement from the midpoint MD of the medial and lateral epicondyle points of the humerus to the center of the circle O is the amount of the reference axis to the center of the circle.
- step 3 for any time ta in the process, the coordinate system is translated, and a is the local coordinate system of the coordinate origin, then at time t a , the inverse vector of the vertical vector from the marker points M1, M2, M3 to the reference axis vector satisfy the relation in representation vector
- n 1, 2, 3.
- step 4 the central axis of the cylinder is corrected by introducing a proportional coefficient n of the height of the upper arm surface marking point in the cylinder to the total height of the cylinder.
- step 4 comprises:
- Step 41 Project the three marking points M1, M2 and M3 on the upper arm surface to the reference axis vector. For any time ta in the process, there is a relational expression:
- Step 42 Note Simultaneous formula 6 and formula 7, we get at time t a :
- Step 43 Select the proportional coefficient of the time t j when the arms are vertically downward in the standing posture of the human body is the standard coefficient, for any time ta add correction make the scale factor Towards to move closer, that is, to get:
- Step 44 According to the correction amount does not change the modulus of the axis vector get:
- Step 45 In the conical generatrix set satisfying the first column of Equation 6, the first column of Equation 7 and Equation 8, the conical generatrix set satisfying the second column of Equation 6, the second column of Equation 7 and Equation 8, and the conical generatrix set satisfying Equation 6 the third column, the third column of formula 7 and the conical generatrix of formula 8 are concentrated, and the ones closest to before correction are selected respectively.
- the solution is synthesized to get to get the final correction According to the final correction amount Rewrite formula 1 as:
- step 5 after obtaining the height compensation for the cylinder, the final calculation formula of FRCS is:
- l rm is the height compensation coefficient of the cylinder.
- Using the functional shoulder joint rotation center positioning method based on the rigid upper arm model of the present invention has higher accuracy for the FRCS positioning result, and the FRCS positioning result has good stability relative to the upper arm and the torso, and can be used to establish a more accurate digital dynamic of the human body model and more accurate human pose estimation.
- FIG. 1 is a flow chart of a preferred embodiment of a method for locating a functional shoulder joint rotation center based on a rigid upper arm model according to the present invention.
- FIG. 2 is a schematic diagram of the reference axis vector and the axial vector of the embodiment shown in FIG. 1 according to the method for locating the rotational center of the functional shoulder joint based on the rigid upper arm model according to the present invention.
- FIG. 3 is a schematic diagram of three marker points of the embodiment shown in FIG. 1 according to the method for locating the rotation center of a functional shoulder joint based on a rigid upper arm model according to the present invention.
- FIG. 4-6 are schematic diagrams showing the correction of the direction of the central axis of the embodiment shown in FIG. 1 according to the method for locating the rotation center of the functional shoulder joint based on the rigid upper arm model according to the present invention.
- FIG. 7 is a schematic diagram of the positioning process of the embodiment shown in FIG. 1 according to the method for positioning the rotation center of the functional shoulder joint based on the rigid upper arm model according to the present invention.
- FIG. 8 is a schematic diagram of the experimental environment of another embodiment of the method for locating the rotation center of the functional shoulder joint based on the rigid upper arm model according to the present invention.
- FIG. 9 is a schematic diagram showing the sticking position of the marker points on the upper arm of the human body during the experiment of the embodiment shown in FIG. 8 according to the method for locating the rotation center of the functional shoulder joint based on the rigid upper arm model of the present invention.
- Fig. 10 is a data collection result of a certain subject marked point in the embodiment shown in Fig. 8 according to the method for locating the functional shoulder joint rotation center based on the rigid upper arm model of the present invention.
- FIG. 11 is the motion trajectory of the right upper arm of a subject in the embodiment shown in FIG. 8 according to the method for locating the functional shoulder joint rotation center based on the rigid upper arm model of the present invention.
- Fig. 12 is a schematic diagram showing the relative position of the FRCS localization result in the torso of subject No. 1 in the embodiment shown in Fig. 8 according to the method for locating the functional shoulder joint rotation center based on the rigid upper arm model of the present invention.
- Fig. 13 shows that the three marked points M1, M2 and M3 on the upper arm of subject No. 1 according to the embodiment of the present invention as shown in Fig. 8 correspond to the corrected axis The coefficient n of the quantity.
- Fig. 14 is a pair of three marked points M1, M2 and M3 on the upper arm of subject No. 1 in the test time of the embodiment shown in Fig. 8 according to the method for locating the functional shoulder joint rotation center based on the rigid upper arm model of the present invention
- the change trend of the coefficient n of the axial vector before and after the correction is a pair of three marked points M1, M2 and M3 on the upper arm of subject No. 1 in the test time of the embodiment shown in Fig. 8 according to the method for locating the functional shoulder joint rotation center based on the rigid upper arm model of the present invention.
- Fig. 15 is a schematic diagram showing the translation correction of the position of the central axis of the embodiment shown in Fig. 8 according to the method for locating the rotation center of the functional shoulder joint based on the rigid upper arm model of the present invention.
- Fig. 16 shows the FRCS positioning result of subject No. 1 before compensation according to the embodiment shown in Fig. 8 to three marker points M1, M2, M3 of the upper arm according to the method for locating the functional shoulder joint rotation center based on the rigid upper arm model of the present invention distance changes.
- Fig. 17 is the FRCS positioning result after compensation of subject No. 1 according to the embodiment shown in Fig. 8 to three marker points M1, M2, M3 of the upper arm according to the method for locating the functional shoulder joint rotation center based on the rigid upper arm model of the present invention distance changes.
- FIG. 18 is the standard deviation of the distance change from the FRCS positioning results of the right shoulder of 28 subjects to the three marked points of the upper arm in the embodiment shown in FIG. 8 according to the method for locating the functional shoulder joint rotation center based on the rigid upper arm model of the present invention .
- Step 1 Abstract the upper arm of the human body into a cylinder with FRCS as the top center;
- Step 2 Determine the reference axis vector of the cylinder
- Step 3 Determine the axial vector of the cylinder and the displacement from the reference axial vector to the axial vector;
- Step 4 Correct the direction of the central axis of the cylinder
- Step 5 Determine the height compensation of the cylinder, and position the FRCS.
- step 1 the upper arm of the human body is abstracted into a cylinder with the FRCS as the center of the top surface, in this embodiment:
- the main way of upper arm movement is rotation.
- the range of motion of the distal end of the humerus is much larger than that of the top of the humerus, ignoring the deformation of the upper arm during motion, the upper arm approximately rotates around the FRCS during motion.
- the position of the FRCS can be determined. Therefore, in step 1, the upper arm of the human body is abstracted into a cylinder with the FRCS as the center of the top surface, and correspondingly, the skin surface of the upper arm of the human body is abstracted as the side surface of the cylinder.
- step 2 determine the reference axis vector of the cylinder, in this example:
- step 2 the midpoint of the medial and lateral epicondyles of the humerus on the surface of the human body (indicated by the mark MD) is the starting point, and the vector pointing to the point of the acromion (indicated by the mark MU) is the reference axis vector of the cylinder, and its direction is the reference direction of the cylinder, there are
- the M U [X U Y U Z U ] T represents the position information of the acromion point MU
- the M D [X D Y D Z D ] T represents the position of the midpoint MD of the medial and lateral epicondyle points of the humerus. location information.
- the measurement process will last for a period of time.
- the starting time of the test process is represented by t 0 and the end time is represented by t s .
- the selected human surface markers will be continuously collected. to obtain the position information of the marker points on the surface of the human body in the duration period.
- step 3 determine the axial vector of the cylinder and the displacement from the reference axial vector to the axial vector, in this embodiment:
- step 3 the reference axis vector translate in a direction perpendicular to the reference direction
- the axial vector is obtained, and the axial vector is equidistant from each point on the skin surface of the upper arm.
- the end point of the axial vector is the vertex of the cylinder, that is, the FRCS, and the position information of the FRCS is expressed as:
- the axial vector is translated according to the reference axis vector in the direction perpendicular to the reference direction, the distances to the upper arm marking points are equal, so if three marking points are selected on the skin surface of the upper arm, according to the spatial geometry
- the section of a cylinder is of the nature of a circle. In the section of a cylinder, the center of the circle enclosed by the projection points of the three marking points of the upper arm on the section along the reference direction is the intersection of the axial vector and the section.
- Step 31 As shown in Figure 3, determine 3 marking points M1, M2, M3 on the skin surface of the upper arm, and translate the marking points M1, M2, M3 to the vertical vector of the reference axis vector vertical vector vertical vector The starting point of each vertical vector is all located at the position of the midpoint MD of the medial and lateral epicondyle points of the humerus at this moment;
- Step 32 Determine the center of the circle where the end point of each vertical vector after translation is located (indicated by mark O), and the displacement from the midpoint MD of the medial and lateral epicondyle points of the humerus to the center of the circle O is the amount of the reference axis to the center of the circle.
- the coordinate system is translated to establish is the local coordinate system of the coordinate origin, then at time t a , the inverse vector of the vertical vector from the marker points M1, M2, M3 to the reference axis vector satisfy the relation in representation vector
- the coordinates of the end point, n 1, 2, 3. in coordinates and In the plane where the three points represented are located, find the center of the circle where the three points are located: because the three points and the center of the circle where the three points are located belong to the same plane, there are:
- step 4 correct the direction of the central axis of the cylinder, in this embodiment:
- Reference axis vector It is determined according to the bone-shaped landmarks. Geometrically, it has deviations from the central axis of the cylinder (the straight line where the axial vector is located). In order to make the calculation results more accurate, the direction of the central axis of the cylinder model needs to be corrected. .
- the rigid cylinder does not deform in translation and rotation, so the relative position of its surface points in the cylinder is unchanged, and the cutting ratio of the intersection of the cross section and the central axis to the central axis segment is unchanged.
- the central axis of the cylinder is corrected by introducing a proportional coefficient n of the height of the upper arm surface marking point in the cylinder to the total height of the cylinder.
- step 4 specifically includes:
- Step 41 Project the three marked points M1, M2 and M3 on the upper arm surface to the reference axis vector. For any time ta in the measurement process, there is a relational expression:
- Step 42 Note Simultaneous formula 6 and formula 7, we get at time t a :
- Step 43 The proportional coefficient n describes the ratio of the height of the marker point in the cylinder to the total height of the cylinder.
- the coefficient n corresponding to the same marker point does not change with its movement. But due to It is not parallel to the real central axis.
- the coefficients n of the same mark point at different times are not all the same, so the time t j when the arms are vertically downward in the standing posture of the human body is selected.
- scale factor of is the standard coefficient, for any time ta add correction make the scale factor Towards to move closer, that is, to get:
- Step 44 According to the correction amount does not change the modulus of the axis vector get:
- Step 45 In the conical generatrix set satisfying the first column of Equation 6, the first column of Equation 7 and Equation 8, the conical generatrix set satisfying the second column of Equation 6, the second column of Equation 7 and Equation 8, and the conical generatrix set satisfying Equation 6 the third column, the third column of formula 7 and the conical generatrix of formula 8 are concentrated, and the ones closest to before correction are selected respectively.
- the solution is synthesized to get to get the final correction According to the final correction amount Rewrite formula 1 as:
- the correction amount that satisfies the first column of formula 6, the first column of formula 7 and formula 8 in space is infinite, as shown in Figure 5, satisfying the conditions set around Rotating conical generatrix; similarly, the second column of formula 6, the second column of formula 7 and formula 8 are satisfied set around The rotating conical generatrix satisfies the third column of formula 6, the third column of formula 7 and formula 8 set around Rotating conic generatrix; therefore, the result of simultaneous equations 6, 7 and equation 8 in space is the generatrix that these three common vertex cones intersect together, as shown in Figure 6.
- the vertices of the three cones are the same
- the directions of the central axes of the three cones are and
- the generatrix lengths of the three cones are The three marked points M1, M2 and M3 cut the busbars by the coefficient n al' to their respective busbar footholds.
- the three cones have the situation that the busbars do not intersect, that is, there is no solution for the simultaneous equations 6, 7 and 8. Therefore, in each of the three conic generatrix sets, select the closest before correction The solution is synthesized to get to get the final correction
- n c For the marked point M1, when the vector and coplanar with its compensation result, there is a minimum Set the coefficient n c to be a multiple of extending or shortening the vertical line from the marked point to the axis, so that it intersects the axis after compensation, then n c satisfies the relationship:
- Mode Describes the vertical foot from the upper arm marked point M1 to the post-compensated central axis according to the standard coefficient Cutting axis vector.
- step 5 determine the height compensation of the cylinder, and position the FRCS, in this embodiment:
- steps 1 to 4 the upper arm of the human body is abstracted into a standard rigid cylinder, but in the actual motion of the human body, the abstraction will be inaccurate due to the deformation of the upper arm of the human body, especially the change of the upper arm circumference will This directly causes the radius of the cylinder to change, thereby causing the distance from the FRCS positioning result to the marked point to change. Therefore, the FRCS positioning result needs to be compensated.
- the FRCS generated by the change of the circumference of the upper arm can be changed by stretching the height of the cylinder.
- the positioning result error is compensated.
- the specific compensation method is:
- the scaling ratio of the three marking points M1, M2 and M3 is used and Synthesizing the expansion and contraction ratio of the cylinder, that is, the height compensation coefficient Specific synthesis basis:
- k 1 represents the range of the distance from the marker point M1 to the detected value during the measurement time
- k 2 represents the range of the distance from the marker point M2 to the FRCS during the measurement time
- k 3 represents the range of the distance from the marker point M3 to the FRCS during the measurement time .
- l rm is the height compensation coefficient of the cylinder.
- the process of the FRCS positioning method is shown in Figure 7.
- the upper arm of the human body is abstracted as a rigid cylinder, the reference axis vector and the axis vector of the cylinder are determined, and then the reference axis vector is added to the Correction amount Corrected, the corrected result is Redetermines the translation of the reference axis vector axis vector
- the corrected result is Redetermines the translation of the reference axis vector axis vector
- perform height compensation on the cylinder determine the height compensation coefficient l rm , and obtain the final positioning result of the FRCS.
- the process of localization analysis of FRCS 6 markers were used for each arm, namely: acromion, medial and medial epicondyle of humerus, and three markers of upper arm.
- the pasting positions of the three marking points M1, M2 and M3 on the upper arm satisfy two rules: (1) the three points cannot form a straight line; (2) the distance between the three points should be as large as possible.
- the sticking positions of the three points not only conform to the above two principles, but also ensure that the projection of the cross-section of the upper arm bisects the cross-section circle as much as possible.
- the thoracic vertebrae points corresponding to the height of the head vertex, neck point, upper chest point, lower chest point, and lower chest point can be added.
- Figure 10 shows the results of data collection on the marked points of a subject
- Figure 11 shows the motion trajectory of a subject's right upper arm. It can be found that the subject's upper arm has not only rotational motion, but also translational motion. sports.
- Figure 12 shows the relative position of the FRCS positioning results in the torso.
- the calculation results show that the FRCS of the right shoulder is about 5 cm in the direction of the left acromion and about 1 cm below the right acromion. Slightly back 0.5 cm.
- Table 2 shows the correction amount of the central axis of the cylinder at the partial moment of subject No. 1
- Figure 13 shows the coefficient n of the three marked points M1, M2 and M3 on the upper arm to the corrected axial vector
- Figure 14 shows the three marked points M1, M2 and M3 on the upper arm during the test time
- Table 3 shows the statistical parameters of the coefficient n before and after the correction of the axial vector at the three marked points M1, M2 and M3 of the upper arm.
- Figure 15 shows the translation correction of the central axis position, where the amount of translation is the translation correction of the axial vector; R is the radius of the rigid cylinder of the upper arm, and the statistical parameters of R are shown in Table 4.
- Figure 16 shows the distance changes from the FRCS positioning results to the three marker points M1, M2, and M3 on the upper arm before compensation. The trends of these three distances are very similar, and the standard deviations of the distances are 3.0763mm, 2.9816mm, and 2.5329mm, respectively. ; Figure 17 shows the change of the distance between the FRCS and the three marked points of the upper arm after compensation, and the standard deviation of the distance is reduced to 0.7202mm, 0.4144mm and 0.3971mm, respectively.
- Table 5 shows the expansion coefficient l rm of the cylinder height during the compensation process.
- FRCS is the center of rotation of the upper arm in motion.
- the distances from the FRCS to the three marked points M1, M2, and M3 of the upper arm should be consistent, so the standard deviation of the distance changes is very important to describe the reliability of the method.
- Figure 18 shows the standard deviation of the distance changes from the FRCS positioning results of the right shoulder to the three markers on the upper arm for 28 subjects.
- the error of the 27th subject is unreasonable, especially the error of the 3rd marker is far more than the average.
- Table 6 records the standard deviation of the distance change from the FRCS to the marking point for the remaining 27 subjects during the test. related value.
- the standard deviation of the distance change between the FRCS positioning result and the three marked points M1, M2, and M3 of the upper arm is in the range of 0.081 to 2.2973. , indicating that the FRCS positioning method provided by the present invention has high accuracy and reliability of the positioning results, and the positioning results of the FRCS have good stability relative to the upper arm and the torso, which can be used to establish a more accurate digital dynamic model of the human body and perform more accurate Human pose estimation.
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Abstract
一种基于刚性上臂模型的功能性肩关节旋转中心定位方法,其包括步骤1:将人体上臂抽象成以FRCS为顶面圆心的圆柱体;步骤2:确定圆柱体的参考轴向量;步骤3:确定圆柱体的轴向量以及参考轴向量至轴向量的位移量;步骤4:对圆柱体的中轴线方向进行修正;步骤5:确定圆柱体的高度补偿,对FRCS进行定位。功能性肩关节旋转中心定位方法对FRCS定位结果精度更高,FRCS的定位结果相对于上臂与躯干的稳定性很好,可以用于建立更精确的人体数字化动态模型以及进行更加精准的人体姿态预估。
Description
本发明涉及人体运动测量技术领域,具体涉及一种基于刚性上臂模型的功能性肩关节旋转中心定位方法。
当前人体运动测量及姿态预测技术在各个领域都发挥着重要的作用,如在运动员选拔领域、体育运动的动作捕捉领域、计算机视觉领域、生物医学和医疗器械领域等。在人体运动测量及姿态预测过程中,肩关节作为人体上肢中最灵活的关节,其定位是建立人体数字化动态模型的重要环节。
在生物医学领域,肩关节解剖中心(GHAC,glenohumeral anatomical center)根据解剖学中肱骨头位置推断出来的;在人体运动测量领域,功能性肩关节旋转中心(FRCS,Functional Rotation Center of Shoulder)被定义为运动中上臂的旋转中心,其通过人体上臂的运动学参数进行定位。
在FRCS的概念被提出来之前,肩关节的旋转中心的定位借鉴了定位肩关节解剖中心的方法,即根据人体肩部轮廓的扫描结果,结合复杂的解剖学知识,对肱骨与肩胛骨的骨形包络进行预测与数字化研究进而定位肩关节旋转中心。但是因为肩关节解剖中心的测量是在静态或者近似静态的条件下完成的,因此,即使对肱骨和肩胛骨的骨形包络进行了非常准确地估计,定位的肩关节旋转中心用于建立人体数字化动态模型方面仍有很大不足。
FRCS的概念被提出之后,早期的FRCS是使用尸体进行定位的,通过在尸体上臂三个自由度的旋转轴上订入长钉的方法定位三个旋转轴的交点,即FRCS。但是因为尸体的运动是非主观的,因此此种方法确定的FRCS用于建立人体数字化动态模型方面仍然具有精度不足的缺陷。
日本数字人体化研究中心提出了一种测量运动中人体FRCS的方法,该方法完全抛弃了解剖学知识对FRCS的限制,运用几何算法获得了精确的上肢可达域。这种方法的优点在于FRCS是根据运动中人体求出的,更符合人体的运动姿态,并且,运动中人体FRCS的位置与肢体角度之间存在着相关性,这可以用来建立更精确的人体数字化动态模型。在失去解剖学知识作为几何限制的情况下,由于系统误差,皮肤形变等造成的FRCS定位误差在几何计算中会被传递与放大,使FRCS定位结果偏移严重。
发明内容
为解决以上现有技术中存在的FRCS定位结果精度不足的问题,本发明提供了一种基于刚性上臂模型的功能性肩关节旋转中心定位方法。
基于刚性上臂模型的功能性肩关节旋转中心定位方法,包括
步骤1:将人体上臂抽象成以FRCS为顶面圆心的圆柱体;
步骤2:确定所述圆柱体的参考轴向量;
步骤3:确定所述圆柱体的轴向量以及所述参考轴向量至所述轴向量的位移量;
步骤4:对所述圆柱体的中轴线方向进行修正;
步骤5:确定所述圆柱体的高度补偿,对所述FRCS进行定位。
优选的是,步骤1中,人体上臂皮肤表面抽象为所述圆柱体的侧面。
上述任一方案优选的是,对于人体上臂皮肤表面的任一点A,点A从起始时刻t
0到截至时刻t
s的位置信息表示为M
A,
其中t
s=t
0+kΔt,k≥3,Δt为采样间隔。
上述任一方案优选的是,所述轴向量的终点即为所述圆柱体的顶点,即FRCS,所述FRCS的位置信息表示为
上述任一方案优选的是,步骤3包括:
上述任一方案优选的是,步骤3中,对于过程中的任意时刻t
a,平移坐标系,建立以
为坐标原点的局部坐标系,则t
a时刻,所述标记点M1、M2、M3到所述参考轴向量的垂向量的逆向量
满足关系式
其中
表示向量
的终点坐标,n=1、2、3。
上述任一方案优选的是,根据公式
及公式
上述任一方案优选的是,步骤4中,引入上臂表面标记点在所述圆柱体中的高度占所述圆柱体总高度的比例系数n对所述圆柱体的中轴线进行修正。
上述任一方案优选的是,步骤4包括:
步骤41:将上臂表面3个标记点M1、M2、M3向所述参考轴向量做投影,对于过程中的任意时刻t
a,存在关系式:
和
其中
表示t
a时刻以标记点M1到向量
的垂足为起点且指向标记点M1的向量,
和
表示的含义以此类推;
和
分别表示时刻t
a以MD为起点且指向标记点M1、M2和M3垂足的向量对
的占比;
表示t
a时刻标记点M1的位置坐标,
表示的含义以此类推。
步骤45:在满足式⑥第一列、式⑦第一列和式⑧的圆锥母线集、满足式⑥第二列、式⑦第二列和式⑧的圆锥母线集、以及满足式⑥第三列、式⑦第三列和式⑧的圆锥母线集中,各自选取最贴近修正前
的解进行合成得到
进而得到最终的修正量
根据最终的修正量
将式①改写为:
上述任一方案优选的是,步骤5中,得到对所述圆柱体进行高度补偿后,FRCS的最终计算公式为:
其中,l
rm为所述圆柱体的高度补偿系数。
采用本发明的基于刚性上臂模型的功能性肩关节旋转中心定位方法对FRCS定位结果精度更高,FRCS的定位结果相对于上臂与躯干的稳定性很好,可以用于建立更精确的人体数字化动态模型以及进行更加精准的人体姿态预估。
图1为按照本发明的基于刚性上臂模型的功能性肩关节旋转中心定位方法的一优选实施例的流程图。
图2为按照本发明的基于刚性上臂模型的功能性肩关节旋转中心定位方法的如图1所示实施例的参考轴向量及轴向量示意图。
图3为按照本发明的基于刚性上臂模型的功能性肩关节旋转中心定位方法的如图1所示实施例的三个标志点示意图。
图4-图6为按照本发明的基于刚性上臂模型的功能性肩关节旋转中心定位方法的如图1所示实施例的中轴线方向修正示意图。
图7为按照本发明的基于刚性上臂模型的功能性肩关节旋转中心定位方法的如图1所示实施例的定位过程示意图。
图8为按照本发明的基于刚性上臂模型的功能性肩关节旋转中心定位方法的另一实施例的实验环境示意图。
图9为按照本发明的基于刚性上臂模型的功能性肩关节旋转中心定位方法的如图8所示实施例的实验过程中人体上臂上标记点的粘贴位置示意图。
图10为按照本发明的基于刚性上臂模型的功能性肩关节旋转中心定位方法的如图8所示实施例的某一受试者标记点数据采集结果。
图11为按照本发明的基于刚性上臂模型的功能性肩关节旋转中心定位方法的如图8所示实施例的某一受试者右侧上臂的运动轨迹。
图12为按照本发明的基于刚性上臂模型的功能性肩关节旋转中心定位方法的如图8所示实 施例的1号受试者FRCS定位结果在躯干中的相对位置示意图。
图13为按照本发明的基于刚性上臂模型的功能性肩关节旋转中心定位方法的如图8所示实施例的1号受试者其上臂三个标记点M1、M2和M3对修正后轴向量的系数n。
图14为按照本发明的基于刚性上臂模型的功能性肩关节旋转中心定位方法的如图8所示实施例的1号受试者测试时间内其上臂三个标记点M1、M2和M3对对修正前后轴向量的系数n的变化趋势。
图15为按照本发明的基于刚性上臂模型的功能性肩关节旋转中心定位方法的如图8所示实施例的中轴线位置的平移修正示意图。
图16为按照本发明的基于刚性上臂模型的功能性肩关节旋转中心定位方法的如图8所示实施例的1号受试者补偿前FRCS定位结果到上臂三个标记点M1、M2、M3的距离变化。
图17为按照本发明的基于刚性上臂模型的功能性肩关节旋转中心定位方法的如图8所示实施例的1号受试者补偿后FRCS定位结果到上臂三个标记点M1、M2、M3的距离变化。
图18为按照本发明的基于刚性上臂模型的功能性肩关节旋转中心定位方法的如图8所示实施例的28位受试者右肩FRCS定位结果到上臂三个标记点距离变化的标准差。
为了更好地理解本发明,下面结合具体实施例对本发明作详细说明。
实施例1
如图1所示,基于刚性上臂模型的功能性肩关节旋转中心定位方法,包括
步骤1:将人体上臂抽象成以FRCS为顶面圆心的圆柱体;
步骤2:确定所述圆柱体的参考轴向量;
步骤3:确定所述圆柱体的轴向量以及所述参考轴向量至所述轴向量的位移量;
步骤4:对所述圆柱体的中轴线方向进行修正;
步骤5:确定所述圆柱体的高度补偿,对所述FRCS进行定位。
对于步骤1:将人体上臂抽象成以FRCS为顶面圆心的圆柱体,在本实施例中:
当人体躯干固定的时候,上臂运动的主要方式是旋转。在极短时间内肱骨末端的运动幅度远大于肱骨顶端,忽略上臂运动中的形变,则运动中上臂近似围绕FRCS旋转。在几何运算中,如果可以得到上臂表面至少三个点的空间位置变化,那么FRCS的位置就可以被确定。因此,在步骤1中,将人体上臂抽象成以FRCS为顶面圆心的圆柱体,相应的,将人体上臂皮肤表面抽象为所述圆柱体的侧面。
对于步骤2:确定所述圆柱体的参考轴向量,在本实施例中:
如图2所示,在步骤2中,以人体表面肱骨内、外上髁点中点(用标记MD表示)为起点,指向肩峰点(用标记MU表示)的向量
为圆柱的参考轴向量,其方向为所述圆柱体的参考方向,有
其中所述M
U=[X
U Y
U Z
U]
T表示肩峰点MU的位置信息,所述M
D=[X
D Y
D Z
D]
T表示肱骨内、外上髁点中点MD的位置信息。
在运动测量中,测量过程会持续一段时间,为描述方便,将测试过程起始时刻用t
0表示,截 止时刻用t
s表示,在这一段时间内,会连续采集选定的人体表面标记点的位置,得到持续时间段内人体表面标记点的位置信息。对于人体上臂皮肤表面的任一点A,点A从起始时刻t
0到截至时刻t
s的位置信息表示为M
A,
其中t
s=t
0+kΔt,k≥3,Δt为采样间隔。对于测量过程中的任意时刻t
i,点A的位置坐标
在本实施例中,综合考虑计算的方便性、实验条件的限制以及计算结果的准确性与重复性,设置k=500,Δt=0.01ms。
对于步骤3:确定所述圆柱体的轴向量以及所述参考轴向量至所述轴向量的位移量,在本实施例中:
如图2所示,步骤3中,将所述参考轴向量
沿与所述参考方向垂直的方向平移
得到所述轴向量,所述轴向量到上臂皮肤表面各点的距离相等。所述轴向量的终点即为所述圆柱体的顶点,即FRCS,则所述FRCS的位置信息表示为:
因为轴向量是根据参考轴向量沿与参考方向垂直的方向平移而来的,其到上臂标记点的距离均相等,因此若在上臂皮肤表面选定三个标记点,则根据空间几何中圆柱体截面是圆的性质,在圆柱体的截面中,上臂三标记点沿参考方向在截面上的投影点所围成圆的圆心即轴向量与该截面的交点。基于以上理论,步骤3中,确定所述参考轴向量至所述轴向量的位移量
的具体过程包括:
步骤31:如图3所示,在上臂皮肤表面确定3个标记点M1、M2、M3,平移所述标记点M1、M2、M3到所述参考轴向量的垂向量
垂向量
垂向量
使各垂向量的起点均位于该时刻肱骨内、外上髁点中点MD的位置处;
具体地说,对于测量过程中的任意时刻t
a,平移坐标系,建立以
为坐标原点的局部坐标系,则t
a时刻,所述标记点M1、M2、M3到所述参考轴向量的垂向量的逆向量
满足关系式
其中
表示向量
的终点坐标,n=1、2、3。在坐标
和
表示的三个点所在平面内,寻找这三点所在圆形的圆心:因为所述三点与三点所在圆的圆心属于同一平面,则有:
同时,因为所述三点到其所在圆的圆心的距离相等,有:
对于步骤4:对所述圆柱体的中轴线方向进行修正,在本实施例中:
刚性圆柱体在平移与旋转运动中不会产生形变,因此其表面点在圆柱体中的相对位置是不变的,进而表面点所在横截面与中轴线交点对中轴线段的切割比例是不变的,引入上臂表面标记点在所述圆柱体中的高度占所述圆柱体总高度的比例系数n对所述圆柱体的中轴线进行修正。
如图4所示,步骤4具体包括:
步骤41:将上臂表面3个标记点M1、M2、M3向所述参考轴向量做投影,对于测量过程中的任意时刻t
a,存在关系式:
和
其中
表示t
a时刻以标记点M1到向量
的垂足为起点且指向标记点M1的向量,
和
表示的含义以此类推;
和
分别表示时刻t
a以MD为起点且指向标记点M1、M2和M3垂足的向量对
的占比;
表示t
a时刻标记点M1的位置坐标,
表示的含义以此类推。
步骤43:比例系数n描述了标记点在圆柱中的高度占圆柱总高度的比例,在刚性圆柱体中同一标记点对应的系数n是不随其运动而变化的。但由于
与真实中轴线之间是不平行的,在整个测试时间段(t
s-t
0)内,同一标记点不同时刻的系数n不全相同,因此选取人体站立姿态下双臂垂直向下时刻t
j的比例系数
为标准系数,对任意时刻t
a的
加入修正量
使得比例 系数
向
靠拢,即使得:
步骤45:在满足式⑥第一列、式⑦第一列和式⑧的圆锥母线集、满足式⑥第二列、式⑦第二列和式⑧的圆锥母线集、以及满足式⑥第三列、式⑦第三列和式⑧的圆锥母线集中,各自选取最贴近修正前
的解进行合成得到
进而得到最终的修正量
根据最终的修正量
将式①改写为:
在空间中满足式⑥第一列、式⑦第一列和式⑧的修正量
是无穷多个的,如图5所示,满足条件的
集为绕
旋转的圆锥母线;同样的,满足式⑥第二列、式⑦第二列与式⑧的
集为绕
旋转的圆锥母线,满足式⑥第三列、式⑦第三列与式⑧的
集为绕
旋转的圆锥母线;因此空间中联立式⑥、式⑦和式⑧的结果为这三个共顶点圆锥共同相交的母线,如图6所示。所述三个圆锥的顶点相同,均为
三个圆锥的中轴线方向分别为
和
三个圆锥的母线长度均为
三个标记点M1、M2和M3到各自母线垂足按系数n
al′切割母线。但是,实际情况下,所述三个圆锥存在母线不相交的情况,即联立式⑥、式⑦和式⑧存在没有解的情况。因此在三个圆锥母线集中各自选取最贴近修正前
的解进行合成得到
进而得到最终的修正量
经过修正后,将式①进行改写,得到FRCS的计算公式为:
对于步骤5:确定所述圆柱体的高度补偿,对所述FRCS进行定位,在本实施例中:
在步骤1至步骤4中,人体上臂均被抽象成了标准刚性圆柱体,但是在人体实际运动中,因为人体上臂的形变会使得该抽象具有一定的不准确性,尤其上臂围度的变化会直接导致所述圆柱体的半径发生变化进而导致FRCS的定位结果到标记点的距离发生变化,因此需要对FRCS的定位结果进行补偿。
鉴于圆柱体表面上的点到圆柱体顶面圆心的距离与圆柱体半径和圆柱体表面上的点到顶面的高度有关,因此,可以通过伸缩圆柱体的高度使上臂围度变化产生的FRCS的定位结果误差得到补偿。具体的补偿方法为:
其中,k
1表示测量时间内标记点M1到检测值距离的极差,k
2表示测量时间内标记点M2到FRCS距离的极差,k
3表示测量时间内标记点M3到FRCS距离的极差。
其中,l
rm为所述圆柱体的高度补偿系数。
综上所述,FRCS定位方法的过程如图7所示,首先将人体上臂抽象为刚性圆柱体,确定所述圆柱体的参考轴向量和轴向量,然后对所述参考轴向量加入修正量
进行修正,修正后的结果为
重新确定参考轴向量向轴向量的平移量
最后对圆柱体进行高度补偿,确定高度补偿系数l
rm,得到FRCS的最终定位结果。
实施例2
为了验证所述FRCS定位方法的准确性,进行了实验,并对实验结果进行了分析。
(一)实验
实验选择28名无上肢功能障碍的成年男性(18-55岁),受试者参加,所述受试者的形态学参数如表1所示。在测试前,所有受试者得知实验目的和实验程序并签署同意书。在实际测量过程中,使用了Qualisys三维运动采集与分析系统,。该系统是由瑞典Qualisys公司生产的,由运动捕捉摄像机、分析软件、获取单元、校准设备、标记球和设备固定装置组成。实验中,共设置17个摄像头,分别为4个视频摄像头和13个测量摄像头,所述17个摄像头均匀分布在实验场地四周,具体分布如图8所示。调整所有摄像头角度使得实验场地在镜头拍摄范围中心。每次实验的校准精度均保持在0.7mm以下。
表1 28位受试者形态学参数
上臂角度的测量需要躯干的直立,并且为了使肩胛骨尽可能少地参与到上臂运动中,因此对受试者的步态进行测试。71个标记点被粘贴在受试者身上,图9显示了人体上臂上标记点的粘贴位置。实验过程中,测试时间为30s,在测试时间内,受试者做出站立、行走、转身等动作,采集每一个标记点3000帧位置信息。
在FRCS的定位分析过程中,每条手臂都用到了6个标记点,分别为:肩峰点、肱骨内外上髁点和上臂三标记点。上臂三标记点M1、M2和M3的粘贴位置满足两个规则:(1)三点不能呈一条直线;(2)三点之间的距离应尽可能的大。在本实施例中,三点的粘贴位置不仅符合以上两条原则,还保证了其上臂横截面的投影尽可能地将截面圆三等分。为了简化计算与进行结果校验,可以增加头顶点、颈点、胸上点、胸下点、胸下点对应高度的胸椎点。
图10展示了对某一受试者的标记点进行数据采集的结果,图11展示了某一受试者右侧上臂的运动轨迹,可以发现该受试者的上臂不仅存在旋转运动,也有平移运动。
(二)实验结果分析
以1号受试者为例,图12展示了FRCS定位结果在躯干中的相对位置,计算结果显示右肩的FRCS在人体内部靠近左肩峰方向大约5厘米,低于右肩峰大约1厘米,稍靠后0.5厘米。表2展示了1号受试者部分时刻圆柱体中轴线的修正量
对于1号受试者,图13显示了其上臂三个标记点M1、M2和M3对修正后轴向量的系数n,图14显示了测试时间内其上臂三个标记点M1、M2和M3对对修正前后轴向量的系数n的变化趋势,表3展示了其上臂三个标记点M1、M2和M3对轴向量修正前后系数n的统计学参数。
表3 上臂轴向量方向修正前后的系数n对比
表4 上臂围度半径R
图16展示了补偿前FRCS定位结果到上臂三个标记点M1、M2、M3的距离变化,这三个距离的变化趋势是非常相似的,距离的标准差分别为3.0763mm、2.9816mm和2.5329mm;图17展示了补偿后FRCS到上臂三个标记点的距离变化,距离的标准差分别缩小到了0.7202mm、 0.4144mm和0.3971mm。
表5 展示了补偿过程中圆柱高度的伸缩系数l
rm。
表5 圆柱高度伸缩系数l
rm
FRCS是运动中上臂的旋转中心,理想状态下,FRCS到上臂三个标记点M1、M2、M3的距离应该分别保持一致,因此距离变化过程中的标准差对描述方法可靠性是非常重要的。图18展示了28位受试者右肩FRCS定位结果到上臂三个标记点距离变化的标准差,其中第27号受试者的误差是不合理的,尤其是第3标记点误差远超过平均值与三倍标准差的和,这可能是实验过程中标记点粘贴不牢固造成其晃动剧烈导致的,表6记录了其余27位受试者在测试过程中FRCS到标记点距离变化标准差的相关值。
通过图16-18、以及表6可以看出,本发明提供的FRCS定位方法,FRCS定位结果与上臂三个标记点M1、M2、M3之间距离变化的标准差介于范围0.081~2.2973之间,表示本发明提供的FRCS定位方法,其定位结果精度及可靠性高,FRCS的定位结果相对于上臂与躯干的稳定性很好,可以用于建立更精确的人体数字化动态模型以及进行更加精准的人体姿态预估。
表6 27位受试者在测试过程中FRCS到标记点距离变化标准差
需要说明的是,以上实施例仅用于说明本发明的技术方案,而非对其限制;尽管前述实施例对本发明进行了详细的说明,本领域的技术人员应该理解:其可以对前述实施例记载的技术方案进行修改,或者对其中部分或者全部技术特征进行等同替换,而这些替换,并不使相应技术方案的本质脱离本发明技术方案的范围。
Claims (10)
- 基于刚性上臂模型的功能性肩关节旋转中心定位方法,包括:步骤1:将人体上臂抽象成以FRCS为顶面圆心的圆柱体;步骤2:确定所述圆柱体的参考轴向量;步骤3:确定所述圆柱体的轴向量以及所述参考轴向量至所述轴向量的位移量;步骤4:对所述圆柱体的中轴线方向进行修正;步骤5:确定所述圆柱体的高度补偿,对所述FRCS进行定位。
- 如权利要求7所述的基于刚性上臂模型的功能性肩关节旋转中心定位方法,其特征在于:步骤4中,引入上臂表面标记点在所述圆柱体中的高度占所述圆柱体总高度的比例系数n对所述圆柱体的中轴线进行修正。
- 如权利要求8所述的基于刚性上臂模型的功能性肩关节旋转中心定位方法,其特征在于:步骤4包括:步骤41:将上臂表面3个标记点M1、M2、M3向所述参考轴向量做投影,对于过程中的任意时刻t a,存在关系式:和其中 表示t a时刻以标记点M1到向量 的垂足为起点且指向标记点M1的向量, 和 表示的含义以此类推; 和 分别表示时刻t a以MD为起点且指向标记点M1、M2和M3垂足的向量对 的占比; 表示t a时刻标记点M1的位置坐标, 表示的含义以此类推。步骤45:在满足式⑥第一列、式⑦第一列和式⑧的圆锥母线集、满足式⑥第二列、式⑦第二列和式⑧的圆锥母线集、以及满足式⑥第三列、式⑦第三列和式⑧的圆锥母线集中,各自选取最贴近修正前 的解进行合成得到 进而得到最终的修正量 根据最终的修正量 将式①改写为:
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