+ All Categories
Home > Documents > Relative Pose Estimation for the Femoral Component in Computer ... · The first kind of pattern is...

Relative Pose Estimation for the Femoral Component in Computer ... · The first kind of pattern is...

Date post: 10-Aug-2020
Category:
Upload: others
View: 0 times
Download: 0 times
Share this document with a friend
8
Relative Pose Estimation for the Femoral Component in Computer- Assisted Total Hip Replacement Surgeries Jiyang Gao 1 , Hong Chen 1+ , Shaojie Su 1 and Zhihua Wang 1 1 Institute of Microelectronics, Tsinghua University, Haidian, Beijing, China Abstract. Numerous factors influence the rate of dislocation after total hip replacement (THR) surgeries and malposition of the acetabular and femoral component has long been recognized as an important cause. To help surgeons improve the accuracy of the positioning of the components, a computer-assisted system for THR surgeries that estimates and displays the relative pose of femoral and acetabular component is proposed. The system consists of a miniature camera that is fixed inside the femoral prosthesis trial and a set of designated reference patterns that are printed on the internal surface of the acetabular prosthesis trial. In the initialization process, the image, which contains reference patterns on the internal surface of the acetabular cup, is captured and analyzed. As the femoral component moves, images are captured at different poses and compared with the initial image to establish correspondences of feature points. The relative pose matrix of femoral component is recovered from the fundamental matrix that is estimated by the correspondences of feature points. The system has been evaluated under the simulation with rotation matrix and translation vector and the experimental results have validated the effectiveness of the proposed pose estimation method. Keywords: THR, fundamental matrix, reference patterns, feature points 1. Introduction Numerous factors influence the rate of dislocation after THR such as greater age [1], previous surgery to the affected hip [2], concomitant neurological deficiencies [1], excessive alcohol intake [3], and nonunion of the greater trochanter [4]. Malposition has long been recognized as an important cause of dislocation [5], [6]. Accurate positioning of the acetabular component at the time of surgery is crucial in preventing post- operative dislocation [7]. However the positioning of the components within the safe zone is not guaranteed when using the freehand technique of operation [8]. If the placement is not in the safe zone, the dislocation risk of the prostheses is highly increased and the range of the movement is restricted. The prevalence of dislocation has been reported to be between 0.3% and 10% following primary total hip replacement and up to 28% after revision arthroplasty [9]. To help surgeons improve the accuracy of the placement of the acetabular components, some navigation system have been proposed and developed. The first kind of navigation system is based on CT. The accuracy improvement is significant but CT-based navigation system has not become an established standard routine due to the additional operation time, expense and exposure to radiation [10]. Several CT-free navigation systems for THR surgeries are developed both in industry and academia. Orthopilot is a computer assisted, CT-free navigation system that estimates the relative pose between femoral head and acetabular component using kinematical calculations without pre-operative scanning [11]. The rotation and translation of the femoral head are shown in Fig. 1. But extra body landmark equipments are needed in Orthopilot and the operating process can cause extra damage to the patients’ body. To overcome aforementioned problems, a visual aided system [12] for THR surgeries has been proposed. That system estimate the pose of the femoral head using a miniature camera which is placed inside the femoral prosthesis trial and a set of reference patterns printed on the internal surface of the femoral Corresponding author. Tel.: +86-10-62795097; fax: +86-10-62771130. E-mail address: [email protected]. 2015 5th International Conference on Biomedical Engineering and Technology (ICBET 2015) IPCBEE vol.81 (2015) © (2015) IACSIT Press, Singapore DOI: 10.7763/IPCBEE. 2015. V81. 6 25
Transcript
Page 1: Relative Pose Estimation for the Femoral Component in Computer ... · The first kind of pattern is designed as a circular ring, as shown in Fig. 3, which is used as a landmark to

Relative Pose Estimation for the Femoral Component in Computer-

Assisted Total Hip Replacement Surgeries

Jiyang Gao 1, Hong Chen

1+, Shaojie Su

1 and Zhihua Wang

1

1 Institute of Microelectronics, Tsinghua University, Haidian, Beijing, China

Abstract. Numerous factors influence the rate of dislocation after total hip replacement (THR) surgeries

and malposition of the acetabular and femoral component has long been recognized as an important cause.

To help surgeons improve the accuracy of the positioning of the components, a computer-assisted system for

THR surgeries that estimates and displays the relative pose of femoral and acetabular component is proposed.

The system consists of a miniature camera that is fixed inside the femoral prosthesis trial and a set of

designated reference patterns that are printed on the internal surface of the acetabular prosthesis trial. In the

initialization process, the image, which contains reference patterns on the internal surface of the acetabular

cup, is captured and analyzed. As the femoral component moves, images are captured at different poses and

compared with the initial image to establish correspondences of feature points. The relative pose matrix of

femoral component is recovered from the fundamental matrix that is estimated by the correspondences of

feature points. The system has been evaluated under the simulation with rotation matrix and translation

vector and the experimental results have validated the effectiveness of the proposed pose estimation method.

Keywords: THR, fundamental matrix, reference patterns, feature points

1. Introduction

Numerous factors influence the rate of dislocation after THR such as greater age [1], previous surgery to

the affected hip [2], concomitant neurological deficiencies [1], excessive alcohol intake [3], and nonunion of

the greater trochanter [4]. Malposition has long been recognized as an important cause of dislocation [5], [6].

Accurate positioning of the acetabular component at the time of surgery is crucial in preventing post-

operative dislocation [7]. However the positioning of the components within the safe zone is not guaranteed

when using the freehand technique of operation [8]. If the placement is not in the safe zone, the dislocation

risk of the prostheses is highly increased and the range of the movement is restricted. The prevalence of

dislocation has been reported to be between 0.3% and 10% following primary total hip replacement and up

to 28% after revision arthroplasty [9].

To help surgeons improve the accuracy of the placement of the acetabular components, some navigation

system have been proposed and developed. The first kind of navigation system is based on CT. The accuracy

improvement is significant but CT-based navigation system has not become an established standard routine

due to the additional operation time, expense and exposure to radiation [10]. Several CT-free navigation

systems for THR surgeries are developed both in industry and academia. Orthopilot is a computer assisted,

CT-free navigation system that estimates the relative pose between femoral head and acetabular component

using kinematical calculations without pre-operative scanning [11]. The rotation and translation of the

femoral head are shown in Fig. 1. But extra body landmark equipments are needed in Orthopilot and the

operating process can cause extra damage to the patients’ body.

To overcome aforementioned problems, a visual aided system [12] for THR surgeries has been proposed.

That system estimate the pose of the femoral head using a miniature camera which is placed inside the

femoral prosthesis trial and a set of reference patterns printed on the internal surface of the femoral

Corresponding author. Tel.: +86-10-62795097; fax: +86-10-62771130.

E-mail address: [email protected].

2015 5th International Conference on Biomedical Engineering and Technology (ICBET 2015)

IPCBEE vol.81 (2015) © (2015) IACSIT Press, Singapore

DOI: 10.7763/IPCBEE. 2015. V81. 6

25

Page 2: Relative Pose Estimation for the Femoral Component in Computer ... · The first kind of pattern is designed as a circular ring, as shown in Fig. 3, which is used as a landmark to

prosthesis trial. The pose estimation problem is converted to a PNP problem [13]. Basically, the PNP

algorithm uses a set of correspondence of 3D points and their 2D projection to estimate the pose of the

camera. The feature points used in the visual aided system [12] are the vertexes of each reference pattern. It

means that the accurate 3D coordinates of each vertex should be known in advance. However, the problem is

that the accuracy of the position of the patterns can’t be guaranteed in the realistic printing process. The

inaccuracy of the positions of the feature points could lead to a worse pose estimation result.

Fig. 1: The relative pose between the acetabular cup and femoral component.

To get rid of the reliance of the accurate 3D position of each feature point, a more robust pose estimation

method for femoral head based on feature point matches between image pairs and the fundamental matrix is

proposed in this paper. In the remainder of the paper, the system design is introduced in Section II, and then

the algorithm design is discussed in Section III. In Section IV, the analyses of experiment results are given.

2. System Design

2.1. System Design

Fig. 2: The relative pose between the acetabular cup and femoral component.

As shown in Fig. 2, the system contains two major parts. One is for image processing and model

rendering which consists of a computing platform and a transceiver. The other part is to capture images and

transfer data which is placed inside of the femoral head. The image sensor captures an image of the internal

surface of the acetabular, which was covered by reference patterns, and the image was sent to computer

wirelessly by transceivers. Computer algorithms process the image and estimate the camera pose, which is

also the pose of the femoral head, because the camera was firmly fixed to the femoral component.

The pose estimation problem is formulated in the following coordinate systems. Femoral coordinate

frame (with three axes Xc Yc Zc shown in Fig. 2) is attached to the femoral head and its origin located in the 26

Page 3: Relative Pose Estimation for the Femoral Component in Computer ... · The first kind of pattern is designed as a circular ring, as shown in Fig. 3, which is used as a landmark to

camera center. The camera is fixed inside the femoral head so it is rigidly aligned and attached to the femoral

component. As a result, camera coordinate frame is also the femoral coordinate frame. Acetabular coordinate

frame (with three axes Xa Ya Za shown in Fig. 2) is attached to the patient’s body and it is the reference

frame to the femoral frame. Its origin is located in the center of the acetabular cup that is approximately a

hemisphere.

2.2. Reference Patterns Design

To estimate the pose of the camera, two kinds of reference patterns are designed and printed on the

internal surface of the acetabular prosthesis trial liner during the production process. The surface

development of it is shown in Fig. 3.

Fig. 3: Surface development of the reference patterns printed on the internal surface of the liner.

The first kind of pattern is designed as a circular ring, as shown in Fig. 3, which is used as a landmark to

adjust the femur to a preset pose in the initialization step. The projection of a circular ring onto the image

plane is an elliptical ring due to the pinhole camera model [14]. When the camera is right above the pattern I,

the elliptical ring turns to a circular ring on the image plane and the distance between the camera and the

pattern influences the ratio.

The second kind of patterns (as shown in Fig. 3) are designed by the following rules: (1) Pattern II is a

square with black border; (2) Four vertexes of it are used as feature points; (3) Nine small blocks are set

inside the border with three columns and three rows and their colors can be white or black, which represents

1 or 0. Samplings at each block from top left corner to bottom right corner make up a binary sequence that is

the ID of the pattern. In order to make the feature points distinguishable, each reference pattern must have

four different IDs in four directions. For example, the ID sequence of the first pattern in Fig. 3 is

“011111111”. After a clockwise rotation of 90, 180 and 270 degrees, the ID sequences are “110111111”,

“111111110” and “111111011”. So the four vertexes of it are distinguishable. However, the fifth pattern and

the sixth pattern are indistinguishable because the ID sequences are the same “011111110”. So these kinds of

patterns should be avoided.

3. Algorithm Design

Fig. 4: System initialization and pose estimation software pipeline.

27

Page 4: Relative Pose Estimation for the Femoral Component in Computer ... · The first kind of pattern is designed as a circular ring, as shown in Fig. 3, which is used as a landmark to

The algorithm contains two major parts. The first part is system initialization and the second part is pose

estimation. The software pipeline is shown in Fig. 4. An initial image is captured and analyzed in system

initialization stage. To estimate the pose, system captures a current image and matches the feature points of it

with the initial image to establish point correspondences. Then fundamental matrix between these two views

is estimated and the pose matrix is recovered from the fundamental matrix.

3.1. System Initialization

Please acknowledge collaborators or anyone who has helped with the paper at the end of the text. Two

problems are solved in the initialization process. The first one is to adjust the femoral head to the preset pose

and the second problem is to initialize the coordination system by the image taken at the preset pose.

When femoral head is inside the acetabular cup, pattern I is in the visual range of the camera. If the

camera’s axis is not perpendicular to the circular ring’s plane and the projection of it is an elliptical ring as

shown in left picture of Fig. 5. When the femoral head is adjusted to the preset position where the camera’s

axis is perpendicular to the circular ring’s plane and the distance between the center of camera and the center

of the ring is exactly (a preset value), a pink circle will appear as shown in right picture of Fig. 5. The pink

circle means that the femoral head is at the preset position inside the acetabular cup and then the motion of

femur could be tracked from that initial position.

Fig. 5: A random pose of the camera and the ellipse in the center (left); the preset pose of the camera and the pink circle

projection of the circle (right).

At the preset pose, an initial image of the reference patterns is captured by image sensors and then is

analyzed to pick out every single reference pattern, as shown in Fig. 6. To search and identify the patterns,

the image is processed in the following steps: (1). Convert the RGB image to gray scale image. (2). Conduct

the adaptive threshold processing to the image. (3). Find the contour in the image. (4). Conduct polygonal

approximation. (5). Pick out the quadrilateral and eliminate the error.

Fig. 6: The analysis of the initial image.

28

Page 5: Relative Pose Estimation for the Femoral Component in Computer ... · The first kind of pattern is designed as a circular ring, as shown in Fig. 3, which is used as a landmark to

After picking out the reference patterns in the image, samples are taken at nine points in each reference

pattern to determine nine small blocks’ colors. White represents “1” and black represents “0”. After sampling,

the 9-bit binary sequence is converted to a decimal number that is the ID of the reference pattern. Then the

information of the patterns is stored for further use.

3.2. Pose Estimation

After initialization, the system starts tracking the motion of the femoral head. Suppose we capture an

image at current pose, the following algorithms are used to estimate the pose of the camera, which is also the

pose of the femoral head.

A. Searching and matching feature points

An image of the liner’s internal surface contains reference patterns and is analyzed in the same steps as

shown in the former section. The feature points in the current image are matched with those in the initial

image as shown in Fig. 7. As we can see, the vertexes of the same reference pattern are matched together and

there is no outlier.

Fig. 7: Match feature points between initial image (left) and current image (right).

3.2.1. Estimating fundamental matrix

To estimate the fundamental matrix, a method similar to [14] is used in the computer-assisted system.

Suppose that there is a point correspondence x '« x between two images, one point is x = (u,v,1)T in the

initial image, the other point is x ' = (u ',v ',1)T in the current image, then the fundamental matrix is defined

by the equation

x 'T Fx = 0 (1)

From a set of n point matches, a set of linear equation can be obtained

1 1 1 1 1 1 1 1 1 1 1 1' ' ' ' ' ' 1

: : : : : : : : : 0

' ' ' ' ' ' 1n n n n n n n n n n n n

u u u v u v u v v v u v

Af f

u u u v u u v u v v u v

(2)

11 12 13 21 22 23 31 32 33

Tf f f f f f f f f f (3)

where A is a 9n matrix. Given at least 8 pairs of matches, which means at least 2 reference patterns should

be found in the image, equation (2) could be used to calculate the fundamental matrix F.

3.2.2. Recovering pose matrix

If the camera calibration matrices K andK ' are known, the essential matrix can be defined as

' [ ]TE K FK T R (4)

29

Page 6: Relative Pose Estimation for the Femoral Component in Computer ... · The first kind of pattern is designed as a circular ring, as shown in Fig. 3, which is used as a landmark to

which could be decomposed into a skew-symmetric matrix corresponding to translation and a orthonormal

matrix corresponding to rotation between the two views. On the other hand, the single value decomposition

of the essential matrix is TE U V (5)

where 1 2 3( , , )diag and the matrices U and V are orthonormal. According to equation (4) and

equation (5), there are four possible camera pose matrices relative to the initial camera pose.

P ' = R ' | t '[ ] = [UWVT | +u3] or [UWV T | -u3] or [UW TV T | +u3] or [UW TV T | -u3] (6)

where

0 1 0

1 0 0

0 0 1

W

(7)

The correct pose matrix can be distinguished by ensuring that the reconstructed points lie in front of the

camera. After confirming the correct relative pose matrix, the absolute pose matrix can be calculated by

P = P 'P0 (8)

where P0 is the initial camera matrix. As shown in Fig. 8, the green tetrahedron represents the initial pose of

the camera and the blue one represents the current pose of the camera.

Fig. 8: The initial pose and the current pose of the camera.

4. Experiment Result Analysis

An experimental platform as shown in Fig. 9 was set up to simulate the relative movement between

femoral head and acetabular cup. The camera is fixed to a handle that can rotate around x-axis and z-axis and

it faces the acetabular cup that has reference patterns on its internal surface. The camera and the handle are a

test model of the femoral component and their rotations simulate the motion between femoral head and

acetabular cup. The images are transmitted to computer through USB and then the relative rotation matrix R

and the relative translation vector T of the camera are calculated by the algorithm on computer.

The true camera rotation and translation are measured using the scales on the experimental

platform and the relative error of the estimated rotation R is computed the by

(%)ture

rot

R RE

R

(9)

where and R are the normalized rotation matrices. Similarly, the relative error of the estimated

translation T is determined by

(%)ture

trans

T TE

T

(10)

30

Page 7: Relative Pose Estimation for the Femoral Component in Computer ... · The first kind of pattern is designed as a circular ring, as shown in Fig. 3, which is used as a landmark to

The relative error of rotation and translation by rotating the femur about x-axis from -35 degrees to 35

degrees and about z-axis from 0 degree to 170 degrees is illustrated in Fig. 10 and Fig. 11 respectively.

Fig. 9: The experimental platform.

Fig. 10: Relative error of rotation and translation by rotating the femur about x-axis from -35 degrees to 35 degrees.

Fig. 11: Relative error of rotation and translation by rotating the femur about z-axis from 0 degree to 170 degrees.

The experimental results show that the relative error of rotation is less than 6% and the actual relative

error of translation is less than 9%, which is more accurate and robust than the PnP-based algorithm in [12].

In addition, the pose estimation algorithm does not rely on the 3D coordinate of feature points which means

that the printing error introduced in the production process would not influence the accuracy of pose

estimation.

5. Conclusion

31

Page 8: Relative Pose Estimation for the Femoral Component in Computer ... · The first kind of pattern is designed as a circular ring, as shown in Fig. 3, which is used as a landmark to

This paper presents a method based on feature points between image pairs to estimate relative position

between the femoral and acetabular component. A miniature camera is placed inside the femoral prosthesis

trial and two kinds of reference patterns are designed and printed on the internal surface of the acetabular

prosthesis trial liner. The system acquires an image of at the preset pose and analyzes the reference patterns

to initialize the system. Images captured in the running stage are compared with the initial image to establish

matches of feature points. In the next step, the pose matrix is recovered from the fundamental matrix that is

calculated by matches of feature points. Finally, the relative pose of the acetabular cup and femoral head is

displayed in 3D graphics in vivo, which is very helpful for surgeons to make decision of the position of the

prosthesis during the surgery. The method proposed in this paper does not need any extra landmarks and

does not rely on accurate 3D positions of the feature points. The experimental results show that the relative

error of rotation is less than 6% and the actual relative error of translation is less than 9%, which is more

accurate and robust than the PnP-based algorithm. In future, inertial sensors will also be set inside the

femoral head to improve the accuracy of the estimation and clinic experiments will be carried on.

6. References

[1] Woolson, S. T.., Rahimtoola, Z. O., “Risk factors for dislocation during the first 3 months after primary total hip

replacement,” J. Arthroplasty 14(6), 662–668, Elsevier (1999).

[2] Blom, A. W., Rogers, M., Taylor, A. H., Pattison, G., Whitehouse, S.., Bannister, G. C., “Dislocation following

total hip replacement: the Avon Orthopaedic Centre experience.,” Ann. R. Coll. Surg. Engl. 90(8), 658–662 (2008).

[3] Jenkins, P. J., Duckworth, A. D., Robertson, F. P. C., Howie, C. R.., Huntley, J. S., “Profiles of biomarkers of

excess alcohol consumption in patients undergoing total hip replacement: correlation with function.,”

ScientificWorldJournal. 11, 1804–1811 (2011).

[4] Callaghan, J. J., Heithoff, B. E., Goetz, D. D., Sullivan, P. M., Pedersen, D. R.., Johnston, R. C., “Prevention of

dislocation after hip arthroplasty: lessons from long-term followup.,” Clin. Orthop. Relat. Res.(393), 157–162

(2001).

[5] De Haan, R., Campbell, P. A., Su, E. P.., De Smet, K. A., “Revision of metal-on-metal resurfacing arthroplasty of

the hip: the influence of malpositioning of the components.,” J. Bone Joint Surg. Br. 90(9), 1158–1163 (2008).

[6] Biedermann, R., Tonin, A., Krismer, M., Rachbauer, F., Eibl, G.., Stöckl, B., “Reducing the risk of dislocation

after total hip arthroplasty: the effect of orientation of the acetabular component.,” J. Bone Joint Surg. Br. 87(6),

762–769 (2005).

[7] McCollum, D. E.., Gray, W. J., “Dislocation after total hip arthroplasty. Causes and prevention.,” Clin. Orthop.

Relat. Res.(261), 159–170 (1990).

[8] Saxler, G., Marx, A., Vandevelde, D., Langlotz, U., Tannast, M., Wiese, M., Michaelis, U.,Kemper, G., Grützner,

P. A., and Steffen, R., "The accuracy of free-hand cup positioning-a CT based measurement of cup placement in

105 total hip arthroplasties," International orthopaedics, vol. 28, pp. 198-201, (2004).

[9] Parvizi, J., Picinic, E.., Sharkey, P. F., “Revision total hip arthroplasty for instability: surgical techniques and

principles.,” Instr. Course Lect. 58, 183–191 (2009).

[10] Kalteis, T., Handel, M., Bäthis, H., Perlick, L., Tingart, M., and Grifka, J., "Imageless navigation for insertion of

the acetabular component in total hip arthroplasty IS IT AS ACCURATE AS CT-BASED NAVIGATION?"

Journal of Bone & Joint Surgery, British Volume, vol. 88, pp. 163-167, (2006).

[11] Kiefer, H. and Othman, A., "OrthoPilot total hip arthroplasty workflow and surgery," Orthopedics, vol. 28, p.

S1221, (2005).

[12] Gao, J., Su, S.,Chen, H., Jiang, H., Zhang, C., Wang, Z., " Estimation of the Relative Pose of the Femoral and

Acetabular Components in a Visual Aided System for Total Hip Replacement Surgeries " NEWCAS (2014).

[13] Lepetit, V., Moreno-Noguer, F.., Fua, P., “EPnP: An Accurate O(n) Solution to the PnP Problem,” Int. J. Comput.

Vis. 81(2), 155–166 (2008).

[14] Hartley ,R. and Zisserman A., "Multiple view geometry in computer vision" vol. 2: Cambridge Univ Press, 153-

158, (2000).

32


Recommended