geometrical calibration of bi-planar radiography of the ... · geometrical calibration of bi-planar...

INE

B -

In

sti

tuto

de

En

ge

nh

ari

a

Bio

mé

dic

aGeometrical calibration of bi-planar

radiography of the spinefor common imaging systems

Daniel Moura, Jorge Barbosa, Joao Tavares, Ana Reis

INEB – Instituto de Engenharia Biomedica, Laboratorio de Sinal e ImagemFEUP – Faculdade de Engenharia da Universidade do PortoSMIC – Servico Medico de Imagem Computorizada, S. A

[email protected]

Introduction

Computer Tomography (CT) is the gold standardfor 3D reconstructions and accurate measurementsof bone structures.

However, not adequate for large bone structures(high radiation)

Alternative: using Plain Radiography (2D)Requires 2+ radiographs from different views.Accomplished for: spine, pelvis, distal and proximalfemur.

( INEB – FEUP – SMIC ) Calibration of bi-planar radiography Enc. Ciencias Jun/08 2 / 22

Introduction: Geometrical calibration

For mapping 2D → 3D coordinates the imagingsystem must be calibrated on every examination.

Calibration of the spine is usually performed usinglarge calibration apparatus.Attempts have been made for using smallercalibration objects, but:

reconstruction errors are highercalibration objects overlap bone structures


Introduction: Goal

GoalAchieving accurate calibrations, while

making the method easy to implement in commonclinics

minimising the impact of calibration objects


Radiography calibration

Projection of a 3D point into a radiograph:w ·uw ·vw

= M ·

XYZ1



Projection of a 3D point: bi-planar radiographywi ·ui

wi ·vi

wi

= Mi ·

XYZ1

for i = 1, 2



Calibration Matrix (for flat detectors)

Mi =

fi/s 0 upi0

0 fi/s vpi0

0 0 1 0

· [Ri ti0T 1

]

f - focal length

(up, vp) - principal point

R, t - geometricaltransformation




Mi =

fi/s 0 upi0

0 fi/s vpi0

0 0 1 0

· [Ri ti0T 1

]

f - focal length



f

X-ray device

X-ray source

Table

Detector( INEB – FEUP – SMIC ) Calibration of bi-planar radiography Enc. Ciencias Jun/08 7 / 22



Mi =

fi/s 0 upi0

0 fi/s vpi0

0 0 1 0

· [Ri ti0T 1

]

f - focal length



f

X-ray device

X-ray source

Table

Detector

(up,vp)




Mi =

fi/s 0 upi0

0 fi/s vpi0

0 0 1 0

· [Ri ti0T 1

]

f - focal length



t

X-ray device

X-ray source

Table

Detector

R




Mi =

fi/s 0 upi0

0 fi/s vpi0

0 0 1 0

· [Ri ti0T 1

]

f - focal length



Calibration GoalFinding the values forthese parameters forboth views.


Determining the parameters values

1 Inputs:Initial solution for the parametersA set of point matches

2 Optimisation process (NLSQ):1 Triangulate point matches → 3D points2 Project 3D points → projected 2D points3 Minimise residuals between the original and the projected

points





points

�(�TSMRX�SRMQEKI��

�(�TSMRX�SRMQEKI��

�(�TSMRX

4VSNIGXIH�(�TSMRX

4VSNIGXIH�(�TSMRX

QMRMQMWI�HMÙIVIRGI

QMRMQMWI�HMÙIVIRGI( INEB – FEUP – SMIC ) Calibration of bi-planar radiography Enc. Ciencias Jun/08 8 / 22




points

ProblemOptimisation gets easily trapped in local minima.





points

SolutionGood inputs :-)


Initial solution for spine radiographs

R1 =

[0◦ 0◦ 0◦

]t1 =

[0 0 ?

](up1 , vp1) = size(img1)/2f1 =?

R2 =[0◦ 90◦ 0◦

]t2 =

[0 0 ?

](up2 , vp2) = size(img2)/2f2 =?


Determining missing parameters

For narrowing the search space of solutions wepropose using a distance measuring device.

X-Ray imaging system




X-ray device

X-ray source

Table

Detector

X-Ray imaging systemrepresentation




f

X-ray device

X-ray source

Table

Detector

f – Focal distance

Distance between thex-ray source and thedetector

Can’t be measureddirectly




t z

X-ray device

X-ray source

Table

Detector

tz – Z translation

Distance between thex-ray source and theobject

Can’t be measureddirectly




fd m

X-ray device

X-ray source

Table

Detector

Distance measurer A distance measurer mayonly read dm




f

d sd d

d m

X-ray device

X-ray source

Table

Detector

Distance measurer We implemented aprocedure for determining ds

and dd , which are constantfor a given system.




f

d sd d

d m

X-ray device

X-ray source

Table

Detector

Distance measurer Knowing ds and dd enablesto determine f accuratelywith a distance measurer...




t z

d sd m

X-ray device

X-ray source

Table

Detector

Distance measurer ... and to have an initialguess of tz .


Correcting scale

Even with this extension, this method is only able tocalculate up to scale solutions.

A reference distance (visible in both x-rays) isneeded to determine the scaling factor.

We propose using a simple calibration object (C.O.),which may be a bar of 8-12cm attached to patientsbacks.

scaling factor =known reference distance

reconstructed distance


Experiments

Currently, the main experiments are:Validation with a phantom object:

Validation in real environmentAccurate results in the presence of noiseTo appear in: CARS’08 (poster)

Simulation study with humanspines:

Validation in simulated environmentData extracted from CT scansUndergoing experiments show promisingresults


Experiments: Simulation using CT scan

Resolution:0.4× 0.4× 0.5mm3/voxel

Volume:205× 205× 517mm3



DRR - AP projection DRR - Lateral projection



3D landmarks: 6 per vertebra

DRR - AP projection DRR - Lateral projection


Simulation Process


Evaluation

3D reconstruction error (after aligning)

Spinal Length (SL)

Vertebral Body Height (VBH)


First Experiment

Does the position of the C.O. affects results?If so, can we tell where to place the C.O. for bestresults?


First Experiment: Conclusions

Effects of the C.O. positionMean 3D errors: negligibleMean VBH: negligibleSL: highly dependable

Experimentally, we determined that the best C.O.position (left vs. right) depends of two factors:

1 Patient rotation2 C.O. position: anterior vs. posterior


Second Experiment

Experiment goal: simulating a real scenarioConditions:

Noise: Gaussian, typical range of values1

C.O.: placed only in good positions

Results (mm):

VBH SL

In Vivo1

3D

In Vitro2

RMS 0.9 1.4 1.8Mean 0.9 0.9

2.1

1.8

2.1

StD 0.2 1.2

1.0

0.4

1.5

1Kadoury et al. (2007). Med. Bio. Eng. Comp., 45(6):591–602.2Aubin et al. (1997). Med. Bio. Eng. Comp., 35(6):611–618.


Second Experiment




Results (mm):

VBH SL In Vivo1 3D

In Vitro2

RMS 0.9 1.4 1.8Mean 0.9 0.9 2.1 1.8

2.1

StD 0.2 1.2 1.0 0.4

1.5

1Kadoury et al. (2007). Med. Bio. Eng. Comp., 45(6):591–602.

2Aubin et al. (1997). Med. Bio. Eng. Comp., 35(6):611–618.


Second Experiment




Results (mm):

VBH SL In Vivo1 3D In Vitro2

RMS 0.9 1.4 1.8Mean 0.9 0.9 2.1 1.8 2.1StD 0.2 1.2 1.0 0.4 1.5

1Kadoury et al. (2007). Med. Bio. Eng. Comp., 45(6):591–602.2Aubin et al. (1997). Med. Bio. Eng. Comp., 35(6):611–618.( INEB – FEUP – SMIC ) Calibration of bi-planar radiography Enc. Ciencias Jun/08 19 / 22

Conclusions

Simulations show that the method has comparableaccuracy with other methods

... still, in vivo or in vitro validation should be performed.

Advantageous:C.O. does not need to overlap the spineC.O. is easy to buildCompensates patient movement between acquisitionsLow budget

Main Disadvantageous:Requires several points to be handmarkedNeeds an initial calibration procedureInstallation of a measuring device


Future work

1 Simulations with more CT scans (VHP)2 Designing and prototyping the Calibration Object3 In vitro experiment with a dried human spine4 Experiments using 2 calibration objects

5 Semi-automatic detection of landmarks


INE

B -

In

sti

tuto

de

En

ge

nh

ari

a

Bio

mé

dic

a

Thank You!

Daniel Moura, Jorge Barbosa, Joao Tavares, Ana Reis

INEB – Instituto de Engenharia Biomedica, Laboratorio de Sinal e ImagemFEUP – Faculdade de Engenharia da Universidade do PortoSMIC – Servico Medico de Imagem Computorizada, S. A

[email protected]

geometrical calibration of bi-planar radiography of the ... · geometrical calibration of bi-planar...

Documents