3D X-RAY TOMOGRAPHY
GEOMETRIC CALIBRATION

In short

This project was my final year internship at Thales Electron Devices. I was responsible of the whole development of a calibration module for 3D X-Ray tomography platform. The challenge was to have to most efficient and accurate calibration, to be able to have the best possible results for 3D recontruction. This was a complex and complete project as I had to do many different things, such as:

  • Mathematical Modeling, Linear Algebra and Spatial geometry
  • Computer Vision and Image Processing
  • Numerical Optimisation
  • Software R&D and parallel programming

Technologies used: C++, Boost Library, OpenCV, Qt, OpenMP, SVN.

THE PROJECT

My internship was part of the Voxelo Project (in partnership with ANR and CEA List) whose goal is to reconstruct a knee in 3D from XRay images in order to diagnose early osteoarthritis lowering XRay dose and cost.

X-Ray Arthrose Image

3D X-RAY TOMOGRAPHY

Cone Beam Computed Tomography (CBCT) is a medical imaging technique consisting of reconstructing an object in 3D from a set of X-Ray images taken at different angles of view. The aim is to analyse precisely with a computer the 3D object (volume, or the mesh) and to be able to "see details inside it".

CBCT Illustration

GEOMETRIC CALIBRATION

The calibration is a very important step in the process because it determines the accuracy of the 3D reconstruction. Calibrate the system means find for each angle of view what is linking the 3D world of the scene to the 2D world of the image. This "link" can be seen as a geometric transformation called a projection. As I chose to modelize the system as a pinhole camera model, this transformation is fully represented by the projection matrix.

Pinhole model Illustration

The Pinhole Model

The pinhole camera model reprents how a point of the 3D space is projected to a 2D plan to form an image. There are 3 coordinates systems in the model: Rw (for the 3D world), Rc (for the camera) and Rim (for the 2D image plan).

The projection matrix is the 3x4 matrix M that links Rw to Rim:

Projection equation

M can be decomposed into 3 successives geometric transformations:

Decomposition of M

It is then a 3x4 matrix depending on 10 parameters:

The 10 parameters of M

To calibrate a pinhole model, we must find either the 12 coefficients of the 3x4 matrix (implicit calibration) or the 10 parameters (explicit calibration) of its decomposition. To do so, we take an image of a target in which we know the exact position of a set of points, we detect those points in the image and solve an equation with numerical methods.

I can't give more details about the process, but the calibration module that I developped, reached an accuracy far better than expected at the beginnning of the internship.

RESULTS

Reconstruction results on a Knee

Example of a high resolution 3D reconstruction of a knee.
The accuracy of my calibration module allows the reconstruction algorithm to be accurate enough to see internal structures of bones thanks to far better reprojection errors for every matrices.

About Thales

Thales Group is a French multinational company that designs and builds electrical systems and provides services for the aerospace, defence, transportation and security markets. The group employs around 70 000 persons all around the world and has a revenue of more than 14 billion € (2014).

I worked in the Microwave and Imaging Subsystems (MIS) division. Its products are at the heart of today's most complex high-tech systems and are used to generate and amplify Radio Frequencies and microwave power sources. These products are found in satellites, radars, missile seekers, particle accelerators, but also in most of the equipment for radiological imaging.

© 2020 Copyright: Pierre BARET