3D reconstruction from projection matrices in a C-arm based 3D-angiography system

Abstract

3D reconstruction of arterial vessels from planar radiographs obtained at several angles around the object has gained increasing interest. The motivating application has been interventional angiography. In order to obtain a three-dimensional reconstruction from a C-arm mounted X-Ray Image Intensifier (XRII) traditionally the trajectory of the source and the detector system is characterized and the pixel size is estimated. The main use of the imaging geometry characterization is to provide a correct 3D-2D mapping between the 3D voxels to be reconstructed and the 2D pixels on the radiographic images. We propose using projection matrices directly in a voxel driven backprojection for the reconstruction as opposed to that of computing all the geometrical parameters, including the imaging parameters. We discuss the simplicity of the entire calibration-reconstruction process, and the fact that it makes the computation of the pixel size, source to detector distance, and other explicit imaging parameters unnecessary. A usual step in the reconstruction is sinogram weighting, in which the projections containing corresponding data from opposing directions have to be weighted before they are filtered and backprojected into the object space. The rotation angle of the C-arm is used in the sinogram weighting. This means that the C-arm motion parameters must be computed from projection matrices. The numerical instability associated with the decomposition of the projection matrices into intrinsic and extrinsic parameters is discussed in the context. The paper then describes our method of computing motion parameters without matrix decomposition. Examples of the calibration results and the associated volume reconstruction are also shown.

Tomographic Reconstruction for Truncated Cone Beam Data Using Prior CT Information

“…While the filtering steps were implemented using fast Fourier space methods using FFT, back-projection steps were efficiently implemented by using projection matrices that intrinsically describe the projection geometry [8], [9] and [10]. 4.…”

Camera-Augmented Mobile C-arm (CAMC) Application: 3D Reconstruction Using a Low-Cost Mobile C-arm

“…Direct motion estimation from consecutive projection matrices as shown in [7] is more precise than motion estimation by decomposing these projection matrices and computing the extrinsic parameters for each frame. We therefore propose a scenario in which we do not need to compute the intrinsic parameters of either our X-ray imaging system or the optical one.…”

“…On-line calibration: For each frame, the motion of the X-ray source relative to its position in the off-line calibration step is computed using optical cameras. This is done by computing the projection matrix for optical camera and estimating the motion without ever computing its intrinsic parameters: ([R, t] = f (P c , P c )), see [7] for more details on direct motion estimation. We then apply this motion to the reference X-ray projection matrix P x , resulting in X-ray projection matrixP x = P x · R t 0 T 1 .…”

“…We use the Xray phantom and calibration process used in [7]. X-ray phantoms interfere with the patient's X-ray image and cannot be used for mobile C-arm systems in real application.…”

“…1 In order to obtain the three-dimensional reconstruction the position of the C-arm mounted X-ray source and detector relative to the patient has to be measured. If the C-arm geometry is reproducible, the geometrical calibration can be done off-line using X-ray phantoms [9,2,7] and the pose information can be used for the patient examination. However mobile C-arm systems do not guarantee reproducible motion for consecutive examinations.…”