Rajesh et al. : Proceedings of the National Seminar & Exhibition on Non-Destructive Evaluation DEVELOPMENT OF CONE BEAM TOMOGRAPHIC RECONSTRUCTION SOFTWARE MODULE Rajesh V Acharya, Umesh Kumar, Gursharan Singh Industrial Tomography and Instrumentation Section Isotope Applications Division (IAD), Bhabha Atomic Research Centre (BARC), Mumbai 400 085 ABSTRACT. Cone beam tomography is analogous to the well established fan beam tomography also known as 2D tomography. In it the divergent beam of x-rays coming from the target material which is in the form of a cone, hence the name, is allowed to pass through a specimen and the transmitted radiations are collected on a detector which is generally a flat panel detector. The projection data obtained on the detector is essentially the direct digital radiograph of the specimen. Many such radiographs are acquired in various angular positions of the specimen either by rotating the specimen or the source and detector assembly as the case may be. This data is later processed/filtered and back-projected at various vertical planes to generate multiple slices of cross-sectional attenuation coefficient distributions. The 3D version of tomography therefore saves on the acquisition time without compromising on the reconstruction quality since it follows the accurate analytical method of reconstruction. To make a 3D solid model of a specimen one can use these multiple slices which otherwise in case of 2D tomography will have to be separately acquired and reconstructed. However even then it would be impossible to cover the entire specimen continuously because of the finite size of the detector and therefore simple stacking doesn t help but needs further processing (like overlapping of images and de-convolution etc). This consumes lot of time. This paper describes the software developed for reconstructing tomographic images using multiple digital radiographs of a specimen. An amorphous-si based Flat Panel Detector (FPD) with pixel size 125 micron and 14bit ADC, 420kV X-ray generating machine have been used. The software module named DRIShTI (Software for Digital Radiography based Tomography Imaging) reconstructs the desired number of slices using the classical filtered back-projection algorithm. Keywords: Cone Beam Tomography, Transmission Tomography, 3D Tomographic Reconstruction, Digital Radiography PACS: 81.70.Tx, 87.57.Q INTRODUCTION The main advantage in cone beam tomography is the reduction in the data acquisition time. With a point source the ray integrals are measured through every point in the object in the time it takes to measure a single slice in a conventional 2d scanner [1]. However, the cone beam geometry is much more complex than the parallel beam geometry as far as reconstruction is concerned. As in case of 2d reconstruction the slices along the z-direction can no longer be treated independently because a single ray traverses different slices. An additional problem is the fact that the intensity of the beam drops as it expands along a given direction. All this makes cone beam reconstruction more complicated, more memory demanding and slower to reconstruct. The most efficient cone-beam reconstruction algorithm is that of Feldkamp et al.[5] known as the filtered back projection (FBP) algorithm and the same has been used in the current implementation. Part of the implementation of the cone beam reconstruction code is analogous to the 2D FBP, in that the backprojection which happens to be computationally most expensive part is common and the difference is in the geometrical rebinning of the input data or the direct digital radiograph in this case, into equivalent parallel beam data and the formulation of
NDE 2011, December 8-10, 2011 FIGURE 1 Schematic block diagram and coordinate system details of Cone Beam Geometry appropriate filter function. The reconstruction code presented here is based on the detailed mathematical analysis given in [1]. In terms of speed and accuracy, Filtered Backprojection is preferred more than other methods of reconstruction, especially algebraic, and may produce better spatial and contrast resolution. Another reason is that this reconstruction technique is more practical and straightforward to implement. The common weakness of the reconstruction algorithms is that the projection data are implicitly assumed to be noise-free (theoretically, the function is reconstructed from projections that contain no noise). However, in practice, one needs to take into account the noise of the detector, the sampling errors, etc. It also introduces artifacts in the image. Figure 1 shows the Cone Beam Computed Tomography (CBCT) setup in block diagram form and also describes the co-ordinate geometry with projections of a point on different planes. In case of CBCT it is necessary to ensure that the object is completely covered in all the FIGURE 2 Block diagram and photographic view of Digital Radiography and Computed Tomography (DR&CT) Lab at IAD, BARC.
Rajesh et al. : Proceedings of the National Seminar & Exhibition on Non-Destructive Evaluation radiographs for accurate reconstruction. FIGURE 3 GUI of CBCT reconstruction software DRIShTI METHOD In our laboratory, a dedicated imaging system has been developed which makes use of a variable energy 420 kv (max) X-ray generating device, a high-resolution (127µm 2 ) amorphous-silicon flat panel detector array and a multi-axis mechanical manipulator system. Figure 2 shows the actual set-up inside a shielded enclosure incorporating 2D FPD, a six axis manipulator and the 420 kv X-ray tube head. The system can operate in specified DIR geometry and volume tomography mode within its technical capabilities. The cone beam tomography makes use of standard reconstruction routines and there are software packages available for 3D data processing and management. A computer program in Visual Basic (.NET) using the.dll functions of FPD and mechanical manipulator is built to trigger these hardware in a predefined sequence. The series of Direct Digital Radiographs (DDR) thus generated are stored in a directory in tiff form. These images are later fed to the reconstruction software, DRIShTI, for CBCT reconstruction. The implementation of the cone beam algorithm is based on the following broad mathematical equations [1]. The basic law of radiation attenuation is Where, -Intensity of Incident radiation; - Intensity of transmitted radiations; -Absorber length; µ- Linear attenuation coefficient. The, and in our case are obtained by taking series of DDRs without and with specimen respectively as described above. To reduce the computation time the images may be cropped, using a built in routine, since in most of the cases only a part of the full image is occupied by the object. The beam is then normalized w.r.t space for compensating the intensity fluctuations in different areas of the cone beam owing to its shape using a predefined background image and if required normalization w.r.t time to compensate for beam energy fluctuations during the course of the experiment can also be carried by selecting a region in the radiograph which is never obstructed by the sample. The data after this pre-processing can be arranged in the form of sinogram. A sinogram is nothing but data rearranged in such a way that each image now shows a particular slice from 0 to 360 0 stacked vertically. The total number of slices desired to be reconstructed on either sides of the center line can be declared on the GUI. The images are first rebinned to equivalent parallel beam images, then filtered and finally back-projected. Bilinear interpolations are used where necessary. The aforesaid three principal steps can be explained mathematically as follows
NDE 2011, December 8-10, 2011 Step 1: FIGURE 4 Tomographic reconstruction of an object shown in photograph at (a) with its direct digital radiograph at (b) and results of the tomographic reconstruction at various randomly chosen sections at (c) Where is the projection data, is the source to object distance, ξ is elevation of the slice, is the abscissa of the point. Step 2: Convolve the weighted projection with. This convolution is done independently for each elevation. The result is written as:, Where, ω is indicating signal frequency and is the sampling range. Step 3: Finally each weighted projection is backprojected over the three dimensional reconstruction grid: is the abscissa and is the ordinate of the CBCT image. The two arguments of the weighted projection,, represent the transformation of a point in the object into the coordinate system. EVALUATION The program when run on a 2.13 GHz, Intel core 2 duo processor with 2 GB RAM, takes about 35 seconds per slice of size 300 x 300. The timings mentioned here is just a rough indication and the actual time was variable depending on the position of the slice being reconstructed and geometry of cone beam. The major computation time is consumed by the backprojection process. The rebinning and convolution indicated in step1 and step 2 respectively are comparatively less demanding in that respect. Once the multiple tomographic images are available (figure 4) then using standard image processing modules the three dimensional iso-.
Rajesh et al. : Proceedings of the National Seminar & Exhibition on Non-Destructive Evaluation FIGURE 5 Three dimensional data in different forms built using cone beam CT images surface solids can be constructed and other information from different types of cross-sections can be easily extracted as shown in figure 5. RESULTS AND DISCUSSIONS It is observed from the resulting CT images not presented here that there are some artifacts like beam hardening and ring artifacts. The CT images, as seen from their 3D reconstructions, also have some noise. These and other such sources of errors and artifacts coming from dead pixels, bad pixels from the data acquisition system etc are under study and will be incorporated in future versions. It is also proposed to use hardware networking and parallel processing power for reducing overall reconstruction time. There are different graphic processing units (GPU) available which can also be used for reducing the overall reconstruction time. CONCLUSION DRIShTI can evolve as a effective cone beam tomography reconstruction tool for troubleshooting and research purpose. It can definitely be improved further in its future versions to add functionalities like parallel processing, error and artifact correction and other image post processing operations. Other beam geometries like equiangular fan beam, parallel beam, spiral or helical beam reconstructions can be added to make it a comprehensive package. ACKNOWLEDGEMENT REFERENCES 1. A. C. Kak and M. Slaney. Principles of Computerized Tomographic Imaging. IEEE Press, 1988. 2. Bruce D. Smith, Optical Engineering 29(5). 524-534 (May 1990).
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