Object reconstruction algorithm

To achieve that, an object reconstruction algorithm detects connected components (blobs) in the binary images of each material class. In a first step, blobs that do not meet pre-defined size restrictions are considered as classification errors and filtered out (e.g. the black line due to a faulty camera pixel in object D). The binary image of each material class (material and overlay) is then morphologically dilated... 

Fig. 8. Reconstruction of Young s modulus map in a simulated object. A 3D breast phantom was first designed in silico from MR anatomical images. Then a given 3D Young s modulus distribution was supposed with a 1 cm diameter stiff inclusion of 200 kPa (A). The forward problem was the computing of the 3D-displacement field using the partial differential equation [Eq. (5)]. The efficiency of the 3D reconstruction (inverse problem) of the mechanical properties from the 3D strain data corrupted with 15% added noise can be assessed in (B). The stiff inclusion is detected by the reconstruction algorithm, but its calculated Young s modulus is about 130 kPa instead of 200 kPa. From Ref. 44, reprinted by permission of Wiley-Liss, Inc., a subsidiary of John Wiley Sons, Inc.

For the second case, a hollow ball was dipped inside a jar filled with water and scanned. The diameters of the ball and jar were 6.98 and 18.95 cm, respectively, as shown in Fig. 5a. A scan area of 27 cm in diameter was reproduced using the reconstruction algorithm. The dimensions of the objects as reproduced by the scan were 6.97 and 19.20 cm, respectively, as shown in Fig. 5b, which give a maximum spatial error of about 2.5 mm. This is good enough to resolve relatively small maldistribution, if it exists, inside the 30.48-cm-diameter column used in this study. The figure shows that the overall error in the estimated total holdup is within 12.8%. 

Function indicating the signal contribution of an infinitesimal object to each position along the z axis. SSP is determined by section collimation, size of the focal spot, and the spiral reconstruction algorithm. 

The aim of ECT, therefore, is to reeonstruct the distribution of dielectric permittivity e(x,y), which corresponds to gas-solids distribution, from the capacitance measurements. It is worth pointing out, however, that the equation (2) is non-linear as it couples the dielectric permittivity distribution with the potential field, which results from that distribution. In simple terms, a change of permittivity in one place affects the electric field in the whole domain. This is unlike the nucleonic transmission tomography, where the introduction of a small object in the domain (see Figure 5) affects only the detectors in the objects shadow . This property of electrical field makes the reconstruction algorithms a much more challenging task than those... 

The main disadvantage of the presented method is the fact that the results of the reconstruction depend, for certain shapes, from the orientation of the chosen coordinate system. Fig. 8 depicts this fact. A thin circular plate is registered in two different coordinate systems. System A is the one used in the presented results. From all three directions the projections of the analyzed object are of elliptic shape. Therefore the reconstruction algorithm produces an ellipsoid as the three dimensional reconstruction. In example B, the same object is viewed in a special coordinate system adapted to the shape. In consequence, the reconstructed structure corresponds much better to the original. 

Using the theorem that the sufficiency condition for mathematical correctness in 3D-reconstruction is fulfilled if all planes intersecting the object have to intersect the source-trajectory at least in one point [8], it is possible to generalise Feldkamp s method. Using projection data measured after changing the sotuce-trajectory from circular to spiral focus orbit it is possible to reconstruct the sample volume in a better way with the Wang algorithm [9]. 

Another efficient and practical method for exact 3D-reconstruction is the Grangeat algorithm [11]. First the derivative of the three-dimensional Radon transfomi is computed from the Cone-Beam projections. Afterwards the 3D-Object is reconstructed from the derivative of the Radon transform. At present time this method is not available for spiral orbits, instead two perpendicular circular trajectories are suitable to meet the above sufficiency condition. 

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