“CONTOUR” Algorithm for Finding and Visualizing Flat Sections of 3D-Objects

Algebraic Reconstruction and Post-Processing in Incomplete Data Computed Tomography: from X-rays to Laser Beams

“…With the above differences, it becomes clear that the inversion of equation (4) with the linear reconstruction model requires certain assumptions which may affect the quality of reconstructed images. Nevertheless, our earlier studies 2006b;2007;Lyubimov et al, 2002;2003) and results presented in Sections 3 and 4 show that the PAT method is quite effective in the context of the tomogram quality versus reconstruction speed trade-off.…”

“…As a result, each point in the volume significantly contributes to the detected signal. If, for example, we deal with absorbing inhomogeneities of tissues examined by pulsed probing with the time-domain measurement technique, integral (1), in the approximation of the perturbation theory by Born or Rytov, takes the form (Lyubimov et al, 2002;2003) is the distribution function of the absorbing inhomogeneities. Local linearization of the inverse problem of DOT is usually done with multi-step reconstruction algorithms based on the variational formulation of the radiation transport equation (or its diffusion approximation).…”

“…There is a unique opportunity to accelerate the reconstruction procedure: to change in expression (3) from volume integration to integration along a conventional line connecting point source and point receiver. Using a probabilistic interpretation of light transfer by Vision Systems: Applications 490 means of the conditional probability density P , Lyubimov et al (2002;2003) proved that integral (3) could be presented as…”

“…Figure 13(a). For comparison, a variety of methods based on binary operations and visualization algorithms (Mogilenskikh & Pavlov, 2002;Mogilenskikh, 2003) can be used. In our case, processing of the photo includes the construction of the same-level isolines, clearing of half-tones between the isolines, and filling of the isolines-bounded areas by black (Figure 21(a)).…”

“…We use a priori information on whether the solution is non-negative and on the presence of structure-free zones in the reconstruction region. For post-processing of reconstructed tomograms, we use space-varying restoration (Konovalov et al, 2007), methods for enhancing informativity of images based on its nonlinear color interpretation (Mogilenskikh, 2000) and methods for estimating image informativity based on binary operations and visualization algorithms (Mogilenskikh & Pavlov, 2002;Mogilenskikh, 2003). Results of investigation help decide how spatial resolution depends on the degree of data incompleteness and draw inferences on whether the modified reconstruction techniques are effective and on the investigated post-processing methods are capable of making tomograms more informative.…”