7.1 Conclusions
This thesis has proposed methods for the computation of several structural parameters of binary volume datasets coming from both phantom and real samples. The Extreme Vertices Model and a new proposed decomposition model, Compact Union of Disjoint Boxes (CUDB), have been used to represent the datasets and to compute structural parameters in an efficient and compact way. Moreover, a new EVM-based method to simplify binary volumes has been also presented. The main contributions of the thesis are summarized as follows:
• An improved decomposition model for OPP. Experimental results show that CUDB has several advantages compared with other decomposition models such as OUDB-extended, mainly its performance in methods such as CCL and collision detection used in the struc-tural parameters computation.
• A CUDB-based virtual porosimeter, which simulate mercury intrusion at increasing pre-ssures, like the porosimeter lab device. The main advantage of this method is its perfor-mance with respect to previous approaches as it does not require a prior computation of the skeleton.
• A method to compute the Euler characteristic and the genus of binary volumes. This method exploits the advantages of CUDB and is notably faster (up to two orders of magnitude) than previous approaches.
• Methods to estimate sphericity and roundness indices based on the computation of the ob-ject’s OBB from EVM. Several sphericity indices have been computed from the OBB. An EVM-based roundness method based on a ray-casting-like approach has been presented, which shows good correlations with previous methods and is faster than them.
• A new approach to simplify binary images represented with EVM. It generates a LOD sequence of BOPP, which fulfill common properties of bounding structures. The method deals with OPP with any number of holes and connected components, and it encodes in a
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progressive and lossless way the generated LOD sequence. Compared with other approa-ches, the method gives good compression rates and run times, and the approximations are tighter, in general, maintaining concavities, genus and other shape features. More-over, this simplification method can be employed as support in the structural parameter computation since the approximations provide enough relevant information and have a faster run time than the original object.
• Two practical applications used by experts. Hot-stage Microscopy Tool has been satisfac-torily used to detect characteristic viscosity points of basalt and glass samples. Sphericity and roundness methods have been applied in a real silica nano CT.
The main advantage of the methods presented in this thesis to compute structural para-meters is its performance with respect to previous approaches. On the other hand, real samples scanned at high resolution usually generate huge datasets that require a lot of memory and large processing time to permit their analysis. However, experimental test show that simplified objects generated by the proposed simplification method, provide enough relevant information while allowing faster run times.
7.2 Future Work
In this thesis, three different research fields related with binary volumes have been dealt: model representation, structural parameters computation and model simplification. Several activities can be proposed for each of these fields as future work:
• Development of the CUDB to B-Rep conversion. An interesting method would be the conversion from CUDB to B-Rep. We think it is possible to obtain a B-Rep model analyzing the boxes and its neighborhood.
• Analyze if any of the six ABC-sortings in CUDB produces an optimal number of disjoint boxes. CUDB represents objects with a small number of elements. However, if any ABC-sorting produces the smallest number of orthogonal disjoint boxes that cover the OPP has not been studied. Otherwise, one could think of allowing overlapping boxes in order to further reduce this number. Although this implies modifying the developed algorithms.
• Development of a method for pore space partitioning using a different approach to virtual porosimetry and avoiding the skeleton computation. The narrow throats detection pre-sented in Section 4.2.3 can be applied to this method. If the lengths of all throats in the porous space are computed at once, they can be analyzed in order to detect the shortest paths that connect the solid space. Then, those paths that best split the porous space can be determined. In 2D this method is simple, since throats are represented as lines. How-ever, in 3D case, the throats are represented as rectangles and the general oblique throat by three rectangles, which requires some thought in order to provide a robust technique.
• Improvement of the connectivity computation. In the proposed method, the object’s complement is computed from EVM, therefore, conversions from CUDB to EVM and vice versa are required. The development of a method to compute the object’s comple-ment directly from its CUDB-representation will improve the run time of the connectivity computation.
• Development of a method that, from an EVM model, detects the surface voxels and classifies them into the nine classes defined by the voxel-based scheme [181] used in Section 4.4.2 to estimate the real surface area of an object. From the EVM to B-Rep algorithm [3], it can studied an approach that directly detects and classifies the surface voxels.
• Development of a variant of the simplification method, which preserves the connectivity, i.e., the genus. It implies defining a new treatment of the void space, where the faces that define the holes must be exhaustively analyzed in order to prevent them from closing completely.
• We have compared PEVE in storage and processing cost with methods that produce a progressive LOD sequence of bounding volumes. With the aforementioned variant of the method, the comparison can be extended to methods that use other lossless representation models for binary volumes such as run-length-encoding [117], ray representation [95] or triangle meshes obtained with a high accuracy to the voxel models [8, 9].
• Study of an EVM or CUDB-based data structure to encode time-varying datasets. A variant of the PEVE structure used by the simplification method presented in this thesis can be applied to this kind of datasets, where each 3D frame corresponds to one object.
If a dataset slightly changes frame-to-frame, it can be efficiently encoded. However, in the opposite case, PEVE structure is not suitable and a new approach must be devised.
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