Fast neighborhood operations for images and volume data sets

Compact Union of Disjoint Boxes: An Efficient Decomposition Model for Binary Volumes

“…The Ordered Union of Disjoint Boxes (OUDB) [1,42] is a special kind of spatial partitioning representation derived from EVM, where an OPP is decomposed in a list of disjoint boxes. EVM can be obtained from the voxel model, in turn, OUDB is obtained from EVM.…”

“…EVM can be obtained from the voxel model, in turn, OUDB is obtained from EVM. The conversions algorithms have been published [42]. To introduce later the CUDB model, we first briefly introduce OUDB.…”

“…In this sense, OUDB has been proved to be efficient for CCL [42,43]. With regard to semi-boundary representations, it has been concluded that CCL is better in OUDB than in semi-boundary representations when the number of boxes in the OUDB is less than the number of boundary voxels, which generally occurs.…”

“…CUDB can be computed directly from the EVM, and the merging of boxes is performed on the fly. The strategy is similar to the process to compute OUDB [42]. Cuts of the EVM-represented OPP are obtained sequentially, and sections are computed from them.…”

“…EVM stores only a sorted subset of vertices of the OPP boundary, whereas OUDB keeps a sorted list of boxes that compose the whole object. EVM has been used to prove the suitability of OPP as geometric bounds in CSG [2,1], and for many other 3D applications such as: erosion and dilation operations [42], skeleton computation [4], virtual porosimetry without skeleton computation [44], biomaterials structural parameters computation [54] and model simplification [15]. OUDB has been used to perform CCL [5,42] and also for biomaterials structural parameters computation such as connectivity [7] and center of gravity [6].…”