NonLocal via Local–NonLinear via Linear: A New Part-coding Distance Field via Screened Poisson Equation

SHREC’21: Quantifying shape complexity

“…Discrepancy [15] by A. Genctav, § 4.3, 4. PARCELLIN distance [14] by M. Genctav, § 4.4, 5. 2D multi-view based shape convexity measures C 1 , C 2 , [22], [23] by P. L. Rosin § 4.5 6.…”

“…For the first family, the evaluation produced the following five groups in which shapes are listed in increasing order of complexity: Group 1: (16,14,12,17,18,19,20) Group 2: (15, 13, 24, 22) Group 3: (23, 21, 25) Group 4: (11, 10, 7, 1, 2) Group 5: (9,8,4,5,6,3) For the second family, the evaluation produced the following six groups in which shapes are considered to be of equal complexity: Group 1: (18,24,17,20) Group 2: (25,21,22,19) Group 3: (5, 3, 2) Group 4: (23,16,15) Group 5: (6, 4, 14, 12, 13) Group 6: (7,9,10,1,11,8) As the shapes from different groups are incommensurate, we provide ground truths only for the shapes in the same group. While many qualitative notions of complexity could equally apply to shapes of the kind we use in this collection, we consider the aforementioned notion of executional complexity one of the best determinants of complexity for 3D models representing design objects (i.e.…”

“…In this method, following the idea presented in [14], ( 3) is solved simultaneously with different source functions, which are designed for exploration of the shape volume, subject to homogeneous Dirichlet boundary conditions.…”

“…In several works ( [1,3]) it is used as a measure of the complexity along with other indicators. In most other works [4,12,13,14,15,16], tools from information theory, on top of various geometric features are used to quantify complexity. Work that relates complexity to algorithmic information theory and is applied to objects of art and de-sign can also be found in Stiny and Gips [17].…”

Mobile adaptive crowd optimization scheme based on distance field

“…The projection image generation algorithm [11] was proposed to design and fabricate a complex 3D scaffold, which automatically and robustly generates 2D projection image data. The author of article [12] proposed a repeated use of screened Poisson to compute a part coding and extracting distance field. A highly scalable method was proposed in article [13] for computing 3D distance fields on massively parallel distributed-memory machines.…”