Practical reliable Bayesian recognition of 2D and 3D objects using implicit polynomials and algebraic invariants

1996 ◽  
Vol 18 (5) ◽  
pp. 505-519 ◽  
Author(s):  
J. Subrahmonia ◽  
D.B. Cooper ◽  
D. Keren
Keyword(s):  
3D Objects ◽  
Algebraic Invariants ◽  
Implicit Polynomials ◽  
2D And 3D

scholarly journals Voxelisation Algorithms and Data Structures: A Review

Sensors ◽  
2021 ◽  
Vol 21 (24) ◽  
pp. 8241
Author(s):  
Mitko Aleksandrov ◽  
Sisi Zlatanova ◽  
David J. Heslop
Keyword(s):  
Data Structure ◽  
Data Structures ◽  
State Of The Art ◽  
Algorithms And Data Structures ◽  
3D Objects ◽  
Digital Representations ◽  
Memory Footprint ◽  
Voxel Data ◽  
2D And 3D ◽  
Geometric Primitives

Voxel-based data structures, algorithms, frameworks, and interfaces have been used in computer graphics and many other applications for decades. There is a general necessity to seek adequate digital representations, such as voxels, that would secure unified data structures, multi-resolution options, robust validation procedures and flexible algorithms for different 3D tasks. In this review, we evaluate the most common properties and algorithms for voxelisation of 2D and 3D objects. Thus, many voxelisation algorithms and their characteristics are presented targeting points, lines, triangles, surfaces and solids as geometric primitives. For lines, we identify three groups of algorithms, where the first two achieve different voxelisation connectivity, while the third one presents voxelisation of curves. We can say that surface voxelisation is a more desired voxelisation type compared to solid voxelisation, as it can be achieved faster and requires less memory if voxels are stored in a sparse way. At the same time, we evaluate in the paper the available voxel data structures. We split all data structures into static and dynamic grids considering the frequency to update a data structure. Static grids are dominated by SVO-based data structures focusing on memory footprint reduction and attributes preservation, where SVDAG and SSVDAG are the most advanced methods. The state-of-the-art dynamic voxel data structure is NanoVDB which is superior to the rest in terms of speed as well as support for out-of-core processing and data management, which is the key to handling large dynamically changing scenes. Overall, we can say that this is the first review evaluating the available voxelisation algorithms for different geometric primitives as well as voxel data structures.

Patterned 2D and 3D Assemblies of Nanoparticles on Molecular Printboards

2006 ◽  
Vol 51 ◽  
pp. 105-114 ◽  
Author(s):  
Jurriaan Huskens
Keyword(s):  
Silica Nanoparticles ◽  
Nanoimprint Lithography ◽  
Three Dimensions ◽  
Host Recognition ◽  
Self Assembled Monolayers ◽  
Layer By Layer ◽  
3D Objects ◽  
Lbl Assembly ◽  
Assembled Monolayers ◽  
2D And 3D

Functionalized nanoparticles have powerful applications as intermediates between solution and surface chemistry and as tools for nanofabrication. Two main examples of these have been shown. The functionalization of 3 nm gold and 55 nm silica nanoparticles with cyclodextrin (CD) host sites has been achieved, which allows: (i) the controlled aggregation with guestfunctionalized dendrimers in solution, (ii) the specific adsorption onto dendrimer-patterned substrates, and (iii) the fabrication of larger architectures using the layer-by-layer methodology. Aggregation in solution was shown to proceed through specific host-guest recognition. The adsorption onto surfaces employed so-called “molecular printboards”, which are self-assembled monolayers with the same cyclodextrin host recognition sites which allow the stable assembly of molecules and nanoparticles through multivalent host-guest interactions. CD silica nanoparticles were shown to adsorb specifically onto areas of such molecular printboards which were patterned with adamantyl-functionalized dendrimers. The layer-by-layer (LBL) assembly of such dendrimers and CD gold nanoparticles led to a controllable multilayer architecture with a thickness increase of about 2 nm per bilayer. The combination of the (bottom-up) particle LBL assembly and top-down surface structuring, in particular nanoimprint lithography, was shown to result in the formation of 3D objects down to sub-100 nm in all three dimensions.

Recognition of 3D Objects Based on Implicit Polynomials

2010 ◽  
Vol 32 (5) ◽  
pp. 954-960 ◽  
Author(s):  
H. Ben-Yaacov ◽  
D. Malah ◽  
M. Barzohar
Keyword(s):  
3D Objects ◽  
Implicit Polynomials
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