Local Cause of Non-Convergence in a Convex Decomposition Using Convex Hulls

1989 ◽  
Author(s):  
Y. S.-Kim ◽  
D. J. Wilde
Keyword(s):  
Decomposition Method ◽  
Convex Hulls ◽  
Convex Decomposition ◽  
Polyhedral Objects

Abstract A convex decomposition method of polyhedral objects uses convex hulls and set difference operations. This decomposition may not converge. In this article, we formalize this decomposition method and find local cause of non-convergence.

A Convex Decomposition Using Convex Hulls and Local Cause of Its Non-Convergence

1992 ◽  
Vol 114 (3) ◽  
pp. 459-467 ◽  
Author(s):  
Yong Se Kim ◽  
D. J. Wilde
Keyword(s):  
Decomposition Method ◽  
Convex Hulls ◽  
Boolean Combination ◽  
Convex Object ◽  
Convex Decomposition ◽  
Polyhedral Objects

To exploit convexity, a non-convex object can be represented by a boolean combination of convex components. A convex decomposition method of polyhedral objects uses convex hulls and set difference operations. This decomposition, however, may not converge. In this article, we formalize this decomposition method and find local cause of non-convergence.

A Convergent Convex Decomposition of Polyhedral Objects

1992 ◽  
Vol 114 (3) ◽  
pp. 468-476 ◽  
Author(s):  
Yong Se Kim ◽  
D. J. Wilde
Keyword(s):  
Decomposition Method ◽  
Feature Recognition ◽  
Current Method ◽  
Convex Decomposition ◽  
Object Based ◽  
Geometric Objects ◽  
Polyhedral Objects ◽  
Volumetric Representation ◽  
Boundary Information ◽  
The Given

A convex decomposition method, called Alternating Sum of Volumes (ASV), uses convex hulls and set difference operations. ASV decomposition, however, may not converge, which severely limits the domain of geometric objects that the current method can handle. We investigate the cause of non-convergence and present a remedy; we propose a new convex decomposition called Alternating Sum of Volumes with Partitioning (ASVP) and prove its convergence. ASVP decomposition is a hierarchical volumetric representation which is obtained from the boundary information of the given object based on convexity. As an application, from feature recognition by ASVP decomposition if briefly discussed.

Form Feature Recognition by Convex Decomposition

1991 ◽  
Author(s):  
Yong Se Kim
Keyword(s):  
Decomposition Method ◽  
Feature Recognition ◽  
Convex Hulls ◽  
Convex Decomposition ◽  
Geometric Objects ◽  
Volumetric Representation ◽  
Feature Information ◽  
Form Features ◽  
Form Feature

Abstract A convex decomposition method, called Alternating Sum of Volumes (ASV), uses convex hulls and set difference operations. ASV decomposition may not converge, which severely limits the domain of geometric objects that can be handled. By combining ASV decomposition and remedial partitioning for the non-convergence, we have proposed a convergent convex decomposition called Alternating Sum of Volumes with Partitioning (ASVP). In this article, we describe how ASVP decomposition is used for recognition of form features. ASVP decomposition can be viewed as a hierarchical volumetric representation of form features. Adjacency and interaction between form features are inherently represented in the decomposition in a hierarchical way. Several methods to enhance the feature information obtained by ASVP decomposition are also discussed.

Conversions in Form Feature Recognition Using Convex Decomposition

1992 ◽  
Author(s):  
Yong Se Kim ◽  
Kenneth D. Roe
Keyword(s):  
Decomposition Method ◽  
Feature Recognition ◽  
Inductive Learning ◽  
The Other ◽  
New Combination ◽  
Convex Decomposition ◽  
Feature Information ◽  
Form Features ◽  
Primal And Dual ◽  
Form Feature

Abstract A convergent convex decomposition method called Alternating Sum of Volumes with Partitioning (ASVP) has been used to recognize volumetric form features intrinsic to the product shape. The recognition process is done by converting the ASVP decomposition into a form feature decomposition by successively applying combination operations on ASVP components. In this paper, we describe a method to generate new combination operations through inductive learning from conversion processes of primal and dual ASVP decompositions when one decomposition produces more desirable form feature information than the other.

Feature Recognition by Volume Decomposition Using Half-Space Partitioning

1994 ◽  
Author(s):  
Yan Shen ◽  
Jami J. Shah
Keyword(s):  
Half Space ◽  
Decomposition Method ◽  
Feature Recognition ◽  
Boundary Representation ◽  
Solid Model ◽  
Space Partitioning ◽  
Machining Features ◽  
Convex Decomposition ◽  
Volume Decomposition ◽  
Convex Cell

Abstract A volume decomposition method called minimum convex decomposition by half space partitioning has been developed to recognize machining features from the boundary representation of the solid model. First, the total volume to be removed by machining is obtained by subtracting the part from the stock. This volume is decomposed into minimum convex cells by half space partitioning at every concave edge. A method called maximum convex cell composition is developed to generate all alternative volume decompositions. The composing sub volumes are classified based on degree of freedom analysis. This paper focuses on the first part of our system, i.e., the volume decomposition. The other part of the work will be submitted for publication at a leter date.

Polyhedral Objects Metamorphosis Using Convex Decomposition and Morphology

2003 ◽  
Vol 6 (4) ◽  
pp. 196-204
Author(s):  
Wen-Yu Liu ◽  
Hua Li ◽  
Fei Wang ◽  
Guang-Xi Zhu
Keyword(s):  
Convex Decomposition ◽  
Polyhedral Objects

A decomposition method in non-linear programmm

Optimization ◽  
1975 ◽  
Vol 6 (4) ◽  
pp. 549-559
Author(s):  
L. Gerencsér
Keyword(s):  
Decomposition Method ◽  
Non Linear

DECOMPOSITION METHOD FOR DETERMINING THE HIGH REFLECTED SECTIONS OF A COMPLEX OBJECT SURFACE

2018 ◽  
Vol 77 (11) ◽  
pp. 945-956 ◽  
Author(s):  
N. N. Kolchigin ◽  
M. N. Legenkiy ◽  
A. A. Maslovskiy ◽  
А. Demchenko ◽  
S. Vinnichenko ◽  
...  
Keyword(s):  
Decomposition Method ◽  
Complex Object ◽  
Object Surface

A Spectrum-Adaptive Decomposition Method for Effective Atomic Number Estimation Using Dual Energy CT

2020 ◽  
Vol 2020 (14) ◽  
pp. 293-1-293-7
Author(s):  
Ankit Manerikar ◽  
Fangda Li ◽  
Avinash C. Kak
Keyword(s):  
Atomic Number ◽  
Decomposition Method ◽  
Traditional Approach ◽  
Effective Atomic Number ◽  
Dual Energy ◽  
Performance Comparison ◽  
Estimation Methods ◽  
Dual Energy Ct ◽  
Projection Data ◽  
X Ray

Dual Energy Computed Tomography (DECT) is expected to become a significant tool for voxel-based detection of hazardous materials in airport baggage screening. The traditional approach to DECT imaging involves collecting the projection data using two different X-ray spectra and then decomposing the data thus collected into line integrals of two independent characterizations of the material properties. Typically, one of these characterizations involves the effective atomic number (Zeff) of the materials. However, with the X-ray spectral energies typically used for DECT imaging, the current best-practice approaches for dualenergy decomposition yield Zeff values whose accuracy range is limited to only a subset of the periodic-table elements, more specifically to (Z < 30). Although this estimation can be improved by using a system-independent ρe — Ze (SIRZ) space, the SIRZ transformation does not efficiently model the polychromatic nature of the X-ray spectra typically used in physical CT scanners. In this paper, we present a new decomposition method, AdaSIRZ, that corrects this shortcoming by adapting the SIRZ decomposition to the entire spectrum of an X-ray source. The method reformulates the X-ray attenuation equations as direct functions of (ρe, Ze) and solves for the coefficients using bounded nonlinear least-squares optimization. Performance comparison of AdaSIRZ with other Zeff estimation methods on different sets of real DECT images shows that AdaSIRZ provides a higher output accuracy for Zeff image reconstructions for a wider range of object materials.

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