Beta-decomposition for the volume and area of the union of three-dimensional balls and their offsets.

Given a set of spherical balls, called atoms, in three-dimensional space, its mass properties such as the volume and the boundary area of the union of the atoms are important for many disciplines, particularly for computational chemistry/biology and structural molecular biology. Despite many previous studies, this seemingly easy problem of computing mass properties has not been well-solved. If the mass properties of the union of the offset of the atoms are to be computed as well, the problem gets even harder. In this article, we propose algorithms that compute the mass properties of both the union of atoms and their offsets both correctly and efficiently. The proposed algorithms employ an approach, called the Beta-decomposition, based on the recent theory of the beta-complex. Given the beta-complex of an atom set, these algorithms decompose the target mass property into a set of primitives using the simplexes of the beta-complex. Then, the molecular mass property is computed by appropriately summing up the mass property corresponding to each simplex. The time complexity of the proposed algorithm is O(m) in the worst case where m is the number of simplexes in the beta-complex that can be efficiently computed from the Voronoi diagram of the atoms. It is known in ℝ(3) that m = O(n) on average for biomolecules and m = O(n(2)) in the worst case for general spheres where n is the number of atoms. The theory is first introduced in ℝ(2) and extended to ℝ(3). The proposed algorithms were implemented into the software BetaMass and thoroughly tested using molecular structures available in the Protein Data Bank. BetaMass is freely available at the Voronoi Diagram Research Center web site.

Copula-Based Approach to Synthetic Population Generation.

Generating synthetic baseline populations is a fundamental step of agent-based modeling and simulation, which is growing fast in a wide range of socio-economic areas including transportation planning research. Traditionally, in many commercial and non-commercial microsimulation systems, the iterative proportional fitting (IPF) procedure has been used for creating the joint distribution of individuals when combining a reference joint distribution with target marginal distributions. Although IPF is simple, computationally efficient, and rigorously founded, it is unclear whether IPF well preserves the dependence structure of the reference joint table sufficiently when fitting it to target margins. In this paper, a novel method is proposed based on the copula concept in order to provide an alternative approach to the problem that IPF resolves. The dependency characteristic measures were computed and the results from the proposed method and IPF were compared. In most test cases, the proposed method outperformed IPF in preserving the dependence structure of the reference joint distribution.

Automatic reconstruction of the arterial and venous trees on volumetric chest CT.

PURPOSE: This paper introduces a novel approach to classify pulmonary arteries and veins from volumetric chest computed tomography (CT) images. Although there is known to be a relationship between the alteration of vessel distributions and the progress of various pulmonary diseases, there has been relatively little research on the quantification of pulmonary vessels in vivo due to morphological difficulties. In particular, there have been few efforts to quantify the morphology and distribution of only arteries or veins through automated algorithms despite the clinical importance of such work. In this study, the authors classify different types of vessels by constructing a tree structure from vascular points while minimizing the construction cost using the vascular geometries and features of CT images. METHODS: First, a vascular point set is extracted from an input volume and the weights of the points are calculated using the intensity, distance from the boundaries, and the Laplacian of the distance field. The tree construction cost is then defined as the summation of edge connection costs depending on the vertex weights. As a solution, the authors can obtain a minimum spanning tree whose branches correspond to different vessels. By cutting the edges in the mediastinal region, branches can be separated. From the root points of each branch, the cut region is regrouped toward the entries of pulmonary vessels in the same framework of the initial tree construction. After merging branches with the same orientation as much as possible, it can be determined manually whether a given vessel is an artery or vein. Our approach can handle with noncontrast CT images as well as vascular contrast enhanced images. RESULTS: For the validation, mathematical virtual phantoms and ten chronic obstructive pulmonary disease (COPD) noncontrast volumetric chest CT scans with submillimeter thickness were used. Based on experimental findings, the suggested approach shows 9.18 ± 0.33 (mean ± SD) visual scores for ten datasets, 91% and 98% quantitative accuracies for two cases, a result which is clinically acceptable in terms of classification capability. CONCLUSIONS: This automatic classification approach with minimal user interactions may be useful in assessing many pulmonary disease, such as pulmonary hypertension, interstitial lung disease and COPD.