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Advances in fluorescence microscopy enable acquisition of 3D image volumes with better image quality and deeper penetration into tissue. Segmentation is a required step to characterize and analyze biological structures in the images and…
Volume estimation in large indoor spaces is an important challenge in robotic inspection of industrial warehouses. We propose an approach for volume estimation for autonomous systems using visual features for indoor localization and surface…
The $\texttt{IntegerHull}$ function is part of Maple's $\texttt{PolyhedralSets}$ library, which calculates the integer hull of a given polyhedral set. This algorithm works by translating the supporting hyperplanes of the facets of the input…
This paper presents a new algorithm, Weighted Squared Volume Minimization (WSVM), for generating high-quality tetrahedral meshes from closed triangle meshes. Drawing inspiration from the principle of minimal surfaces that minimize squared…
This paper presents a finite volume method for simulating two-phase flows using a level set approach coupled with volume of fluid method capable of simulating sharp fluid interfaces. The efficiency of the method is a result of the fact that…
Cell segmentation in microscopy is a challenging problem, since cells are often asymmetric and densely packed. This becomes particularly challenging for extremely large images, since manual intervention and processing time can make…
We observe structure in the sequences of quotients and remainders of the Euclidean algorithm with two families of inputs. Analyzing the remainders, we obtain new algorithms for computing modular inverses and representating prime numbers by…
We provide a polynomial time cutting plane algorithm based on split cuts to solve integer programs in the plane. We also prove that the split closure of a polyhedron in the plane has polynomial size.
This paper presents a new method for automatic quantification of ellipse-like cells in images, an important and challenging problem that has been studied by the computer vision community. The proposed method can be described by two main…
Point containment queries on trimmed surfaces are fundamental to CAD modeling, solid geometry processing, and surface tessellation. Existing approaches such as ray casting and generalized winding numbers often face limitations in robustness…
This paper investigates how the inherent quantization of camera sensors introduces uncertainty in the calculated position of an observed feature during 3-D mapping. It is typically assumed that pixels and scene features are points, however,…
For power spectrum estimation it's important that the pixelization of a CMB sky map be smooth and regular to high degree. With this criterion in mind the ``COBE sky cube" was defined. This paper has as central theme to further improve on…
In this paper, we give an algorithm to infer the positions of the vertices of an unknown tetrahedron, given a sample of points which are uniformly distributed within the tetrahedron. The accuracy of the algorithm is demonstrated using some…
An example of the volume and boundary face area of a curved polyhedron for the case of regular spherical and hyperbolic tetrahedron is discussed. An exact formula is explicitly derived as a function of the scalar curvature and the edge…
In this paper, we propose a method to segment regions in three-dimensional point clouds. We assume that (i) the shape and the number of regions in the point cloud are not known and (ii) the point cloud may be noisy. The method consists of…
A quantum algorithm is developed to calculate decay rates and cross sections using quantum resources that scale polynomially in the system size assuming similar scaling for state preparation and time evolution. This is done by computing…
Ray tracing is an efficient channel modeling method. However, the traditional ray tracing method has high computation complexity. To solve this problem, an improved bounding volume hierarchies (BVH) algorithm is proposed in this paper.…
We describe an algorithm for using a quantum computer to calculate mean values of observables and the partition function of a quantum system. Our algorithm includes two sub-algorithms. The first sub-algorithm is for calculating, with…
An algorithm to efficiently compute the moments of volumetric images is disclosed. The approach demonstrates a reduction in processing time by reducing the computational complexity significantly. Specifically, the algorithm reduces…
In this article, a Probability Mass Function (PMF) estimation method which tames the curse of dimensionality is proposed. This method, called Partial Coupled Tensor Factorization of 3D marginals or PCTF3D, has for principle to partially…