Related papers: Discrete Tomography of Planar Model Sets
Accurate estimation of the positions and shapes of microscale objects is crucial for automated imaging-guided manipulation using a non-contact technique such as optical tweezers. Perception methods that use traditional computer vision…
Tilting planar samples for multi-zone-axes observation is a routine procedure in electron microscopy. However, this process invariably introduces optical path differences in the electron beam across different sample positions, significantly…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
This article surveys the mathematics of the cut and project method as applied to point sets, called here {\em model sets}. It covers the geometric, arithmetic, and analytical sides of this theory as well as diffraction and the connection…
In dynamic tomography the object undergoes changes while projections are being acquired sequentially in time. The resulting inconsistent set of projections cannot be used directly to reconstruct an object corresponding to a time instant.…
A systematic digital-discrete method for obtaining continuous functions with smoothness to a certain order (C^(n)) from sample data is designed. This method is based on gradually varied functions and the classical finite difference method.…
Ultracold quantum gases offer unique possibilities to study interacting many-body quantum systems. Probing and manipulating such systems with ever increasing degree of control requires novel experimental techniques. Scanning electron…
In the framework of mapped pseudospectral methods, we introduce a new polynomial-type mapping function in order to describe accurately the dynamics of systems developing almost singular structures. Using error criteria related to the…
Accurate delineation of fine-scale structures is a very important yet challenging problem. Existing methods use topological information as an additional training loss, but are ultimately making pixel-wise predictions. In this paper, we…
Tubular structure segmentation in medical images, e.g., segmenting vessels in CT scans, serves as a vital step in the use of computers to aid in screening early stages of related diseases. But automatic tubular structure segmentation in CT…
This paper is one in a series that investigates topological measures on locally compact spaces. A topological measure is a set function which is finitely additive on the collection of open and compact sets, inner regular on open sets, and…
In 20th century mathematics, the field of topology, which concerns the properties of geometric objects under continuous transformation, has proved surprisingly useful in application to the study of discrete mathematics, such as…
Medical image segmentation is an increasingly popular area of research in medical imaging processing and analysis. However, many researchers who are new to the field struggle with basic concepts. This tutorial paper aims to provide an…
The scaled boundary finite element method is known for its capability in reproducing highly-detailed solution fields. This, however, is only attainable in those cases where analytical solutions exist. Many others invoke the use of numerical…
Differential complexes such as the de Rham complex have recently come to play an important role in the design and analysis of numerical methods for partial differential equations. The design of stable discretizations of systems of partial…
We consider the problem of segmenting an image into superpixels in the context of $k$-means clustering, in which we wish to decompose an image into local, homogeneous regions corresponding to the underlying objects. Our novel approach…
This note presents a method to study center families of periodic orbits of complex holomorphic differential equations near singularities, based on some iteration properties of fixed point indices. As an application of this method, we will…
Block copolymers provide a wonderful platform in studying the soft condensed matter systems. Many fascinating ordered structures have been discovered in bulk and confined systems. Among various theories, the self-consistent field theory…
Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…
Vector fields and line fields, their counterparts without orientations on tangent lines, are familiar objects in the theory of dynamical systems. Among the techniques used in their study, the Morse--Smale decomposition of a (generic) field…