Related papers: Digital Euler Characteristic Transform
Electrical Impedance Tomography (EIT) is a powerful imaging modality widely used in medical diagnostics, industrial monitoring, and environmental studies. The EIT inverse problem is about inferring the internal conductivity distribution of…
The emergence of deep learning has significantly enhanced the analysis of electrocardiograms (ECGs), a non-invasive method that is essential for assessing heart health. Despite the complexity of ECG interpretation, advanced deep learning…
Cryo-electron tomography (cryoET) is a technique that captures images of biological samples at different tilts, preserving their native state as much as possible. Along with the partial tilt series and noise, one of the major challenges in…
Tools from topological data analysis have been widely used to represent binary images in many scientific applications. Methods that aim to represent grayscale images (i.e., where pixel intensities instead take on continuous values) have…
Atomic electron tomography (AET) enables the determination of 3D atomic structures by acquiring a sequence of 2D tomographic projection measurements of a particle and then computationally solving for its underlying 3D representation.…
The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on…
We consider the problem of computing the Euler characteristic of an abstract simplicial complex given by its vertices and facets. We show that this problem is #P-complete and present two new practical algorithms for computing Euler…
Convolutional neural networks have made significant progresses in edge detection by progressively exploring the context and semantic features. However, local details are gradually suppressed with the enlarging of receptive fields. Recently,…
Powerful manipulation techniques have made digital image forgeries be easily created and widespread without leaving visual anomalies. The blind localization of tampered regions becomes quite significant for image forensics. In this paper,…
Online optimisation studies the convergence of optimisation methods as the data embedded in the problem changes. Based on this idea, we propose a primal dual online method for nonlinear time-discrete inverse problems. We analyse the method…
Determining physical properties inside an object without access to direct measurements of target regions can be formulated as a specific type of \textit{inverse problem}. One of such problems is applied in \textit{Electrical Impedance…
Geophysical inversion attempts to estimate the distribution of physical properties in the Earth's interior from observations collected at or above the surface. Inverse problems are commonly posed as least-squares optimization problems in…
The Euler scheme is up to date the most important numerical method for ordinary differential inclusions, because the use of the available higher-order methods is prohibited by their enormous complexity after spatial discretization.…
Cardiac digital twins (CDTs) are personalized virtual representations used to understand complex cardiac mechanisms. A critical component of CDT development is solving the ECG inverse problem, which enables the reconstruction of cardiac…
A new iterative image reconstruction algorithm for electrical capacitance tomography (ECT) is proposed that is based on iterative soft thresholding of a total variation penalty and adaptive reweighted compressive sensing. This algorithm…
Error correction codes (ECC) are crucial for ensuring reliable information transmission in communication systems. Choukroun & Wolf (2022b) recently introduced the Error Correction Code Transformer (ECCT), which has demonstrated promising…
Objective: To develop, and demonstrate the feasibility of, a novel image reconstruction method for absolute Electrical Impedance Tomography (a-EIT) that pairs deep learning techniques with real-time robust D-bar methods. Approach: A D-bar…
This study proposes a novel approach to extract topological properties, specifically the Euler characteristic, from input images using neural networks without relying on large pre-existing datasets but with a single geometric image.…
X-ray computed tomography (XCT) has become a reliable metrology tool for measuring internal flaws and other microstructural features in engineering materials. However, tracking of material points to measure three-dimensional (3D)…
A parameterization is described for quantifying translational motion of a point in three-dimensional Euclidean space. The parameterization is similar to well-known parameterizations such as spherical coordinates in that both position and…