Related papers: Localization, Stability, and Resolution of Topolog…
Many loss functions have been derived from cross-entropy loss functions such as large-margin softmax loss and focal loss. The large-margin softmax loss makes the classification more rigorous and prevents overfitting. The focal loss…
Elastographic imaging is a widely used technique which can in principle be implemented on top of every imaging modality. In elastography, the specimen is exposed to a force causing local displacements in the probe, and imaging is performed…
In this work we consider the inverse problem of reconstructing the optical properties of a layered medium from an elastography measurement where optical coherence tomography is used as the imaging method. We hereby model the sample as a…
While the pursuit of higher accuracy in deepfake detection remains a central goal, there is an increasing demand for precise localization of manipulated regions. Despite the remarkable progress made in classification-based detection,…
We present topological derivative and energy based procedures for the imaging of micro and nanostructures using one beam of visible light of a single wavelength. Objects with diameters as small as 10 nm can be located, and their position…
This paper presents a novel multi-scale method for elliptic partial differential equations with arbitrarily rough coefficients. In the spirit of numerical homogenization, the method constructs problem-adapted ansatz spaces with uniform…
This paper concerns a fast, one-step iterative technique of imaging extended perfectly conducting cracks with Dirichlet boundary condition. In order to reconstruct the shape of cracks from scattered field data measured at the boundary, we…
Feature extraction in noisy image datasets presents many challenges in model reliability. In this paper, we use the discrete Fourier transform in conjunction with persistent homology analysis to extract specific frequencies that correspond…
Topography and gravity are geophysical fields whose joint statistical structure derives from interface-loading processes modulated by the underlying mechanics of isostatic and flexural compensation in the shallow lithosphere. Under this…
Convolutional autoencoders have emerged as popular methods for unsupervised defect segmentation on image data. Most commonly, this task is performed by thresholding a pixel-wise reconstruction error based on an $\ell^p$ distance. This…
We investigate a fixed domain approach in shape optimization, using a regularization of the Heaviside function both in the cost functional and in the state system. We consider the compliance minimization problem in linear elasticity, a well…
Image representation is critical for many visual tasks. Instead of representing images discretely with 2D arrays of pixels, a recent study, namely local implicit image function (LIIF), denotes images as a continuous function where pixel…
In this paper we consider the fundamental operations dilation and erosion of mathematical morphology. Many powerful image filtering operations are based on their combinations. We establish homomorphism between max-plus semi-ring of integers…
A recently developed Projection-based Digital Image Correlation (P-DVC) method is here extended to 4D (space and time) displacement field measurement and mechanical identification based on a single radiograph per loading step instead of…
We propose a three-dimensional nonlinear diffusion method to implement the similar autofocusing function of multiple micro-objects and simultaneously remove the defocused images, which can distinguish the locations of certain sized…
Deep learning has significantly advanced medical imaging analysis, yet variations in image resolution remain an overlooked challenge. Most methods address this by resampling images, leading to either information loss or computational…
In this paper, we design a bifocusing-based imaging strategy for the rapid identification of small penetrable dielectric inhomogeneities within a two-dimensional bistatic measurement setup. To address the applicability and limitation, we…
We investigate the two-dimensional elastostatic inclusion problem in an unbounded medium. Building on the recent developments for rigid inclusions \cite{Mattei:2021:EAS} and conductivity inclusions \cite{Jung:2021:SEL}, we extend these…
Learning-based image compression methods have emerged as state-of-the-art, showcasing higher performance compared to conventional compression solutions. These data-driven approaches aim to learn the parameters of a neural network model…
We investigate the density large deviation function for a multidimensional conservation law in the vanishing viscosity limit, when the probability concentrates on weak solutions of a hyperbolic conservation law conservation law. When the…