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It has been argued that an extended, quasi-rigid body evolving freely in curved spacetime can deviate from its natural trajectory by simply performing cyclic deformations. More interestingly, in the limit of rapid cycles, the amount of…
In recent years directional multiscale transformations like the curvelet- or shearlet transformation have gained considerable attention. The reason for this is that these transforms are - unlike more traditional transforms like wavelets -…
Over the last 30 years a plethora of variational regularisation models for image reconstruction has been proposed and thoroughly inspected by the applied mathematics community. Among them, the pioneering prototype often taught and learned…
The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…
This paper examines the existence and region of convergence of Fourier transform of the functions of bicomplex variables with the help of projection on its idempotent components as auxiliary complex planes. Several basic properties of this…
We numerically investigate the athermal creep deformation of amorphous materials having a wide range of stability. The imposed shear stress serves as the control parameter, allowing us to examine the time-dependent transient response…
Deep neural networks have achieved impressive results in many image classification tasks. However, since their performance is usually measured in controlled settings, it is important to ensure that their decisions remain correct when…
This paper focus on the theoretical analysis and simulation of electromagnetic wave transforms, which is widely encountered in teaching physics. When the electromagnetic wave is not consistent with the shape of the object, it is often…
Ptychography is a popular imaging technique that combines diffractive imaging with scanning microscopy. The technique consists of a coherent beam that is scanned across an object in a series of overlapping positions, leading to reliable and…
This is the report for the PRIM project in Telecom Paris. This report is about applications based on spatial-frequency transform and deep learning techniques. In this report, there are two main works. The first work is about the enhanced…
Surface metrology is the area of engineering concerned with the study of geometric variation in surfaces. This paper explores the potential for modern techniques from spatial statistics to act as generative models for geometric variation in…
An experimental apparatus measuring free-surface deformation of a centrifuged granular pile is developed. By horizontally rotating a quasi two-dimensional granular pile whose apex is located at the vertical rotation axis, the resultant…
The class of the hypercomplex pseudo-Hermitian manifolds is considered. The flatness of the considered manifolds with the 3 parallel complex structures is proved. Conformal transformations of the metrics are introduced. The conformal…
A novel approach to 3D surface imaging is proposed, allowing for the continuous sampling of 3D surfaces to extract localized perspective transformation coefficients from Fourier spectrum analysis of projected patterns. The mathematical…
Vision transformer has demonstrated promising performance on challenging computer vision tasks. However, directly training the vision transformers may yield unstable and sub-optimal results. Recent works propose to improve the performance…
Experimental investigations of surface forces generally involve two solid bodies of simple and well-defined geometry interacting across a medium. Direct measurement of their surface interaction can be interpreted to reveal fundamental…
Transformation method provides an efficient way to control wave propagation by materials. However, the degree to which this transformation concept can be applied to other physical phenomena remains an open question. Recently, Hu et al.…
We characterize the class of image plane transformations which realize rigid camera motions and call these transformations `rigidity preserving'. In particular, 2D translations of pinhole images are not rigidity preserving. Hence, when…
In this work we evaluate the impact of digitally altered images on the performance of artificial neural networks. We explore factors that negatively affect the ability of an image classification model to produce consistent and accurate…
We study how robust current ImageNet models are to distribution shifts arising from natural variations in datasets. Most research on robustness focuses on synthetic image perturbations (noise, simulated weather artifacts, adversarial…