Related papers: Ray Transforms on a Conformal Class of Curves
Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…
We reduce the broken ray transform on some Riemannian manifolds (with corners) to the geodesic ray transform on another manifold, which is obtained from the original one by reflection. We give examples of this idea and present injectivity…
Data augmentation in feature space is effective to increase data diversity. Previous methods assume that different classes have the same covariance in their feature distributions. Thus, feature transform between different classes is…
One constructs new operations of pull-back and push-forward on valuations on manifolds with respect to submersions and immersions. A general Radon type transform on valuations is introduced using these operations and the product on…
We first give a constructive answer to the attenuated tensor tomography problem on simple surfaces. We then use this result to propose two approaches to produce vector-valued integral transforms which are fully injective over tensor fields.…
We consider an inverse problem arising in thermo-/photo- acoustic tomography that amounts to reconstructing a function $f$ from its circular or spherical means with the centers lying on a given measurement surface. (Equivalently, these…
Hyperplane is a set of non-injectivity of the spherical Radon transform (SRT) in the space of continuous functions in R^d. In this article, for the reconstruction of an unknown function f from C(R^3) (the support can be non-compact), using…
Capturing the 3D geometry of transparent objects is a challenging task, ill-suited for general-purpose scanning and reconstruction techniques, since these cannot handle specular light transport phenomena. Existing state-of-the-art methods,…
Reconstructing 2D curves from sample points has long been a critical challenge in computer graphics, finding essential applications in vector graphics. The design and editing of curves on surfaces has only recently begun to receive…
A unified method for three-dimensional reconstruction of objects from transmission images collected at multiple illumination directions is described. The method may be applicable to experimental conditions relevant to absorption-based,…
We pose a normal form of transition functions along some Levi-flat hypersurfaces obtained by suspension. By focusing on methods in circle dynamics and linearization theorems, we give a sufficient condition to obtain a normal form as a…
We construct valuations on the space of finite-valued convex functions using integration of differential forms over the differential cycle associated to a convex function. We describe the kernel of this procedure and show that the…
This article introduces the Clarke transform and Clarke coordinates, which present a solution to the disengagement of an arbitrary number of coupled displacement actuation of continuum and soft robots. The Clarke transform utilizes the…
The present article proposes a partial answer to the explicit inversion of the tensor tomography problem in two dimensions, by proving injectivity over certain kinds of tensors and providing reconstruction formulas for them. These tensors…
This paper proposes a new data assimilation method for recovering high fidelity turbulent flow field around airfoil at high Reynolds numbers based on experimental data, which is called Proper Orthogonal Decomposition Inversion…
Curved refractive objects are common in the human environment, and have a complex visual appearance that can cause robotic vision algorithms to fail. Light-field cameras allow us to address this challenge by capturing the view-dependent…
The method of moving frames (rep\`ere mobile) was used by Elie Cartan as a way of organizing the identification of differential invariants and solving equivalence problems. In this expository paper, we discuss how moving frames are used to…
Optimal transport theory has been a powerful tool for the analysis of parabolic equationsviewed as gradient flows of volume forms according to suitable transportation metrics.In this paper, we present an example of gradient flows for closed…
The work develops further the theory of the following inversion problem, which plays the central role in the rapidly developing area of thermoacoustic tomography and has intimate connections with PDEs and integral geometry: {\it Reconstruct…
On a manifold or a closed subset of a Euclidean vector space, a retraction enables to move in the direction of a tangent vector while staying on the set. Retractions are a versatile tool to perform computational tasks such as optimization,…