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This paper aims at recovering the shape of a scene with unknown, non-Lambertian, and possibly spatially-varying surface materials. When the shape of the object is highly complex and that shadows cast on the surface, the task becomes very…
We employ the so-called tangent-point energy as Tikhonov regularizer for ill-conditioned inverse scattering problems in 3D. The tangent-point energy is a self-avoiding functional on the space of embedded surfaces that also penalizes surface…
In image processing, solving inverse problems is the task of finding plausible reconstructions of an image that was corrupted by some (usually known) degradation operator. Commonly, this process is done using a generative image model that…
We present in this paper a novel numerical reconstruction method for solving a 3D coefficient inverse problem with scattering data generated by a single direction of the incident plane wave. This inverse problem is well-known to be a highly…
We study an inverse random obstacle scattering problems in $\mathbb{R}^2$ where the scatterer is formulated by a Gaussian process defined on the angular parameter domain. Equipped with a modified covariance function which is mathematically…
We propose an optimization proxy in terms of iterative implicit gradient methods for solving constrained optimization problems with nonconvex loss functions. This framework can be applied to a broad range of machine learning settings,…
Creating representations of shapes that are invari-ant to isometric or almost-isometric transforma-tions has long been an area of interest in shape anal-ysis, since enforcing invariance allows the learningof more effective and robust shape…
Inverse scattering problem for an operator, which is a sum of the operator of the third derivative and of an operator of multiplication by a real function, is solved. The main closed system of equations of inverse problem is obtained. This…
We are concerned with the reconstruction of a sound-soft obstacle using far field measurements of the scattered waves associated with incident plane waves sent from one direction but at multiple frequencies. We define, for each frequency,…
The Rayleigh conjecture on the representation of the scattered field in the exterior of an obstacle $D$ is widely used in applications. However this conjecture is false for some obstacles. AGR introduced the Modified Rayleigh Conjecture…
We propose a differentiable sphere tracing algorithm to bridge the gap between inverse graphics methods and the recently proposed deep learning based implicit signed distance function. Due to the nature of the implicit function, the…
In this work, we propose an inverse rendering model that estimates 3D shape, spatially-varying reflectance, homogeneous subsurface scattering parameters, and an environment illumination jointly from only a pair of captured images of a…
We introduce a latent 3D representation that models 3D surfaces as probability density functions in 3D, i.e., p(x,y,z), with flow-matching. Our representation is specifically designed for consumption by machine learning models, offering…
Implicit neural representations map a shape-specific latent code and a 3D coordinate to its corresponding signed distance (SDF) value. However, this approach only offers a single level of detail. Emulating low levels of detail can be…
Deep implicit functions have shown remarkable shape modeling ability in various 3D computer vision tasks. One drawback is that it is hard for them to represent a 3D shape as multiple parts. Current solutions learn various primitives and…
Shape priors have long been known to be effective when reconstructing 3D shapes from noisy or incomplete data. When using a deep-learning based shape representation, this often involves learning a latent representation, which can be either…
In this paper we consider a dynamic computer simulator that produces a time-series response $y_t(x)$ over $L$ time points, for every given input parameter $x$. We propose a method for solving inverse problems, which refer to the finding of…
In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential…
A new sampling method for inverse scattering problems is proposed to process far field data of one incident wave. As the linear sampling method, the method sets up ill-posed integral equations and uses the (approximate) solutions to…
We derive a fully discrete Inverse Scattering Transform as a method for solving the initial-value problem for the Q3$_\delta$ lattice (difference-difference) equation for real-valued solutions. The initial condition is given on an infinite…