Related papers: A geometric based preprocessing for weighted ray t…
Creating geometric abstracted models from image-based scene reconstructions is difficult due to noise and irregularities in the reconstructed model. In this paper, we present a geometric modeling method for noisy reconstructions dominated…
Let $\mathcal R$ denote the generalized Radon transform (GRT), which integrates over a family of $N$-dimensional smooth submanifolds $\mathcal S_{\tilde y}\subset\mathcal U$, $1\le N\le n-1$, where an open set $\mathcal U\subset\mathbb R^n$…
We consider weighted Radon transforms $R_W$ along hyperplanes in $R^3$ with strictly positive weights $W$. We construct an example of such a transform with non-trivial kernel $\mathrm{Ker}R_W$ in the space of infinitely smooth compactly…
Positron emission tomography(PET) image reconstruction is an ill-posed inverse problem and suffers from high level of noise due to limited counts received. Recently deep neural networks especially convolutional neural networks(CNN) have…
A new method for estimation of intragranular strain fields in polycrystalline materials based on scanning three-dimensional X-ray diffraction data (scanning-3DXRD) is presented and evaluated. Given an apriori known anisotropic compliance,…
3D Lidar imaging can be a challenging modality when using multiple wavelengths, or when imaging in high noise environments (e.g., imaging through obscurants). This paper presents a hierarchical Bayesian algorithm for the robust…
We consider the reconstruction of the vertex weight in the discrete Gel'fand's inverse boundary spectral problem for the graph Laplacian. Given the boundary vertex weight and the edge weight of the graph, we develop reconstruction…
Methods for 3D reconstruction such as Photometric stereo recover the shape and reflectance properties using multiple images of an object taken with variable lighting conditions from a fixed viewpoint. Photometric stereo assumes that a scene…
Recovering the 3D geometry of a purely texture-less object with generally unknown surface reflectance (e.g. non-Lambertian) is regarded as a challenging task in multi-view reconstruction. The major obstacle revolves around establishing…
In this paper we broadly consider techniques which utilize projections on rays for data collection, with particular emphasis on optical techniques. We formulate a variety of imaging techniques as either special cases or extensions of…
This paper presents several new algorithms for the regularized reconstruction of a surface from its measured gradient field. By taking a matrix-algebraic approach, we establish general framework for the regularized reconstruction problem…
In addition to color and textural information, geometry provides important cues for 3D scene reconstruction. However, current reconstruction methods only include geometry at the feature level thus not fully exploiting the geometric…
The problem of image reconstruction in thermoacoustic tomography requires inversion of a generalized Radon transform, which integrates the unknown function over circles in 2D or spheres in 3D. The paper investigates implementation of the…
This work proposes novel hyperparameter-free losses for single view 3D reconstruction with morphable models (3DMM). We dispense with the hyperparameters used in other works by exploiting geometry, so that the shape of the object and the…
A linear method for inverting noisy observations of the Radon transform is developed based on decomposition systems (needlets) with rapidly decaying elements induced by the Radon transform SVD basis. Upper bounds of the risk of the…
Ray-tracing-based 3D Gaussian splatting (3DGS) methods overcome the limitations of rasterization -- rigid pinhole camera assumptions, inaccurate shadows, and lack of native reflection or refraction -- but remain slower due to the cost of…
Reconstruction of the soft tissues in robotic surgery from endoscopic stereo videos is important for many applications such as intra-operative navigation and image-guided robotic surgery automation. Previous works on this task mainly rely…
The approximate discrete Radon transform (ADRT) is a hierarchical multiscale approximation of the Radon transform. In this paper, we factor the ADRT into a product of linear transforms that resemble convolutions and derive an explicit…
Tomography is a powerful technique for recovering the three-dimensional (3D) density structure of the global solar corona. In this work, we present an improved tomography method by introducing radial weighting in the regularization term.…
Reconstructing the 3D model of a physical object typically requires us to align the depth scans obtained from different camera poses into the same coordinate system. Solutions to this global alignment problem usually proceed in two steps.…