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3D Gaussian Splatting (3DGS) has recently emerged in computer vision as a promising rendering technique. By adapting the principles of Elliptical Weighted Average (EWA) splatting to a modern differentiable pipeline, 3DGS enables real-time,…
The concept of Gaussian process tomography along with nonnegative constraints is applied in the context of high-resolution image reconstruction using segmented planar detectors with few readout channels.Expanding on the concept of 2-D…
Electron tomography is a widely used technique for 3D structural analysis of nanomaterials, but it can cause damage to samples due to high electron doses and long exposure times. To minimize such damage, researchers often reduce beam…
We propose a novel explicit dense 3D reconstruction approach that processes a set of images of a scene with sensor poses and calibrations and estimates a photo-real digital model. One of the key innovations is that the underlying volumetric…
Computed tomography (CT) has been developed as a non-destructive technique for observing minute internal images of samples. It has been difficult to obtain photo-realistic (clean or clear) CT images due to various unwanted artifacts…
3D dense reconstruction refers to the process of obtaining the complete shape and texture features of 3D objects from 2D planar images. 3D reconstruction is an important and extensively studied problem, but it is far from being solved. This…
Electron tomographic reconstruction is a method for obtaining a three-dimensional image of a specimen with a series of two dimensional microscope images taken from different viewing angles. Filtered backprojection, one of the most popular…
This paper tackles the task of uncalibrated photometric stereo for 3D object reconstruction, where both the object shape, object reflectance, and lighting directions are unknown. This is an extremely difficult task, and the challenge is…
Light detection and ranging (Lidar) data can be used to capture the depth and intensity profile of a 3D scene. This modality relies on constructing, for each pixel, a histogram of time delays between emitted light pulses and detected photon…
Uncompressed clinical data from modern positron emission tomography (PET) scanners are very large, exceeding 350 million data points (projection bins). The last decades have seen tremendous advancements in mathematical imaging tools many of…
Reconstructing the 3D shape of an object using several images under different light sources is a very challenging task, especially when realistic assumptions such as light propagation and attenuation, perspective viewing geometry and…
We consider the weighted Radon transforms $R_W$ along hyperplanes in $R^d, \, d \geq 3$, with strictly positive weights $W = W (x, \theta), \, x \in R^d, \, \theta \in S^{d-1}$. We construct an example of such a transform with non-trivial…
Time-resolved CT is an advanced measurement technique that has been widely used to observe dynamic objects, including periodically varying structures such as hearts, lungs, or hearing structures. To reconstruct these objects from CT…
We introduce ART, Articulated Reconstruction Transformer -- a category-agnostic, feed-forward model that reconstructs complete 3D articulated objects from only sparse, multi-state RGB images. Previous methods for articulated object…
Inverse rendering methods that account for global illumination are becoming more popular, but current methods require evaluating and automatically differentiating millions of path integrals by tracing multiple light bounces, which remains…
Reconstructing 2D freehand Ultrasound (US) frames into 3D space without using a tracker has recently seen advances with deep learning. Predicting good frame-to-frame rigid transformations is often accepted as the learning objective,…
Mathematical methods of step-by-step and combined shifts are proposed for experimental data processing to reconstruct the measuring system impulse response distorted by shift-invariant blur. Proposed methods base on direct non-blind…
We give new formulas for reconstructions from band-limited Hankel transform of integer or half-integer order. Our formulas rely on the PSWF-Radon approach to super-resolution in multidimensional Fourier analysis. This approach consists of…
The image reconstruction problem consists in finding an approximation of a function f starting from its Radon transform Rf. This problem arises in the ambit of medical imaging when one tries to reconstruct the internal structure of the…
This work extends the applicability of our recent convexification-based algorithm for constructing images of the dielectric constant of buried or occluded target. We are orientated towards the detection of explosive-like targets such as…