Geometric tomography is a mathematical field that focuses on problems of reconstructing homogeneous (often convex) objects from tomographic data (this might be X-rays, projections, sections, brightness functions, or covariograms). More precisely, according to R.J. Gardner (who introduced the term), "Geometric tomography deals with the retrieval of information about a geometric object from data concerning its projections (shadows) on planes or cross-sections by planes." (Wikipedia).
Example: Ray Tracing with a Diverging Lens
In this video, we find the image and perform ray tracing for a real object and a diverginglens. We find the magnification, image location, and find out whether the image is real or virtual. To support the creation of videos like these, get early access, access to a community, behind-the
From playlist Geometric Optics
Ray Tracing Virtual Objects with a Diverging Lens - Real Image
In this video, I describe how to find the image location and magnification when we have a virtual object imaged by a diverging lens, and how to do the ray tracing in that situation. To support the creation of videos like these, get early access, access to a community, behind-the scenes a
From playlist Geometric Optics
Ray Tracing Virtual Objects with a Diverging Lens - Virtual Image
In this video, I describe how to find the image location and magnification when we have a virtual object imaged by a diverging lens, and how to do the ray tracing in that situation. To support the creation of videos like these, get early access, access to a community, behind-the scenes a
From playlist Geometric Optics
Example: Two-Lens Imaging with converging lenses
In this video, we go over how to trace rays through a two-lens system, and how to calculate the overall magnification, image location, and whether the image is real or virtual. To support the creation of videos like these, get early access, access to a community, behind-the scenes and mo
From playlist Geometric Optics
Geometric Algebra - The Matrix Representation of a Linear Transformation
In this video, we will show how matrices as computational tools may conveniently represent the action of a linear transformation upon a given basis. We will prove that conventional matrix operations, particularly matrix multiplication, conform to the composition of linear transformations.
From playlist Geometric Algebra
Working with lenses, trying to visualize refractive indices. Things are going well-ish. -- Watch live at https://www.twitch.tv/simuleios
From playlist Geometrical Optics
Ray Tracing Virtual Objects with a Converging Lens
In this video, I describe how to find the image location and magnification when we have a virtual object imaged by a converging lens, and how to do the ray tracing in that situation. To support the creation of videos like these, get early access, access to a community, behind-the scenes
From playlist Geometric Optics
Adding Vectors Geometrically: Dynamic Illustration
Link: https://www.geogebra.org/m/tsBer5An
From playlist Trigonometry: Dynamic Interactives!
Lecture 29 | The Fourier Transforms and its Applications
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues to lecture on the general stretch theorem and begins covering medical imaging. The Fourier transform is a tool for solving physical p
From playlist Lecture Collection | The Fourier Transforms and Its Applications
Tim Salditt - Phase Retrieval & Tomographic Reconstruction in X-ray Near-field Diffractive Imaging
Recorded 11 October 2022. Tim Salditt of the Georg-August-Universität zu Göttingen presents "Phase Retrieval and Tomographic Reconstruction in X-ray Near-field Diffractive Imaging: Inverse Problems at Work - An Experimentalist’s View" at IPAM's Diffractive Imaging with Phase Retrieval Work
From playlist 2022 Diffractive Imaging with Phase Retrieval - - Computational Microscopy
Martin Hazelton - Dynamic fibre samplers for linear inverse problems
Professor Martin Hazelton (University of Otago) presents “Dynamic fibre samplers for linear inverse problems”, 23 October 2020 (seminar organised by UNSW).
From playlist Statistics Across Campuses
Samuli Siltanen: Reconstruction methods for ill-posed inverse problems - Part 1
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Partial Differential Equations
Generalized Radon transforms in tomography
Advanced Instructional School on Theoretical and Numerical Aspects of Inverse Problems URL: https://www.icts.res.in/program/IP2014 Dates: Monday 16 Jun, 2014 - Saturday 28 Jun, 2014 Description In Inverse Problems the goal is to determine the properties of the interior of an object from
From playlist Advanced Instructional School on Theoretical and Numerical Aspects of Inverse Problems
Well, we got another function written, one more to go! -- Watch live at https://www.twitch.tv/simuleios
From playlist Geometrical Optics
Quantum mechanics is famous for its uncertainty principle that limits what you can measure. But oddly enough, quantum effects can actually help scientists make *better* measurements. This is what the field of quantum metrology is concerned with. In this video I explain what quantum metrolo
From playlist Physics
Barbara Kaltenbacher: Imaging with nonlinear and fractionally damped waves
The importance of ultrasound is well established in the imaging of human tissue. In order to enhance image quality by exploiting nonlinear effects, recently techniques such as harmonic imaging and nonlinearity parameter tomography have been put forward. These lead to a coefficient identifi
From playlist Analysis and its Applications
Demetri Psaltis - Machine Learning for 3D Optical Imaging - IPAM at UCLA
Recorded 13 October 2022. Demetri Psaltis of the École Polytechnique Fédérale de Lausanne (EPFL) presents "Machine Learning for 3D Optical Imaging" at IPAM's Diffractive Imaging with Phase Retrieval Workshop. Abstract: In optical diffraction tomography (ODT), the 3D shape of an object is r
From playlist 2022 Diffractive Imaging with Phase Retrieval - - Computational Microscopy
Generalized Radon transforms in tomography
Advanced Instructional School on Theoretical and Numerical Aspects of Inverse Problems URL: https://www.icts.res.in/program/IP2014 Dates: Monday 16 Jun, 2014 - Saturday 28 Jun, 2014 Description In Inverse Problems the goal is to determine the properties of the interior of an object from
From playlist Advanced Instructional School on Theoretical and Numerical Aspects of Inverse Problems
Fellow Short Talks: Dr Carola-Bibiane Schönlieb, Cambridge University
Carola-Bibiane Schönlieb is a Reader in Applied and Computational Analysis at the Department of Applied Mathematics and Theoretical Physics (DAMTP), University of Cambridge since 2015. There, she is head of the Cambridge Image Analysis group, Director of the Cantab Capital Institute for Ma
From playlist Short Talks
Well, we got it working after some fuss -- Watch live at https://www.twitch.tv/simuleios
From playlist Geometrical Optics