Fast approximate 4D:3D discrete Radon transform, from light field to focal stack with O(N<sup>4</sup>) sums

Marichal-Hernández, José G.; Luke, J. P.; Rosa, F.; Rodríguez-Ramos, José Manuel

doi:10.1117/12.872359

Cited by 6 publications

(5 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…DRT in dimension three. Just as the continuous Radon transform was defined in (2.1) for arbitrary number of dimensions n, the DRT can also be generalized to higher dimensions [26]. Here we treat the 3D case as an example.…”

Section: Inversion Of Drt With Conjugate Gradient Methodmentioning

confidence: 99%

Dimensional Splitting of Hyperbolic Partial Differential Equations Using the Radon Transform

Rim¹

2018

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

We introduce a dimensional splitting method based on the intertwining property of the Radon transform, with a particular focus on its applications related to hyperbolic partial differential equations (PDEs). This dimensional splitting has remarkable properties that makes it useful in a variety of contexts, including multi-dimensional extension of large time-step (LTS) methods, absorbing boundary conditions, displacement interpolation, and multi-dimensional generalization of transport reversal [34].

show abstract

Section: Inversion Of Drt With Conjugate Gradient Methodmentioning

confidence: 99%

Dimensional Splitting of Hyperbolic Partial Differential Equations Using the Radon Transform

Rim¹

2018

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

show abstract

“…But the plenopticity of the image is intact, proving that it is possible to transform any camera in a 3D sensor using our plenoptic objective. It is possible to increase the depth resolution with the algorithm proposed in Marichal-Hernández et al [14]. This would give refocused planes with equal to the number of pixels behind each microlens.…”

Section: ) Experimental Set-up Alignment and Calibrationmentioning

confidence: 98%

Design and Laboratory Results of a Plenoptic Objective: From 2D to 3D With a Standard Camera

Montilla

Puga

Luke

et al. 2015

J. Display Technol.

View full text Add to dashboard Cite

The plenoptic camera was originally created to allow the capture of the light field, a four-variable volume representation of all rays and their directions, which allows the creation by synthesis of an image of the observed object. This method has several advantages with regard to 3D capture systems based on stereo cameras since it does not need frame synchronization or geometric and color calibration. It also has many applications, from 3DTV to medical imaging. A plenoptic camera uses a microlens array to measure the radiance and direction of all the light rays in a scene. The array is placed at a distance from the principal lens, which is conjugated to the distance where the scene is situated, and the sensor is at the focal plane of the microlenses. We have designed a plenoptic objective that incorporates a microlens array and a relay system that reimages the microlens plane. This novel approach has proven successful. Placing it on a camera, the plenoptic objective creates a virtual microlens plane in front of the camera CCD, allowing it to capture the light field of the scene. In this paper we present the experimental results showing that depth information is perfectly captured when using an external plenoptic objective. Using this objective transforms any camera into a 3D sensor, opening up a wide range of applications from microscopy to astronomy.

show abstract

“…Another body of works uses the Fourier Slice Theorem [5,22,7]. The Fourier Slice Digital Refocusing method [27] proves that spatial light field refocusing is equal to computing the Fourier transform of a 4D light field, selecting a relevant 2D slice and then performing 2D inverse Fourier transform.…”

Section: Related Workmentioning

confidence: 99%

Deep Sparse Light Field Refocusing

Dayan¹,

Mendlovic²,

Giryes³

2020

Preprint

View full text Add to dashboard Cite

Light field photography enables to record 4D images, containing angular information alongside spatial information of the scene. One of the important applications of light field imaging is post-capture refocusing. Current methods require for this purpose a dense field of angle views; those can be acquired with a micro-lens system or with a compressive system. Both techniques have major drawbacks to consider, including bulky structures and angular-spatial resolution trade-off. We present a novel implementation of digital refocusing based on sparse angular information using neural networks. This allows recording high spatial resolution in favor of the angular resolution, thus, enabling to design compact and simple devices with improved hardware as well as better performance of compressive systems. We use a novel convolutional neural network whose relatively small structure enables fast reconstruction with low memory consumption. Moreover, it allows handling without retraining various refocusing ranges and noise levels. Results show major improvement compared to existing methods.

show abstract

Fast approximate 4D:3D discrete Radon transform, from light field to focal stack with O(N⁴) sums

Cited by 6 publications

References 12 publications

Dimensional Splitting of Hyperbolic Partial Differential Equations Using the Radon Transform

Dimensional Splitting of Hyperbolic Partial Differential Equations Using the Radon Transform

Design and Laboratory Results of a Plenoptic Objective: From 2D to 3D With a Standard Camera

Deep Sparse Light Field Refocusing

Contact Info

Product

Resources

About

Fast approximate 4D:3D discrete Radon transform, from light field to focal stack with O(N4) sums

Cited by 6 publications

References 12 publications

Dimensional Splitting of Hyperbolic Partial Differential Equations Using the Radon Transform

Dimensional Splitting of Hyperbolic Partial Differential Equations Using the Radon Transform

Design and Laboratory Results of a Plenoptic Objective: From 2D to 3D With a Standard Camera

Deep Sparse Light Field Refocusing

Contact Info

Product

Resources

About

Fast approximate 4D:3D discrete Radon transform, from light field to focal stack with O(N⁴) sums