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Related Concept Videos

Position and Displacement Vectors01:00

Position and Displacement Vectors

To describe the motion of an object, one should first be able to describe its position (where it is at any particular time). More precisely, the position needs to be specified relative to a convenient frame of reference. A frame of reference is an arbitrary set of axes from which the position and motion of an object are described. Earth is often used as a frame of reference to describe the position of an object in relation to stationary objects on Earth.
Further, several important kinds of...
Position and Displacement Vectors01:00

Position and Displacement Vectors

To describe the motion of an object, one should first be able to describe its position (where it is at any particular time). More precisely, the position needs to be specified relative to a convenient frame of reference. A frame of reference is an arbitrary set of axes from which the position and motion of an object are described. Earth is often used as a frame of reference to describe the position of an object in relation to stationary objects on Earth.
Further, several important kinds of...
Position and Displacement01:31

Position and Displacement

The position of an object defines its location relative to a convenient frame of reference at any particular time. A frame of reference is an arbitrary set of axes from which the position and motion of an object are described. Earth is often used as a frame of reference, and we often describe the position of an object as it relates to stationary objects on Earth. For example, a rocket launch could be described in terms of the position of the rocket with respect to Earth as a whole. On the other...
Position and Displacement01:31

Position and Displacement

The position of an object defines its location relative to a convenient frame of reference at any particular time. A frame of reference is an arbitrary set of axes from which the position and motion of an object are described. Earth is often used as a frame of reference, and we often describe the position of an object as it relates to stationary objects on Earth. For example, a rocket launch could be described in terms of the position of the rocket with respect to Earth as a whole. On the other...
Position Vectors01:29

Position Vectors

A position vector is a fundamental concept in mathematics that helps determine the position of one point with respect to another point in space. It is a vector that describes the direction and distance between two points. Position vectors are highly useful in the field of math and science, as they help represent spatial relationships and make calculations easier.
For instance, we want to locate a point P(x, y, z) relative to the origin of coordinates O. In that case, we can define a position...
Depth Perception and Spatial Vision01:15

Depth Perception and Spatial Vision

Depth perception is the ability to perceive objects three-dimensionally. It relies on two types of cues: binocular and monocular. Binocular cues depend on the combination of images from both eyes and how the eyes work together. Since the eyes are in slightly different positions, each eye captures a slightly different image. This disparity between images, known as binocular disparity, helps the brain interpret depth. When the brain compares these images, it determines the distance to an object.

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Related Experiment Video

Updated: May 9, 2026

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine
07:05

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine

Published on: October 27, 2016

Diffusion-Shock PDEs for Deep Learning on Position-Orientation Space.

Finn M Sherry1, Kristina Schaefer2, Remco Duits1

  • 1CASA and EAISI, Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands.

Journal of Mathematical Imaging and Vision
|May 8, 2026
PubMed
Summary
This summary is machine-generated.

Regularised diffusion-shock (RDS) filtering is extended to position-orientation space, significantly improving the enhancement and inpainting of crossing structures in images. This new method outperforms existing techniques, offering better denoising and restoration capabilities.

Keywords:
Crossing preservingDiffusion–shock filterEquivariant neural networksGeometric deep learningRegularisation

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End-To-End Deep Neural Network for Salient Object Detection in Complex Environments
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End-To-End Deep Neural Network for Salient Object Detection in Complex Environments

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Related Experiment Videos

Last Updated: May 9, 2026

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine
07:05

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine

Published on: October 27, 2016

End-To-End Deep Neural Network for Salient Object Detection in Complex Environments
03:31

End-To-End Deep Neural Network for Salient Object Detection in Complex Environments

Published on: December 15, 2023

Area of Science:

  • Computer Vision
  • Image Processing
  • Differential Geometry

Background:

  • Regularised diffusion-shock (RDS) filtering is an effective image processing technique.
  • Extending RDS filtering to position-orientation space offers potential advantages for handling complex image structures.

Purpose of the Study:

  • To extend regularised diffusion-shock (RDS) filtering from Euclidean space to position-orientation space.
  • To enhance and inpaint crossing structures in images more effectively.
  • To develop a generalized diffusion framework for image processing tasks.

Main Methods:

  • Lifting image data to position-orientation space (M2).
  • Utilizing gauge frames to mitigate orientation lifting issues.
  • Developing generalized diffusion equations not solely reliant on the Laplace-Beltrami operator.
  • Integrating RDS filtering into a geometric deep learning framework (PDE-CNN, PDE-G-CNN).

Main Results:

  • The extended RDS filtering successfully disentangles and enhances crossing structures in position-orientation space.
  • RDS filtering in M2 demonstrates superior performance in denoising images with crossing structures compared to TR-TV flow, NLM, and BM3D.
  • M2 RDS inpainting effectively restores crossing structures, unlike its R2 counterpart.
  • Theoretical results confirm the well-posedness, smoothing, and analytic properties of the generalized diffusions.
  • New RDS filtering PDE layers integrated into deep learning frameworks show benefits in impainting and denoising tasks.

Conclusions:

  • Extending RDS filtering to position-orientation space is a significant advancement for image processing, particularly for images with crossing structures.
  • The developed gauge frame approach and generalized diffusion framework offer robust solutions.
  • The integration with geometric deep learning provides a powerful and versatile tool for various image restoration tasks.