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Divergence Theorem in 3D Space01:20

Divergence Theorem in 3D Space

In vector calculus, flux measures the total flow of a vector field through a surface. For a closed surface in three-dimensional space, this means measuring how much of the field passes outward through every point on the boundary. Directly calculating this flux can be difficult when the surface has a complicated or irregular shape. The Divergence Theorem provides a powerful alternative by relating surface flux to behavior inside the enclosed region.The Divergence Theorem states that the outward...

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Related Experiment Video

Updated: Jun 28, 2026

High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques
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Time-Distributed Framework for 3D Reconstruction Integrating Fringe Projection with Deep Learning.

Andrew-Hieu Nguyen1, Zhaoyang Wang2

  • 1Neuroimaging Research Branch, National Institute on Drug Abuse, National Institutes of Health, Baltimore, MD 21224, USA.

Sensors (Basel, Switzerland)
|August 26, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces a novel deep learning method for 3D shape reconstruction using temporal structured light. The time-distributed approach enhances accuracy and practicality for dynamic applications.

Keywords:
convolutional neural networkdeep learningfringe-to-phase transformationsingle-shot imagingthree-dimensional image acquisitionthree-dimensional sensing

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Area of Science:

  • Computer Vision
  • Optical Metrology
  • Machine Learning

Background:

  • Structured light techniques combined with deep learning offer high precision for 3D shape reconstruction.
  • Existing methods often process data in the spatial domain, limiting applications with dynamic scenes.

Purpose of the Study:

  • To propose a novel time-distributed deep learning approach for temporal structured-light 3D shape reconstruction.
  • To enhance the accuracy and practicality of 3D shape reconstruction for dynamic scenarios.

Main Methods:

  • Utilized an autoencoder network and a time-distributed wrapper for processing temporal fringe patterns.
  • Employed fringe projection profilometry (FPP) for ground truth generation and process depiction.
  • Converted fringe patterns into arctangent function numerators and denominators.

Main Results:

  • The time-distributed 3D reconstruction achieved comparable results to dual-frequency datasets (p = 0.014).
  • Demonstrated significantly higher accuracy than triple-frequency datasets (p = 1.029 × 10-9) via statistical tests.
  • The single-network training approach proved practical for diverse applications.

Conclusions:

  • The proposed time-distributed deep learning method offers a robust and accurate solution for temporal structured-light 3D shape reconstruction.
  • This approach is highly practical for both scientific research and industrial applications due to its simplified implementation.
  • The technique shows significant potential for advancing dynamic 3D measurement capabilities.