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Related Experiment Video

Updated: May 22, 2026

High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques
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Published on: December 3, 2013

Improvements on "Fast space-variant elliptical filtering using box splines".

Kunal Narayan Chaudhury1, Sebanti Sanyal

  • 1Applied and Computational Mathematics Program, Princeton University, Princeton, NJ 08544-1000, USA. kchaudhu@math.princeton.edu

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|May 15, 2012
PubMed
Summary

This study improves a constant-time algorithm for space-variant filtering using Gaussian-like kernels. The enhanced method offers better control over filter shape and accuracy for Gaussian approximations.

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Last Updated: May 22, 2026

High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques
11:34

High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques

Published on: December 3, 2013

Area of Science:

  • Computer Vision
  • Image Processing
  • Computational Mathematics

Background:

  • Box filters are efficiently computed using pre-integration and finite-differences.
  • Previous work proposed a constant-time algorithm for space-variant filtering with Gaussian-like kernels, approximating Gaussians with box splines.
  • This algorithm offered continuous control over filter shape and size (covariance) with fixed computational cost.

Purpose of the Study:

  • To improve a previously developed constant-time algorithm for space-variant filtering.
  • To enhance control over the covariance and accuracy of Gaussian approximations in filtering.
  • To refine the use of box splines for approximating Gaussian kernels in image processing.

Main Methods:

  • Generalizing pre-integration and finite-difference techniques for box filters.
  • Applying a nonstandard variant of the central limit theorem.
  • Utilizing bivariate splines (box splines) for approximating Gaussian kernels.

Main Results:

  • The original algorithm allowed for O(1) computation of space-variant filtering.
  • It provided continuous control over filter covariance and fixed computational cost per pixel.
  • Limitations included restricted control over covariance and approximation accuracy.

Conclusions:

  • The proposed improvements address limitations in covariance control and accuracy of the previous algorithm.
  • The enhanced method offers more precise space-variant filtering using Gaussian-like kernels.
  • Further refinements in approximating Gaussian kernels with box splines are presented.