Efficient Constant-time Gaussian Filtering with Sliding DCT/DST-5and Dual-domain Error Minimization

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17 Citations (Scopus)

Abstract

This paper presents an efficient constant-time algorithm for Gaussian filtering and also Gaussian derivative filtering that provides a high approximate accuracy in a low computational complexity regardless of its filter window size. The proposed algorithm consists of two key techniques: second-order shift properties of the Discrete Cosine/Sine Transforms type-5 and dual-domain error minimization for finding optimal parameters. The former enables us to perform filtering in fewer number of arithmetic operations as compared than some state-of-the-art algorithms without integral images. The latter enables us to find the optimal filter size that provides the most accurate filter kernel approximation. Experiments show that the proposed algorithm clearly outperforms state-of-the-art ones in computational complexity, approximate accuracy, and accuracy stability.

Original languageEnglish
Pages (from-to)12-21
Number of pages10
JournalITE Transactions on Media Technology and Applications
Volume3
Issue number1
Publication statusPublished - 2015

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Computational complexity
Mathematical transformations
Derivatives
Experiments

Keywords

  • Constant-time derivative Gaussian filtering
  • Constant-time Gaussian filtering
  • Frequency sampling method
  • Second-order shift property
  • Sliding DCT/DST

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Signal Processing
  • Media Technology

Cite this

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AB - This paper presents an efficient constant-time algorithm for Gaussian filtering and also Gaussian derivative filtering that provides a high approximate accuracy in a low computational complexity regardless of its filter window size. The proposed algorithm consists of two key techniques: second-order shift properties of the Discrete Cosine/Sine Transforms type-5 and dual-domain error minimization for finding optimal parameters. The former enables us to perform filtering in fewer number of arithmetic operations as compared than some state-of-the-art algorithms without integral images. The latter enables us to find the optimal filter size that provides the most accurate filter kernel approximation. Experiments show that the proposed algorithm clearly outperforms state-of-the-art ones in computational complexity, approximate accuracy, and accuracy stability.

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