Preprint / Version 1

Redundant Wavelet Transform by Range-Fourier Series Expansion

##article.authors##

  • Kohei Hayashi Graduate School of Engineering, Nagoya Institute of Technology
  • Soichiro Honda Graduate School of Engineering, Nagoya Institute of Technology
  • Hirokazu Kamei Graduate School of Engineering, Nagoya Institute of Technology
  • Yoshihiro Maeda College of Engineering, Shibaura Institute of Technology https://researchmap.jp/yoshihiromaeda
  • Norishige Fukushima Graduate School of Engineering, Nagoya Institute of Technology https://researchmap.jp/read0153731/

DOI:

https://doi.org/10.51094/jxiv.761

Keywords:

edge-preserving smoothing, edge-aware enhancement, wavelet transfrom, scale-space

Abstract

スケールスペースフィルタリングは,スケールに応じて画像をベース信号と詳細信号に分解する画像解析の基本的な処理の一つである.このスケールスペースフィルタリングを画像強調に用いるには,詳細信号の係数を増幅させて再構成すればよい.しかしながら急峻なエッジ付近では詳細係数が大きくなるため,その係数を線形に増幅するとオーバーフロー・アンダーフローが発生し,それが halo と呼ばれる「もや」として生じる.
古典的方法として,様々な非線形変換により詳細信号の増幅を抑える方法が取られてきたが輪郭のエッジ付近の応答は非常に大きいため完全な halo 抑制は難しい.そこでエッジ保存平滑化フィルタを用いた分解や,ローカルラプラシアンフィルタなどの局所コントラスト変換を用いたピラミッド分解が提案されてきた.
しかし,局所コントラスト手法で取り扱うことができる現状のピラミッド表現だけでは多様な信号をとらえて解析することは難しい.そこで本論文では,信号解析の中核となるウェーブレット変換を対象として,局所コントラストアダプティブなウェーブレット変換(local contrast adaptive wavelet transform; LCA-WT)を提案する.そして,LCA-WTを値域のフーリエ級数展開を用いた冗長ウェーブレット変換で表す高速化計算方法を提案し,それは画像固有のウェーブレット変換であり,パラメータに依存しない変換であるその形式が新しいウェーブレット変換表現の一つであることを示す.実験の結果,提案手法は少ない回数のウェーブレット変換の線形結合により実現できることを示すとともに,LCA-WTによる係数操作により,方向性画像強調,ガイド付き処理,ウェーブレット合成などのいくつかの画像処理応用が可能なことが示された.

Conflicts of Interest Disclosure

The authors have no conflicts of interest to report.

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Submitted: 2024-06-20 17:39:49 UTC

Published: 2024-06-28 05:40:55 UTC
Section
Information Sciences