Mathematical study on human vision by using framelets and its applications to image processing

2018 Fiscal Year Final Research Report

• Project/Area Number: 15H03629
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Waseda University (2018); The University of Tokyo (2015-2017)
• Principal Investigator: Arai Hitoshi 早稲田大学, 教育・総合科学学術院, 教授 (10175953)
• Project Period (FY): 2015-04-01 – 2019-03-31
• Keywords: 錯視 / かざぐるまフレームレット / 画像処理

Outline of Final Research Achievements

Main theme of my research is study on image processing and visual illusions using mathematical analysis method devised by myself. The main results are as follows: 1. New sharpening techniques for still and moving images from the viewpoint of constructing a hypervision system which is based on the mathematical model of visual perception by H. Arai and S. Arai. This techniques enable us sharpening that looks close to our visual perception. 2. A new type of super hybrid imaging technology which is developed from super hybrid imaging technology due to H. Arai and S. Arai. 3. An image sharpening technique by applying a visual illusion caused by a new type of edge by H.Arai and S. Arai. 4. Improving the filtering method and the visual illusion generation technology by using the levels of generalized multiresolution analysis of pinwheel framelets.

Free Research Field

数学

Academic Significance and Societal Importance of the Research Achievements

本研究の学術的意義は，独自に考案した数理解析的方法により，新しいタイプのスーパーハイブリッド画像，超視覚システムによる静止画及び動画像鮮鋭化，新しいタイプのエッジに起因する錯視を用いた鮮鋭化，かざぐるまフレームレット構造を用いたフィルタ処理など，画像処理技術や錯視アート作成に役立つ成果が得られたことである．本研究成果の一部は他の基盤的成果と合わせて国際特許出願した．なお本研究成果の一部（鮮鋭化）は朝日新聞（2018/11/24）でカラー画像付きで取り上げられた．また本研究成果を含む新井仁之のこれまでの研究の学術的・社会的意義は高く評価され，2018年に第7回藤原洋数理科学賞大賞が授与された．