Harmonic analysis of framelets and applications to image processing

2014 Fiscal Year Final Research Report

• Project/Area Number: 23540123
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: The University of Tokyo
• Principal Investigator: ARAI Hitoshi 東京大学, 数理(科)学研究科(研究院), 教授 (10175953)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: フレームレット / かざぐるまフレームレット / 画像処理 / 錯視

Outline of Final Research Achievements

I established with S. Arai new framelets, simple pinwheel framelets and pinwheel framelets, in 2009. So far I studied applications of pinwheel framelets to image processing and image processing related to visual illusions. The purpose of this project is to study mathematical properties of pinwheel frameletes, and image processing by using these framelets. Some of main results are the following: variants of pinwheel framelets, and stereoscopic edge detection. The latter was obtained by using pinwheel framelets. I was concerned with case studies of stereoscopic edge detection as well as other image processing by using pinwheel framelets. I expect that results by this project will contribute to innovation by mathematics.

Free Research Field

数学