2007 Fiscal Year Final Research Report Summary
A Study of Image Recognition by Statistics, Machine Learning, and Partial differential equations
| Project/Area Number |
17540122
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kyushu University |
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Principal Investigator |
SAKATA Toshio Kyushu University, Faculty of Design, Professor (20117352)
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| Co-Investigator(Kenkyū-buntansha) |
NISHII Ryuei Kyuhsu University, Faculty of Mathematics, Professor (40127684)
SAWAE Ryuichi Okayama University of Science, Faculty of Science, 教授 (20226062)
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| Project Period (FY) |
2005 – 2007
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| Keywords | Statistical and machine learning Image recognition / Inpainting by partial equation methods / Tensor data / Maximal rank of a tensor / Application of Groebner Basis / Segre map / Color inpainting / Recovery of Old documents and old statue photos |
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| Research Abstract |
The purpose of this project was to attack various image recognition problems through a unified way of statistical and machine learning and partial differential equation methods, and as a feedback develop the theory itself First year we explored mainly by machine learning method, and proposed cross entropy based kernel LVQ to solve the recognition of old language, Estrangelo, and proposed iterative kernel PCA for eye glass removing. The result of this were reported in the conference of Computational Statistical Data Analysis in Cypros (presentation[19],[20],[21]). In the second year we explored the inpainting problem of hand written old documents ofEstrangelo by a partial differential equation method. This was reported in the paper [9]. At the same time we explored to handle image data as the tensor data For a basics of this problem we encountered the maximal rank problem of a set of tensors. We proposed to solve the problem for small size cases by using the elimination idela of Groebne
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r basis theory (the paper [8]) and talked in several symposiums (presentions [15],[16],[17]), and published in the book [17]. In the third year we attacked the color inpainting problem by partial equation method, by solving a Poisson equation to recover the color of the old photos of old Japanese statues (the papers [1],[2]). The result is still unsatisfactory however some insights useful for the future work were obtained. An idea is that color axis may be chosen adaptively case by case. Also, in this year, for the tensor ranking problem I proposed “zero forcing method" and pursued the related topics ( the papers [4],[5]). The result about NTF was also reported in the papers [3]. An application to recover the color of photos of statues is very attractive topics, as color image inpainting is related also to Sparse coding and ICA, this line will be pursued in the future our work.. Statistical theory based on tensors will be developed more comprehensively in our future research. Prof. Nishii worked in the field of recognition of remote sensing image data by using machine learning method and published several papers for international journals [6,[10],[16] and gave talks at many international conferences. Prof. Sawae explored the filed of Quantum computing [7],[11][13],[14]. He also gave talks at many international conference. It is very interesting his research might have a connection to tensor data analysis through Segre map. Also their basic research might have a connection to image data storage method in the future. We will unify over handred programs build for the study. Less
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Research Products
(106 results)
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[Presentation] 仏像写真の数理的色彩復元法の試論2007
Author(s)
坂田年男, 竹之内和樹, 能野謙介, 前原一満, 堀内隆彦(2007). 奈良, Dec. 2007.
Organizer
第13回「公開シンポジウム人文科学とデータベース」
Place of Presentation
奈良女子大学コラボレーションセンター
Year and Date
2007-12-22
Description
「研究成果報告書概要(和文)」より
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[Presentation] A simple error correction method for NMR quantum computer2006
Author(s)
Minaru Kawamura, Takuji Mori moto, Yoshiyuki Mori, Ryuichi Sawae and, et al.
Organizer
The 8th International Conference on Quantum Communication, Measurement and Computing
Place of Presentation
Tsukuba International Congress Center, Japan
Year and Date
20061128-20061203
Description
「研究成果報告書概要(和文)」より
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[Presentation] Creation Operators for three way tables2005
Author(s)
Toshio Sakata, Rvuichi Sawae(2005).
Organizer
International Conference on Theoretical Effectivity and Practical Effectivity of Groebner Bases
Place of Presentation
Rikkyo Univ
Year and Date
20050822-20050826
Description
「研究成果報告書概要(和文)」より
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