权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

A Study of Image Recognition by Statistics, Machine Learning, and Partial differential equations

通过统计学、机器学习和偏微分方程进行图像识别的研究

基本信息

批准号：
17540122
负责人：
SAKATA Toshio
金额：
$ 1.61万
依托单位：
Kyushu University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2005
资助国家：
日本
起止时间：
2005 至 2007
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17540122/
关键词：
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 テンソルデータ

项目摘要

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 … More 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

本项目的目的是通过统计和机器学习以及偏微分方程方法的统一方法来解决各种图像识别问题，并作为反馈发展理论本身，第一年我们主要通过机器学习的方法进行探索，提出了基于交叉熵的核LVQ来解决旧语言Estragelo的识别问题，并提出了迭代核PCA来去除眼镜。这一结果在计算统计数据分析会议上作了报告(介绍[19]、[20]、[21])。第二年，我们用偏微分方程法研究了埃斯特兰克罗手写古籍的修复问题。这一点在论文[9]中得到了报道。同时，我们探索将图像数据作为张量数据来处理，对于这个问题的一个基本问题，我们遇到了张量集的最大秩问题。我们提出了利用Groebne…的消去法来解决小尺寸问题。更多的基本理论(论文[8])，并在几个专题讨论会(演示文稿[15]、[16]、[17])中讨论，并发表在书[17]中。在第三年，我们用偏方程法解决了彩色修复问题，通过求解泊松方程来恢复日本老雕像的旧照片的颜色(文献[1]，[2])。研究结果仍然不尽如人意，但也得到了一些对今后工作有益的见解。一种想法是，颜色轴可以根据情况自适应地选择。另外，在这一年里，对于张量排序问题，我提出了“迫零法”，并进行了相关的研究(文献[4]、[5])。文献[3]也报道了有关NTF的研究结果。一个应用于雕像照片的颜色恢复是非常吸引人的话题，因为彩色图像修复也与稀疏编码和独立分量分析有关，这条线将在我们未来的工作中继续下去。基于张量的统计理论将在未来的研究中得到更全面的发展。西井教授致力于利用机器学习方法识别遥感图像数据，并在国际期刊[6，[10]，[16]上发表了多篇论文，并在许多国际会议上发表了演讲。Sawae教授探索了量子计算领域[7]、[11][13]、[14]。他还在许多国际会议上发表了演讲。非常有趣的是，他的研究可能与通过Segre映射进行张量数据分析有关。此外，他们的基础研究可能与未来的图像数据存储方法有关。我们将统一为研究建立的手工程序。较少