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

本课题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式来解决各种图像识别问题，并作为理论本身的反馈发展。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来解决旧语言的识别，隔阂，并提出了迭代核PCA用于眼镜去除。这一结果在Cypros计算统计数据分析会议上报告（演示[19]，[20],[21]）。在第二年，我们用偏微分方程的方法探讨了手写旧文件的喷漆问题。论文b[9]报道了这一点。同时，我们探索将图像数据作为张量数据来处理，作为这个问题的基础，我们遇到了一组张量的最大秩问题。我们提出了利用Groebne…More r基理论的消去思想来解决小尺寸情况下的问题（论文[8]），并在几个研讨会上进行了讨论（演讲[15]，[16],[17]），并发表在[17]一书中。第三年，我们用偏方程方法解决了上色问题，通过求解泊松方程来恢复日本老雕像的老照片的颜色（论文[1]，[2]）。虽然结果还不能令人满意，但是得到了一些对今后工作有用的见解。一个想法是，颜色轴可以根据情况自适应地选择。此外，在这一年，对于张量排序问题，我提出了“零强迫法”，并进行了相关课题的研究（论文[4]，[5]）。关于NTF的研究结果也见于b[3]。应用于雕像照片的颜色恢复是一个非常有吸引力的话题，因为绘画中的彩色图像也与稀疏编码和ICA相关，这将是我们未来工作的方向。基于张量的统计理论将在今后的研究中得到更全面的发展。Nishii教授致力于利用机器学习方法识别遥感图像数据领域，在国际期刊上发表多篇论文[6，[10],[16]]，并在多个国际会议上发表演讲。Sawae教授在量子计算领域进行了[7]，b[11],[13]，[14]的研究。他还在许多国际会议上发表演讲。非常有趣的是，他的研究可能与通过Segre map进行张量数据分析有关。他们的基础研究也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数百个程序。少

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