在本文中,我们研究了拓扑数据分析中的欧拉特征技术。逐点计算由数据构建的单纯复形族的欧拉特征会产生所谓的欧拉特征轮廓。我们表明,这个简单的描述符以极低的计算成本在监督任务中实现了最先进的性能。受信号分析的启发,我们计算了欧拉特征轮廓的混合变换。这些积分变换将欧拉特征技术与勒贝格积分相结合,以提供高效的拓扑信号压缩器。因此,它们在无监督环境中表现出色。在定性方面,我们对欧拉轮廓及其混合变换捕获的拓扑和几何信息提供了大量启发式方法。最后,我们证明了这些描述符的稳定性结果以及随机设置中的渐近保证。关键词:拓扑数据分析、机器学习、多参数持久性、欧拉特征轮廓、混合变换
• Title : Multiview Geometry • Author : Richard Hartely and Andrew Zisserman • Publication date and edition : 2004, Second Edition • ISBN number : 0521540518 Course Schedule Week 1: Introduction to Computer Vision Week 2: Projective Geometry in 2D and Homographies Week 3: Projective Geometry in 3D, Homographies and Camera Calibration Week 4: Fourier Transforms and Convolution Week 5: Sampling定理,边缘检测第6周:特征和特征检测,多分辨率金字塔第7周:图像降解和修复第8周:变异微积分 +正则化; Midterm-1 (on the Thursday of the week) Week 9: Image Segmentation Week 10: Image Segmentation (continued) Week 11: Stereo and Surface reconstruction Week 12: Texture and texture segmentation Week 13: Motion fields and Optical Flow Week 14: Deep Learning and Image classification Week 15: Wrap up and Midterm-2
回想一下位移算符如何变换光子振幅算符,ˆ D ( α )ˆ a † ˆ D † = ˆ a † − α ∗ ,状态可以写成位移和创造的连续
June – July 2024 FIRST YEAR: MA 184: Integral calculus and Laplace transforms MA182: Fourier Series, Matrices and Differential Equations MA134: Matrix Theory, Calculus and Ordinary Differential Equations CE101: Engineering Mechanics CE151: Strength of Materials EE181: Electrical circuits and Machines EC101: Electronic Devices and Circuits THIRD YEAR CE304: Environmental Engineering - 2 CE305: Transportation Engineering - 2 CE307: Engineering Geology EE357: Electrical Machines Lab -II MM301: Steel Making Technology MM302: Mechanical Behaviour of Materials MM303: Powder Metallurgy CH302: Elements of Transport Phenomena CH303: Process Equipment Design CH304: Pollution Control in Process Industries CS301: Operating Systems CS303: Software Engineering CS315: Artificial Intelligence BT302:生物反应工程BT303:基因工程BT305:结构生物学最后一年:EE441:电力转换原理ME401:制冷和空调EC4542:云计算
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