Subpixel localization techniques for estimating the positions of point-like images captured by pixelated image sensors have been widely used in diverse optical measurement fields.With unavoidable imaging noise,there i...Subpixel localization techniques for estimating the positions of point-like images captured by pixelated image sensors have been widely used in diverse optical measurement fields.With unavoidable imaging noise,there is a precision limit(PL)when estimating the target positions on image sensors,which depends on the detected photon count,noise,point spread function(PSF)radius,and PSF’s intra-pixel position.Previous studies have clearly reported the effects of the first three parameters on the PL but have neglected the intra-pixel position information.Here,we develop a localization PL analysis framework for revealing the effect of the intra-pixel position of small PSFs.To accurately estimate the PL in practical applications,we provide effective PSF(e PSF)modeling approaches and apply the Cramér–Rao lower bound.Based on the characteristics of small PSFs,we first derive simplified equations for finding the best PL and the best intra-pixel region for an arbitrary small PSF;we then verify these equations on real PSFs.Next,we use the typical Gaussian PSF to perform a further analysis and find that the final optimum of the PL is achieved at the pixel boundaries when the Gaussian radius is as small as possible,indicating that the optimum is ultimately limited by light diffraction.Finally,we apply the maximum likelihood method.Its combination with e PSF modeling allows us to successfully reach the PL in experiments,making the above theoretical analysis effective.This work provides a new perspective on combining image sensor position control with PSF engineering to make full use of information theory,thereby paving the way for thoroughly understanding and achieving the final optimum of the PL in optical localization.展开更多
针对多类不平衡数据分类准确率低的问题,提出一种基于空间扩展的支持向量机学习算法(support vector machine algorithm based on space spreading,SS-SVM)。根据空间扩展原理,在多维欧式空间中通过空间扩展对少类数据进行上采样,使其...针对多类不平衡数据分类准确率低的问题,提出一种基于空间扩展的支持向量机学习算法(support vector machine algorithm based on space spreading,SS-SVM)。根据空间扩展原理,在多维欧式空间中通过空间扩展对少类数据进行上采样,使其处理数据时减少小区块的影响;降低数据不平衡度以优化分类器组;在扩展的数据集上训练SVM分类器。标准数据集上的实验结果表明,与几种经典的算法相比,SS-SVM在多类不平衡数据分类上可获得令人满意的分类结果,对少类数据分类精度要求较高的问题尤为有效。展开更多
基金the support from the National Natural Science Foundation of China(51827806)the National Key Research and Development Program of China(2016YFB0501201)the Xplorer Prize funded by the Tencent Foundation。
文摘Subpixel localization techniques for estimating the positions of point-like images captured by pixelated image sensors have been widely used in diverse optical measurement fields.With unavoidable imaging noise,there is a precision limit(PL)when estimating the target positions on image sensors,which depends on the detected photon count,noise,point spread function(PSF)radius,and PSF’s intra-pixel position.Previous studies have clearly reported the effects of the first three parameters on the PL but have neglected the intra-pixel position information.Here,we develop a localization PL analysis framework for revealing the effect of the intra-pixel position of small PSFs.To accurately estimate the PL in practical applications,we provide effective PSF(e PSF)modeling approaches and apply the Cramér–Rao lower bound.Based on the characteristics of small PSFs,we first derive simplified equations for finding the best PL and the best intra-pixel region for an arbitrary small PSF;we then verify these equations on real PSFs.Next,we use the typical Gaussian PSF to perform a further analysis and find that the final optimum of the PL is achieved at the pixel boundaries when the Gaussian radius is as small as possible,indicating that the optimum is ultimately limited by light diffraction.Finally,we apply the maximum likelihood method.Its combination with e PSF modeling allows us to successfully reach the PL in experiments,making the above theoretical analysis effective.This work provides a new perspective on combining image sensor position control with PSF engineering to make full use of information theory,thereby paving the way for thoroughly understanding and achieving the final optimum of the PL in optical localization.
文摘针对多类不平衡数据分类准确率低的问题,提出一种基于空间扩展的支持向量机学习算法(support vector machine algorithm based on space spreading,SS-SVM)。根据空间扩展原理,在多维欧式空间中通过空间扩展对少类数据进行上采样,使其处理数据时减少小区块的影响;降低数据不平衡度以优化分类器组;在扩展的数据集上训练SVM分类器。标准数据集上的实验结果表明,与几种经典的算法相比,SS-SVM在多类不平衡数据分类上可获得令人满意的分类结果,对少类数据分类精度要求较高的问题尤为有效。
