Expectation maximization based framework for joint localization and parameter estimation in single particle tracking from segmented images
Single Particle Tracking (SPT) is a well known class of tools for studying the dynamics of biological macromolecules moving inside living cells. In this paper, we focus on the problem of localization and parameter estimation given a sequence of segmented images. In the standard paradigm, the locatio...
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| Vydáno v: | PloS one Ročník 16; číslo 5; s. e0243115 |
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21.05.2021
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| Abstract | Single Particle Tracking (SPT) is a well known class of tools for studying the dynamics of biological macromolecules moving inside living cells. In this paper, we focus on the problem of localization and parameter estimation given a sequence of segmented images. In the standard paradigm, the location of the emitter inside each frame of a sequence of camera images is estimated using, for example, Gaussian fitting (GF), and these locations are linked to provide an estimate of the trajectory. Trajectories are then analyzed by using Mean Square Displacement (MSD) or Maximum Likelihood Estimation (MLE) techniques to determine motion parameters such as diffusion coefficients. However, the problems of localization and parameter estimation are clearly coupled. Motivated by this, we have created an Expectation Maximization (EM) based framework for simultaneous localization and parameter estimation. We demonstrate this framework through two representative methods, namely, Sequential Monte Carlo combined with Expectation Maximization (SMC-EM) and Unscented Kalman Filter combined with Expectation Maximization (U-EM). Using diffusion in two-dimensions as a prototypical example, we conduct quantitative investigations on localization and parameter estimation performance across a wide range of signal to background ratios and diffusion coefficients and compare our methods to the standard techniques based on GF-MSD/MLE. To demonstrate the flexibility of the EM based framework, we do comparisons using two different camera models, an ideal camera with Poisson distributed shot noise but no readout noise, and a camera with both shot noise and the pixel-dependent readout noise that is common to scientific complementary metal-oxide semiconductor (sCMOS) camera. Our results indicate our EM based methods outperform the standard techniques, especially at low signal levels. While U-EM and SMC-EM have similar accuracy, U-EM is significantly more computationally efficient, though the use of the Unscented Kalman Filter limits U-EM to lower diffusion rates. |
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| AbstractList | Single Particle Tracking (SPT) is a well known class of tools for studying the dynamics of biological macromolecules moving inside living cells. In this paper, we focus on the problem of localization and parameter estimation given a sequence of segmented images. In the standard paradigm, the location of the emitter inside each frame of a sequence of camera images is estimated using, for example, Gaussian fitting (GF), and these locations are linked to provide an estimate of the trajectory. Trajectories are then analyzed by using Mean Square Displacement (MSD) or Maximum Likelihood Estimation (MLE) techniques to determine motion parameters such as diffusion coefficients. However, the problems of localization and parameter estimation are clearly coupled. Motivated by this, we have created an Expectation Maximization (EM) based framework for simultaneous localization and parameter estimation. We demonstrate this framework through two representative methods, namely, Sequential Monte Carlo combined with Expectation Maximization (SMC-EM) and Unscented Kalman Filter combined with Expectation Maximization (U-EM). Using diffusion in two-dimensions as a prototypical example, we conduct quantitative investigations on localization and parameter estimation performance across a wide range of signal to background ratios and diffusion coefficients and compare our methods to the standard techniques based on GF-MSD/MLE. To demonstrate the flexibility of the EM based framework, we do comparisons using two different camera models, an ideal camera with Poisson distributed shot noise but no readout noise, and a camera with both shot noise and the pixel-dependent readout noise that is common to scientific complementary metal-oxide semiconductor (sCMOS) camera. Our results indicate our EM based methods outperform the standard techniques, especially at low signal levels. While U-EM and SMC-EM have similar accuracy, U-EM is significantly more computationally efficient, though the use of the Unscented Kalman Filter limits U-EM to lower diffusion rates. About the Authors: Ye Lin Roles Formal analysis, Investigation, Software, Writing – original draft Affiliation: Division of Systems Engineering, Boston University, Boston, MA, United States of America Sean B. Andersson Roles Conceptualization, Funding acquisition, Methodology, Project administration, Visualization, Writing – review & editing * E-mail: sanderss@bu.edu Affiliations Division of Systems Engineering, Boston University, Boston, MA, United States of America, Department of Mechanical Engineering, Boston University, Boston, MA, United States of America ORCID logo https://orcid.org/0000-0001-7575-3507 Introduction Single particle tracking (SPT) is an important class of techniques for studying the motion of single biological macromolecules. Because SPT experiments are often photon-impoverised and subject to significant background, it is important to consider the impact of signal and noise levels when comparing different analysis algorithms. [...]23] investigated the performance of an experimental method in error estimation techniques across a variety of signal and noise values, the comparison work in [11] included the signal level as a core factor in their simulations, [24] generated simulated videos at various levels of signal to noise ratios to validate the use of convolutional neural networks on SPT data, and [25] applied deep learning to analyze particle trajectories based on simulated data over a large range of signal to noise ratios. [...]the measured intensity, Ixy can be described as(1)where G is the peak amplitude of the intensity, (x, y) are the lateral coordinates in the image frame, (xo, yo) are the position of the particle, (σx, σy) are physical parameters describing the width of the PSF, and Nbgd is the background intensity. Single Particle Tracking (SPT) is a well known class of tools for studying the dynamics of biological macromolecules moving inside living cells. In this paper, we focus on the problem of localization and parameter estimation given a sequence of segmented images. In the standard paradigm, the location of the emitter inside each frame of a sequence of camera images is estimated using, for example, Gaussian fitting (GF), and these locations are linked to provide an estimate of the trajectory. Trajectories are then analyzed by using Mean Square Displacement (MSD) or Maximum Likelihood Estimation (MLE) techniques to determine motion parameters such as diffusion coefficients. However, the problems of localization and parameter estimation are clearly coupled. Motivated by this, we have created an Expectation Maximization (EM) based framework for simultaneous localization and parameter estimation. We demonstrate this framework through two representative methods, namely, Sequential Monte Carlo combined with Expectation Maximization (SMC-EM) and Unscented Kalman Filter combined with Expectation Maximization (U-EM). Using diffusion in two-dimensions as a prototypical example, we conduct quantitative investigations on localization and parameter estimation performance across a wide range of signal to background ratios and diffusion coefficients and compare our methods to the standard techniques based on GF-MSD/MLE. To demonstrate the flexibility of the EM based framework, we do comparisons using two different camera models, an ideal camera with Poisson distributed shot noise but no readout noise, and a camera with both shot noise and the pixel-dependent readout noise that is common to scientific complementary metal-oxide semiconductor (sCMOS) camera. Our results indicate our EM based methods outperform the standard techniques, especially at low signal levels. While U-EM and SMC-EM have similar accuracy, U-EM is significantly more computationally efficient, though the use of the Unscented Kalman Filter limits U-EM to lower diffusion rates.Single Particle Tracking (SPT) is a well known class of tools for studying the dynamics of biological macromolecules moving inside living cells. In this paper, we focus on the problem of localization and parameter estimation given a sequence of segmented images. In the standard paradigm, the location of the emitter inside each frame of a sequence of camera images is estimated using, for example, Gaussian fitting (GF), and these locations are linked to provide an estimate of the trajectory. Trajectories are then analyzed by using Mean Square Displacement (MSD) or Maximum Likelihood Estimation (MLE) techniques to determine motion parameters such as diffusion coefficients. However, the problems of localization and parameter estimation are clearly coupled. Motivated by this, we have created an Expectation Maximization (EM) based framework for simultaneous localization and parameter estimation. We demonstrate this framework through two representative methods, namely, Sequential Monte Carlo combined with Expectation Maximization (SMC-EM) and Unscented Kalman Filter combined with Expectation Maximization (U-EM). Using diffusion in two-dimensions as a prototypical example, we conduct quantitative investigations on localization and parameter estimation performance across a wide range of signal to background ratios and diffusion coefficients and compare our methods to the standard techniques based on GF-MSD/MLE. To demonstrate the flexibility of the EM based framework, we do comparisons using two different camera models, an ideal camera with Poisson distributed shot noise but no readout noise, and a camera with both shot noise and the pixel-dependent readout noise that is common to scientific complementary metal-oxide semiconductor (sCMOS) camera. Our results indicate our EM based methods outperform the standard techniques, especially at low signal levels. While U-EM and SMC-EM have similar accuracy, U-EM is significantly more computationally efficient, though the use of the Unscented Kalman Filter limits U-EM to lower diffusion rates. About the Authors: Ye Lin Roles Formal analysis, Investigation, Software, Writing – original draft Affiliation: Division of Systems Engineering, Boston University, Boston, MA, United States of America Sean B. Andersson Roles Conceptualization, Funding acquisition, Methodology, Project administration, Visualization, Writing – review & editing * E-mail: sanderss@bu.edu Affiliations Division of Systems Engineering, Boston University, Boston, MA, United States of America, Department of Mechanical Engineering, Boston University, Boston, MA, United States of America ORCID logo https://orcid.org/0000-0001-7575-3507 Introduction Single particle tracking (SPT) is an important class of techniques for studying the motion of single biological macromolecules. Because SPT experiments are often photon-impoverised and subject to significant background, it is important to consider the impact of signal and noise levels when comparing different analysis algorithms. [...]23] investigated the performance of an experimental method in error estimation techniques across a variety of signal and noise values, the comparison work in [11] included the signal level as a core factor in their simulations, [24] generated simulated videos at various levels of signal to noise ratios to validate the use of convolutional neural networks on SPT data, and [25] applied deep learning to analyze particle trajectories based on simulated data over a large range of signal to noise ratios. [...]the measured intensity, Ixy can be described as(1)where G is the peak amplitude of the intensity, (x, y) are the lateral coordinates in the image frame, (xo, yo) are the position of the particle, (σx, σy) are physical parameters describing the width of the PSF, and Nbgd is the background intensity. |
| Audience | Academic |
| Author | Lin, Ye Andersson, Sean B. |
| AuthorAffiliation | 1 Division of Systems Engineering, Boston University, Boston, MA, United States of America 2 Department of Mechanical Engineering, Boston University, Boston, MA, United States of America Institut de Robotica i Informatica Industrial, SPAIN |
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| ContentType | Journal Article |
| Copyright | COPYRIGHT 2021 Public Library of Science 2021 Lin, Andersson. This is an open access article distributed under the terms of the Creative Commons Attribution License: http://creativecommons.org/licenses/by/4.0/ (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. 2021 Lin, Andersson 2021 Lin, Andersson |
| Copyright_xml | – notice: COPYRIGHT 2021 Public Library of Science – notice: 2021 Lin, Andersson. This is an open access article distributed under the terms of the Creative Commons Attribution License: http://creativecommons.org/licenses/by/4.0/ (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. – notice: 2021 Lin, Andersson 2021 Lin, Andersson |
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| DOI | 10.1371/journal.pone.0243115 |
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| Snippet | Single Particle Tracking (SPT) is a well known class of tools for studying the dynamics of biological macromolecules moving inside living cells. In this paper,... About the Authors: Ye Lin Roles Formal analysis, Investigation, Software, Writing – original draft Affiliation: Division of Systems Engineering, Boston... |
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| SubjectTerms | Algorithms Analysis Artificial neural networks Background noise Cameras CMOS Computer and Information Sciences Computer simulation Deep learning Drafting software Engineering and Technology Experimental methods Image segmentation Kalman filters Localization Machine learning Macromolecules Mechanical engineering Neural networks Noise Noise levels Parameter estimation Parameter identification Particle tracking Particle trajectories Physical properties Physical Sciences Random variables Research and Analysis Methods Systems engineering Trajectory analysis |
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| Title | Expectation maximization based framework for joint localization and parameter estimation in single particle tracking from segmented images |
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