In this paper, we consider the problem of the accuracy of estimating the location and other attributes of a moving single molecule whose trajectory is imaged by fluorescence microscopy. As accuracy in parameter estimation is closely related to the Fisher information matrix, we first give a general expression of the Fisher information matrix for the estimated parameters for a single object moving in three-dimensional (3D) space. Explicit Cramér-Rao lower bound (CRLB) expressions are then obtained from the Fisher information matrix for a single object moving in the two-dimensional (2D) focus plane with the object trajectory being either linear or circular. We also investigate how extraneous noise sources, pixelation, parameters of the detection system and parameters of the trajectory affect the limit of the accuracy. The results obtained in this paper provide insights that enable the experimentalists to optimize their experimental setups for tracking single molecules in order to achieve the best possible accuracy. They are also applicable to the general problem of tracking an object using quantum limited detectors.
Abstract:In fluorescence microscopy, high-speed imaging is often necessary for the proper visualization and analysis of fast subcellular dynamics. Here, we examine how the speed of image acquisition affects the accuracy with which parameters such as the starting position and speed of a microscopic non-stationary fluorescent object can be estimated from the resulting image sequence. Specifically, we use a Fisher information-based performance bound to investigate the detector-dependent effect of frame rate on the accuracy of parameter estimation. We demonstrate that when a charge-coupled device detector is used, the estimation accuracy deteriorates as the frame rate increases beyond a point where the detector's readout noise begins to overwhelm the low number of photons detected in each frame. In contrast, we show that when an electron-multiplying charge-coupled device (EMCCD) detector is used, the estimation accuracy improves with increasing frame rate. In fact, at high frame rates where the low number of photons detected in each frame renders the fluorescent object difficult to detect visually, imaging with an EMCCD detector represents a natural implementation of the Ultrahigh Accuracy Imaging Modality, and enables estimation with an accuracy approaching that which is attainable only when a hypothetical noiseless detector is used.
Biomolecular interactions are central to biological processes and typically take place at nanometer scale distances. They often involve molecular motion which is known to affect the accuracy of the parameter estimates. Therefore, in this paper, we consider a case of two closely spaced molecules with planar trajectory and present a general expression of the Fisher information matrix in terms of their trajectory from which the benchmark for the accuracy of the parameter estimates is obtained. Through simulations, we show its application in the case of two moving objects and another case where only one of the two objects is moving. It is shown that the deterioration of the limit of the accuracy is not only dependent on the proximity of their starting position but also on their speed and direction of movement. The effect of differing photon emission intensities on the limit of the accuracy of parameter estimation is also investigated.
Iris is a promising biometric due to its high reliability and stability. In this paper, a novel iris recognition technique based on Hausdorff distance is proposed. A modified partial Hausdorff distance (a dissimilarity measure) is computed directly between the normalized iris images for comparison and no feature is extracted explicitly. The Hausdorff distance-based iris recognition system is expected to perform well in the case of severe occlusion by eyelids due to the partialness in the measure. Besides, the modified measure is insensitive to lighting conditions. Experimental results on the CASIA database show that the performance of the proposed recognition system is encouraging and comparable to the iris recognition algorithms found in the current literature.
In this paper, we consider the problem of the accuracy of estimating the location and other attributes of a moving single molecule whose trajectory is acquired in a sequence of time intervals by a pixelated detector. We present expressions of the Fisher information matrices from which the benchmark for the accuracy of the parameter estimates is obtained. In the absence of extraneous noise, it is shown that time discretization of the image acquisition process results in a limit of the accuracy of the parameter estimates that is better than or at least as good as that acquired without time discretization. This analytical result is also illustrated by simulations. However, in the presence of extraneous noise, simulations show that finer time discretization may not always lead to better limit of the accuracy than that acquired without time discretization of the image acquisition process.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.