Abstract
Efficient accurate Gaussian localization is an important topic in many applications, e.g. localization based super-resolution microscopy and image scanning microscopy, which requires large-scale Gaussian patterns localization for accurate super-resolution image reconstruction. Existing Gaussian localization methods usually require high signal-to-noise image and the existing standard fitting algorithm usually requires manually inputting a good initial value for all parameters, which could be not convenient to use and difficult to guarantee high robustness for large-scale Gaussian localizations with a computer. It would be even more challenge to detect all the Gaussian patterns with high-dynamic-range of amplitudes, as well as to estimate a good initial value for all parameters for efficient Gaussian fitting and guarantee high robustness of the localization algorithm for low signal-to-noise ratio image data with strong background. In this paper, we propose an efficient Gaussian patterns detection technique and a robust Gaussian fitting method for accurate Gaussian fitting without initial estimation. In our technique, a fast Pearson correlation algorithm is proposed to improve the efficiency of the calculation of normalized cross correlation for large scale object detection with template matching. By introducing blind background estimation, a modified iterative least-squares Gaussian fitting algorithm without initials estimation is proposed for robust Gaussian fitting with noisy data with strong background. The simulation shows that the performance of the proposed detection technique is high for low SNR image and an efficiency improvement of 27% can be achieved; the proposed Gaussian fitting algorithm is capable of calculating all parameters without initial estimation, and the resulting fitting accuracy is very close to exiting standard methods, which indicates that image signal-to-noise ratio higher than 10dB is required to obtain subpixel accuracy.
Highlights
Gaussian fitting problem is an important topic for many applications, such as localization problem in Image Scanning Microscopy [1], [2], correlation curve and surface fitting in Fluorescence Correlation Spectroscopy [3] and the analysis of atomic resolution images [4], etc
The background is set to 200, the sigma value for each Gaussian pattern is set to 2, and the amplitudes are generated randomly, which is set within the range between [100, 200], which is similar to a case with moderate signalto-noise ratio (SNR) in most of general experiments
In this paper, we show a simple algorithm for robust largescale Gaussian localization
Summary
Gaussian fitting problem is an important topic for many applications, such as localization problem in Image Scanning Microscopy [1], [2], correlation curve and surface fitting in Fluorescence Correlation Spectroscopy [3] and the analysis of atomic resolution images [4], etc. A modified version of Caruanas’ algorithm has been proposed [11] for improving the antinoise performance of fitting algorithm and achieving better fitting accuracy This algorithm introduced Taylor expanding to analyze the polynomialized function, which indicates that noise could be magnified by the logarithm operation and that weighting the residual error to reduce the impact of noise is necessary; an iteration form is proposed to reduce the impact of noise for data with long range of Gaussian attenuation, where noise-effect dominates. The background in experiment, always exists in reality and it is not VOLUME 9, 2021 easy to precisely estimate due to measurement environment by algorithm For this reason, this type of methods may not suitable to accurate fitting application, such as surface fitting and localization. Our contribution includes introducing an efficient Gaussian patterns detection technique based on NCC with FFT acceleration and a robust Gaussian fitting algorithm without parameters initial-value estimation.
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