Research by the University of Chicago provides scientists looking at single molecules or into deep space a more accurate way to analyze imaging data captured by microscopes, telescopes, and other devices. The method, known as single-pixel interior filling function (SPIFF), detects and corrects systematic errors in data and image analysis used in many areas of science and engineering.

Scientists studied the motion of insulin-containing vesicles (small green spheres) that contain thousands of insulin molecules within an insulin-secreting cell. Short trajectories (color) are superimposed on a subset of the vesicles to indicate representative localization and short-time motion. (Image: Prof. Norbert Scherer)

Various imaging devices are used to learn about objects on scales ranging from the very small (nanometers) to the very large (astrophysical scales). This often includes tracking the movement of such objects to learn about their behavior and properties.

Many imaging systems and image-based detectors consist of pixels, such as with a megapixel cellphone. Particle tracking allows researchers to determine the position of an object down to a single pixel, and even explore sub-pixel localization to better than one-tenth of a pixel accuracy. With an optical microscope's resolution of about 250 nanometers, and an effective pixel size of about 80 nanometers, particle tracking allows researchers to locate the center or location of an object to within a few nanometers, provided enough photons are measured.

Such sub-pixel resolution depends on algorithms to estimate the position of objects and their trajectories. Using these algorithms often results in errors of precision and accuracy due to factors such as nearby or overlapping objects in the image and background noise. SPIFF can correct the errors with little added computational costs.

Sub-pixel data analysis can be biased by subtle features of the image-formation process, and these biases can shift a trajectory's apparent position by as much as half a pixel relative to its true position. For sensitive measurements of delicate physical processes, that shift is unacceptable. The SPIFF method detects and corrects biases in the outputs of particle-tracking experiments.

The SPIFF approach is based on the histogram of estimated positions within pixels. The deviation of the SPIFF from a uniform distribution is used to test the veracity of tracking analyses from different algorithms. Unbiased SPIFFs correspond to uniform pixel filling, whereas biased ones exhibit pixel locking, in which the estimated particle positions concentrate toward the centers of pixels. Although pixel locking is a well-known phenomenon, SPIFF goes beyond that to correct errors. SPIFF aggregates statistical information from many single-particle images and localizations that are gathered over time or across an ensemble, and this information augments the single-particle data.

SPIFF was applied to experimental data on solids (i.e., colloidal spheres) suspended in a liquid, but the researchers have now applied the method to many other datasets, including nanoscale features of cells (e.g. vesicles), metallic nanoparticles, and even single molecules. The SPIFF method is applicable to all tracking algorithms, and could help determine and correct errors in star-tracking data.

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