The Hessian Blob Algorithm: Precise Particle Detection in Atomic Force Microscopy Imagery

Abstract

Imaging by atomic force microscopy (AFM) offers high-resolution descriptions of many biological systems; however, regardless of resolution, conclusions drawn from AFM images are only as robust as the analysis leading to those conclusions. Vital to the analysis of biomolecules in AFM imagery is the initial detection of individual particles from large-scale images. Threshold and watershed algorithms are conventional for automatic particle detection but demand manual image preprocessing and produce particle boundaries which deform as a function of user-defined parameters, producing imprecise results subject to bias. Here, we introduce the Hessian blob to address these shortcomings. Combining a scale-space framework with measures of local image curvature, the Hessian blob formally defines particle centers and their boundaries, both to subpixel precision. Resulting particle boundaries are independent of user defined parameters, with no image preprocessing required. We demonstrate through direct comparison that the Hessian blob algorithm more accurately detects biomolecules than conventional AFM particle detection techniques. Furthermore, the algorithm proves largely insensitive to common imaging artifacts and noise, delivering a stable framework for particle analysis in AFM.

A machine perspective of atomic defects in scanning transmission electron microscopy

“…Figure 4A shows a visual demonstration of the Hessian blob method on an AFM image. 85 The input image encoding the position and scale information is converted to a set of scale-space representations, that is, a stack of smoothed images convoluted with corresponding kernels of different scales. Blob detection algorithms (eg, a maximum filter method) are implemented in the image stack to extract the position, size, and curvature information of the input image.…”

“…The LoG kernels can be approximated by DoG and HoG kernels. Figure A shows a visual demonstration of the Hessian blob method on an AFM image . The input image encoding the position and scale information is converted to a set of scale‐space representations, that is, a stack of smoothed images convoluted with corresponding kernels of different scales.…”

“…A, The visual illustration of the Hessian blob detection algorithm implemented for an AFM image. Reproduced with permission from Reference Copyright 2018, Springer Nature. B, A recommended routine for atom column detection for structure identification.…”

Applied Medical Informatics in the Detection and Counting of Erythrocytes and Leukocytes RHMF the Image Segmentation Algorithm

“…This developed methodology also uses a 3-D matrix, the first two dimensions being responsible for representing the coordinates of the matrix, which increases each time the circle is drawn around the rays on each edge point. An accumulator is responsible for maintaining proper counting [31,32,33].…”

Light-sheet imaging for the recording of transverse absolute density distributions of gas-phase particle-beams from nanoparticle injectors

“…Images were collected with a 1 ms exposure time and at a frame rate of 82 fps at full-frame size. Collected images were analyzed using a centroiding algorithm based on Hessian blob-finding [13], yielding sub-pixel particle positions as well as an accurate estimate of the number of recorded photons per particle.…”