Particle picking and centering in cryo-electron micrographs via a vanishing radial kernel

A training-free procedure combines particle picking and approximate centering in cryo-electron microscopy through a single convolution of the micrograph with a compact radial kernel, whose weights increase with distance from the origin, saturate in an annulus, and vanish beyond it. Particles are darker than their surroundings and much weaker than the noise; each carves a well in the response, and local minima of the response are candidate centers. Constant background offsets leave these extrema unchanged away from image boundaries, and a local stability bound controls the displacement of a well's minimum under signed perturbations without assuming a symmetric particle. Grid seeds are iteratively updated, nearby endpoints are merged, and two-dimensional classification follows. On the \emph{Plasmodium falciparum} 80S ribosome and $\beta$-galactosidase data sets, reconstructions reach 3.68 and 4.30~\AA{}, compared with 3.77 and 4.36~\AA{} using reference coordinates, with picking at 0.20--0.26~s per micrograph.