Figure 7.

Hessian blobs are stable under image defects commonly seen in AFM images. (a) An unprocessed image of translocase complexes on mica with lateral pixel resolution 3.9 nm. (b) Hessian blobs discovered in (a) with a manually set minimum blob strength 1 × 10⁻¹⁸. Blob centers marked by crosshairs, boundaries calculated to 10 times pixel resolution (0.39 nm) and marked by green contours. Panels c-h demonstrate the discovered Hessian blobs after imposing image perturbations. (c) Constant Offset: All pixels from (a) were given an addition of 2 nm. (d) Discontinuity: A fault line was introduced, all pixels above the line were given an addition of 2 nm. (e) Tilt: A planar tilt reaching 2 nm over the span of the image was added to (a). (f) Parabolic: Each horizontal scan line of pixels was given a parabolic addition of up to 2 nm, mimicking the AFM bowing effect. (g) Scanline Noise: Each scan line was given a random offset according to a Gaussian distribution of standard deviation 1 nm, mimicking scan line noise. (h) Gaussian Noise: Gaussian noise of standard deviation 1 nm was applied to all pixels in (a). Table: Average changes in subpixel particle measurements after imposing image perturbations. Center points calculated to subpixel accuracy via second-order Taylor approximation³⁴. Particle perimeters and projected areas calculated via the polygon approximation as in the scanning probe microscopy analysis software Gwyddion⁵.