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Sholl analysis summarizes the radial arrangement of a traced structure by counting its intersections with concentric Euclidean circles around a chosen center. The resulting Sholl profile reports how the count changes with radius. A computational workflow must specify the center, spatial calibration, sampled radii and the convention used to identify distinct intersections. The software documentation distinguishes analysis of segmented images from analysis of reconstructed tracings.^[ref]

For an original center-choice example, take the straight segment $\Gamma =\{(x,0):0\le x\le 2\}$. With center $(0,0)$, a circle of radius $r$ meets the segment once for $0<r\le 2$. With center $(1,0)$, it meets the same segment twice for $0<r\le 1$ and not at all for $r>1$. At $r=0.75$, therefore, the two center choices give counts 1 and 2, although the traced object has not changed. The center is part of the measurement definition.

For binary images, the foreground also needs an explicit meaning. The SNT documentation treats zero-valued pixels as background independently of the displayed lookup table and illustrates how an inverted segmentation can make the program sample background instead of structure.^[ref] Record the foreground-background polarity and radial sampling interval with the result.

The radial summary is useful for comparing where intersections occur, but a Sholl profile does not determine rooted tree topology. A fitted curve, sampled count sequence and complete ideal Sholl profile are different data objects; none should be silently substituted for another.