Foreground-background polarity

Foreground-background polarity specifies which of two image classes is treated as the selected structure and which as its background. It involves a numerical convention as well as the intended interpretation: high-valued pixels can represent foreground in one encoding, while a dark feature may require the opposite threshold direction. A binary image's appearance alone does not establish its polarity.

For a chosen intensity threshold $T$, define complementary normalized masksThe second is the complement of a set within the declared pixel grid. For the stipulated row $I=(20,80,120,200)$ and $T=120$, the two binary selection masks are $(0,0,0,1)$ and $(1,1,1,0)$. Equality belongs to the second selection. OpenCV's THRESH_BINARY and THRESH_BINARY_INV use these respective comparison directions, with the chosen output maximum replacing 1.^[ref]

An image lookup table is a separate mapping from stored values to displayed colors. ImageJ's Create Mask command writes 255 inside a selection and 0 outside, but its default inverting lookup table can display the selected 255-valued pixels as black.^[ref] Reversing that display mapping does not exchange the stored pixel values.

The distinction has a direct computational consequence. In its binary-image input, the documented Sholl analysis implementation treats zero intensities as background regardless of the lookup table or Black Background option.^[ref] A visually inverted display can therefore leave the selected numerical structure unchanged, whereas replacing an 8-bit mask $B$ by $255-B$ exchanges its zero and 255 classes.

A reproducible geometric measurement records the threshold comparison, the values assigned to selected and excluded pixels, and any display-only inversion. A region of interest can further restrict the grid over which a complement is intended; reversing a mask over the whole image is different from selecting its complement only inside that region.