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Area from a calibrated pixel count assigns an area to a selected collection of complete image pixels. For $N$ selected pixels of calibrated widths $\Delta x$ and $\Delta y$,This rectangular-cell model permits unequal horizontal and vertical spacing. In ImageJ, area is reported in square pixels or calibrated square units according to the spatial calibration and measurement settings.^[ref]

For an original threshold example, let four stored gray values be 40, 90, 130, 200. A rule selecting values at least 128 retains two pixels. If $\Delta x=\Delta y=0.5\mu \mathrm{m}$,At $\Delta x=0.5\mu \mathrm{m}$ and $\Delta y=0.8\mu \mathrm{m}$, the same pixel selection instead represents $0.80\mu {\mathrm{m}}^2$. Pixel count alone is not an area in physical units.

For a binary selection mask $M_{ij}\in \{0,1\}$, the count is $N={\sum }_{ij}{M}_{ij}$. A fractional-coverage model would instead use fractions $0\le f_{ij}\le 1$ and $A=\Delta x\Delta y{\sum }_{ij}{f}_{ij}$; the two rules need not agree at boundaries. A region of interest and an image thresholding rule also select pixels for different reasons. State the selection and calibration before interpreting the result as an estimate of a specimen's geometric area. The numbers above are stipulated image data, not a physical specimen measurement.

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.

An image lookup table maps a stored pixel value or index to a displayed color. For an 8-bit grayscale image with stored values $I_{ij}\in \{0,\dots ,255\}$, a table can be writtenusing an RGB color model triple. Changing $C$ changes the appearance without necessarily changing $I$. ImageJ explicitly distinguishes Invert LUT, which changes the display, from inversion of the pixel values.^[ref]

For an original example, store the rowThe identity grayscale table is $C(v)=(v,v,v)$; an inverted table is $C_{\mathrm{inv}}(v)=(255-v,255-v,255-v)$. The same four stored values appear in opposite brightness order under these tables, but their arithmetic mean remains $447/4=111.75$. An image thresholding rule selecting stored values above 100 still gives the binary selection mask $(0,0,1,1)$.

Numerically replacing the pixels by $255-I$ instead produces $(255,191,127,0)$. Its arithmetic mean is $573/4=143.25$, and the same strict threshold gives $(1,1,1,0)$. Thus an inverted-looking image does not by itself establish that its numerical values or selected subset were inverted.

The distinction is especially visible with binary selection masks: the documented Create Mask command stores 255 inside the selection and 0 outside, while an inverting lookup table can display the selected class as black.^[ref] Record the foreground-background polarity from the stored encoding and algorithm, rather than inferring it from screen brightness.

A program can also apply a lookup mapping to the data. ImageJ's Apply LUT command changes gray values and restores the identity table so that the displayed appearance is retained.^[ref] Distinguish that operation from assigning a display table. A table mapping several input values to the same color can conceal numerical distinctions in the display even while those distinctions remain in the original stored image.

A region of interest in image analysis is a specified subset of image coordinates on which an operation or measurement is restricted. It can be an area, a line or a set of points, so its geometry determines which measurements are meaningful. ImageJ provides rectangular, oval, polygonal, line and point selections; an image region of interest describes their concrete use in that program.^[ref]

For an original example, let an image beChoose the top row as the region of interest, so its binary selection mask is $M=\left(\begin{array}{ccc}1& 1& 1\\ 0& 0& 0\end{array}\right)$. The selected mean isSelecting the bottom row instead gives 8, whereas the whole-image mean is 5. The stored image is unchanged; the question asked of it has changed.

A fixed geometric selection differs from selecting all pixels above an intensity threshold. Their intersection can be used when the intended measurement is a thresholded subset inside a prescribed area. Save the geometry, coordinate convention and image or frame association with the result. A line selection calls for a length or sampled profile, not the same complete-pixel area from a calibrated pixel count used for an area selection.