= Region of interest
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.<ImageJ User Guide by Tiago Ferreira and Wayne Rasband>[Section19, area, line and point selection tools]{ref}
For an original example, let an image be
$$
I=\begin{pmatrix}0&2&4\\6&8&10\end{pmatrix}.
$$
Choose the top row as the <region of interest>, so its <binary selection mask> is $M=\begin{pmatrix}1&1&1\\0&0&0\end{pmatrix}$. The selected mean is
$$
\bar I_M=\frac{\sum_{ij}M_{ij}I_{ij}}{\sum_{ij}M_{ij}}=\frac{0+2+4}{3}=2.
$$
Selecting 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.
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