Fig. 1
From: Stereology with OPEN-Stereo: low-cost, accessible, and accurate cellular quantification
Calibration and feature tracking at a fixed magnification and between magnifications. (a) Calibration for \(\mathbf {K(zk)}\). The calibration pipeline using a series of images automatically collected from a predefined stepper motor movement command. The user selects one unique trackable feature point (must be a corner/edge) on the image (\(I_0\)) using a 10× objective. The feature point must fit inside the tracking window represented as the solid outlined red or blue square. The stepper motor moves the image to a predefined location. Using the brightness constancy equation, the same feature is visually identified by its unique pixel intensity. This process repeats at least 4 times for the feature point (the user can increase the repetitions for increased accuracy). The pixel location and the stepper motor coordinates are then associated in a matrix \(\textbf{K}\) at the specified magnification. (b) Calibration for \(\mathbf {L(zo,zk)}\). Calibration and feature tracking between magnifications. The \(\textbf{L}\) matrix is calculated by selecting four points on a calibration grid (\(\textbf{XY}_{\text {pixel}, z_o, j}\), shown as red squares) at the first magnification (10×; left panel), and then reselecting those same points in the same order at the second magnification (100×; right panel; points respectively identified by red arrows). \(\mathbf {L(zo,zk)}\) is a three by three calibration transformation matrix between reference objective \(\textbf{zo}\) and the objective level \(z_k\), such that \(\textbf{XY}_{\text {pixel}, z_o} = \textbf{L}(z_o, z_k) \cdot \textbf{XY}_{\text {pixel}, z_k}\). The \(\textbf{L}\) matrix maps the changes in pixel locations between two magnifications. This establishes the pixel coordinate mapping between two magnifications.
