= Gear pitting inspection mask
A \b[gear pitting inspection mask] specifies the tooth-flank region over which damage is counted. It separates eligibility for inspection from the classification of an eligible location as pitted. The denominator of a <gear pitting area fraction> depends on this mask, so a change in coverage can change the reported fraction even when the surface has not changed.
For a digital image, let $m_i\in\{0,1\}$ indicate inclusion of pixel $i$ and let $p_i\in\{0,1\}$ indicate its classification as pitted. With represented surface area $a_i$ per pixel,
$$
\phi=\frac{\sum_i m_i p_i a_i}{\sum_i m_i a_i},\qquad \sum_i m_i a_i>0.
$$
The arrays $m_i$ and $p_i$ are different <indicator functions>. Uniform pixel areas cancel, but an oblique view or a curved-surface map can require nonuniform $a_i$. A shadow, occlusion or unrecorded region should not automatically count as intact material.
An original example begins with 200 pitted pixels among 10000 eligible equal-area pixels, giving $2\%$. Cropping to a 5000-pixel region that retains 150 pitted pixels gives $3\%$. The counted damaged area fell while the fraction rose; this comparison alone cannot establish damage growth.
A <gear inspection common-region comparison> first uses <image registration> to put inspections into corresponding surface coordinates. On a common grid, the intersection mask is $m_i^{\rm common}=m_i^{(0)}m_i^{(1)}$. Comparing the two pitting classifications within that same region holds the denominator convention fixed. Coverage outside the intersection should still be reported: excluding a newly obscured damaged edge can hide relevant change.
Useful inspection records retain the raw image, mask, geometric mapping, <image thresholding> or other <image segmentation> rule, and the reason for excluded regions. A primary NASA gear-endurance study combined inspection history with vibration and oil-debris observations, illustrating why damage labels must remain connected to actual inspected surfaces.<Gear Fault Detection Effectiveness as Applied to Tooth Surface Pitting Fatigue Damage by David G. Lewicki and others>[Printed pp. 2–5, test procedure, instrumentation and inspection comparisons]{ref} The mask formalism above is an explicit measurement convention, not a claim that every historical inspection used this pixel algorithm.
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