The misrepresentation problem: Dobrucki warns that objects smaller than the diffraction limit are inflated to ~250 nm in the image. A 7 nm cell membrane appears 250 nm wide — a 35-fold inflation. The measured "membrane intensity" integrates signal from a ~250 nm band that includes the true membrane plus adjacent cytoplasm and extracellular space. This means membrane measurements are inherently contaminated by non-membrane signal. The degree of contamination depends on the PSF width (optical system) and the actual membrane expression level.
Boundary descriptors: Gonzalez & Woods describe boundary descriptors — measurements computed along the contour of an object rather than within its area. Membrane Measurements are boundary descriptors applied to fluorescence intensity: the boundary is the cell membrane, and the measurement is the biomarker intensity sampled along it. Circumferential completeness is a boundary descriptor that combines topology (how much of the boundary is positive) with photometry (how bright the positive segments are).
Why completeness matters clinically: The HER2 IHC scoring system explicitly requires assessing membrane staining completeness: 3+ requires strong complete membrane staining in >10% of tumor cells; 2+ requires complete membrane staining at weaker intensity or incomplete staining at moderate intensity. This distinction between complete and incomplete cannot be captured by a single intensity value — it requires measuring the spatial distribution of signal around the cell boundary.
A 7 nm membrane appears ~250 nm wide under the microscope, so membrane measurements always include some contamination from adjacent cytoplasm. Despite this limitation, measuring intensity specifically at the membrane boundary — rather than across the whole cell — provides much better signal for clinical scoring. The completeness measurement (how much of the membrane is stained) is critical for HER2 scoring, where the difference between complete and incomplete staining determines the clinical grade.
