Sampling and reconstruction: Hanrahan's signal processing framework reminds us that every pixel is a point sample of an underlying continuous signal. The original fluorescence distribution in a cell is continuous; the digitized image samples it on a regular grid. Mean intensity is one reconstruction of this signal — a zeroth-order summary. But the full set of samples contains much more information. Median intensity is more robust to outliers. The 95th percentile captures peak expression better than the mean. Standard deviation measures heterogeneity.
Quantization and gray levels: Pawley emphasizes that the number of meaningful gray levels in a fluorescence image depends on photon counts. With 100 photons per pixel, SNR = 10, giving ~11 distinguishable intensity levels. Below 25 photons/pixel, you have only ~5 gray levels — the intensity "distribution" within a cell becomes too coarse for meaningful analysis. Raw Data is most informative when images are acquired with sufficient photon counts for meaningful intensity quantification.
When the mean lies: Consider a cell expressing a biomarker in a punctate (dotted) pattern — bright spots in a dim background. The mean intensity might be moderate, suggesting moderate expression. But the true pattern is binary: some regions are strongly positive, others are negative. The per-cell histogram would be bimodal. Standard deviation would be high. The 95th percentile would be much higher than the mean. Raw Data reveals the punctate pattern that the mean obscures.
Precision vs. accuracy: Measurement precision (reproducibility) differs from accuracy (correctness). A mean intensity computed from 500 pixels within a nucleus has high precision — repeat the measurement and you get nearly the same value. But its accuracy as a measure of biomarker concentration is limited by all the confounding factors Dobrucki warns about (illumination, focus, bleaching). Raw Data improves precision by providing multiple summary statistics; improving accuracy requires addressing the optical confounds.
Every pixel is a sample of the cell's fluorescence. The mean is just one summary — the median, percentiles, and spread contain additional information. A cell with punctate (spotted) staining has a bimodal intensity distribution: some pixels are bright, others are dim. The mean would suggest moderate expression, hiding the biologically important pattern. Raw Data reveals these distributions, but the information is only meaningful when enough photons were collected to produce reliable pixel values.