M5Image forensicsMicroscopyLayer 1 (Deterministic)

Poisson Noise

Checks whether the noise in a micrograph behaves like the shot noise of a photon-counting detector, where the variance grows linearly with local brightness. The indicator fits per-block variance against per-block mean and flags an image whose noise does not scale with intensity, the signature of signal-independent noise from synthesis or post-processing.

Technical description

Tiles the grayscale image into 16 by 16 blocks, takes each block's mean and variance, and fits a line sigma^2 = a*mean + b by least squares (the photon-transfer relation, with a the system gain and b the read-noise variance). It reads R^2 (how well the line fits) and the slope's t-statistic t = a / stderr(a). The base score penalizes a poor fit, max(0, (0.7 - R^2)/0.7 * 3.0); the slope penalty requires the slope to be significantly positive, scoring 2.0 for a non-positive slope and 2.0(1 - t/3.0) for a weakly significant one. The slope criterion is gain-agnostic and unit-invariant, so genuine microscopy whose gain differs from one is not penalized.

How it works

Layer 1 (deterministic): computes per-block mean and variance, fits a line of variance against mean, and scores from two signals. A low R^2 raises the base score because shot-noise data lie close to the photon-transfer line. The slope must be positive and statistically significant (t at least 3): a non-positive slope scores the full slope penalty and a marginal one scores in proportion, while a clearly significant positive slope scores nothing. The two contributions are summed and capped at 5.0.

Why this matters

Noise in a real micrograph is a physical fingerprint of capture. Photon arrivals follow Poisson statistics, so the variance equals the mean signal in photons, and after detector gain the measured variance follows Var = gain*mean + read_noise. This intensity-dependent noise is the defining property of a photon-limited detector and underpins both quantitative fluorescence microscopy and detector calibration. Synthetic or heavily processed images usually lack it: added noise is uniform across intensity, and denoising flattens the relationship, so a variance that does not grow with brightness is strong evidence the image was not captured.

Score thresholds

0-1: Noise variance scales linearly with intensity with a significant positive slope, consistent with photon-counting capture
2-3: Weak photon-transfer relationship: a poor linear fit or a slope only marginally positive
4-5: Noise variance is essentially independent of intensity, consistent with uniform synthetic noise or heavy denoising

Limitations

Block variance assumes the intensity is roughly uniform within a block, so a block crossing a strong edge or fine texture has structure-driven variance that distorts the fit. Clipping at black and white bends the photon-transfer line, and denoising, gamma correction, and lossy compression all reshape the variance-mean relationship. The 16-pixel block bounds resolution, and the screen returns a single global verdict rather than localizing a region. Whether the noise level is uniform across the frame is a different question answered by the noise-consistency indicator I3, which tests spatial uniformity for splices; M5 tests the intensity dependence of the noise for the photon-counting law, so the two are complementary.