Contrast Consistency
Checks whether local contrast varies smoothly across a micrograph. In a real acquisition the contrast changes gradually with position, because illumination, beam response, and specimen vary continuously, so a map of local contrast is spatially smooth. A figure pasted together from different sources breaks that smoothness: adjacent regions show abrupt contrast jumps, the contrast map loses its spatial coherence, and the contrast values split into two populations. The indicator reads the spatial autocorrelation of the contrast map, its bimodality, and its sharp jumps. It works on the pixels alone, with no model.
Technical description
M7 is a deterministic, generator-agnostic screen for spatial discontinuity in local contrast. Local contrast, the spread of pixel values in a small neighbourhood, is set by the specimen, the illumination, and the detector response, all of which change gradually across a single capture, so the contrast measured on a grid of blocks forms a spatially smooth field. A composite assembled from different sources violates this in three linked ways: the seam between two regions is an abrupt jump in contrast, the field as a whole loses the spatial correlation a single acquisition imprints, and the contrast values cluster into two populations rather than one continuum. M7 tiles the grayscale image into 16 by 16 blocks, takes the standard deviation of each block as its local contrast, and reads the lag-1 spatial autocorrelation of that contrast grid, its bimodality, and the count of abrupt neighbour-to-neighbour jumps. The image must be at least 64 by 64 pixels, or the indicator returns a zero score and records that it was skipped.
How it works
The local contrast of each block is c = std(block), giving a contrast grid the size of the block lattice. Three signals are read from it.
The spatial autocorrelation is the lag-1 correlation of the grid: every block is paired with its right and bottom neighbour, and the Pearson correlation of the two lists of paired values is taken. A single acquisition produces a smooth field with high autocorrelation, near or above 0.5; a composite produces a low or negative value. The contribution is autocorr_score = max(0, (0.5 - r) / 0.5) times 2.0, so it rises from zero at r = 0.5 to 2.0 as the correlation vanishes.
The bimodality is measured with the bimodality coefficient of Pfister and colleagues,
BC = (g1^2 + 1) / (g2 + 3(n - 1)^2 / ((n - 2)(n - 3))),
where g1 is the skewness and g2 the excess kurtosis of the contrast values and n their count. A value above 5/9 indicates two contrast populations and adds a bimodal penalty of 1.5. This coefficient is far more selective than reading kurtosis alone, because a uniform or merely flat spread of contrasts, which a single varied specimen can produce, stays at or below the 5/9 threshold, while two pasted zones cross it.
The jump count flags abrupt seams: a neighbour pair whose contrast differs by more than three times the standard deviation of all block contrasts is counted as a jump, and the jump ratio over all adjacency pairs is scaled to jump_score = min(2.0, 20 times the ratio). The final score is min(5.0, autocorr_score + bimodal_penalty + jump_score). Findings report a low autocorrelation, a bimodal distribution, the total jump count, and the individual worst jumps with bounding boxes. The metadata records the contrast autocorrelation, the bimodality coefficient and kurtosis, the jump count and ratio, and the global contrast mean and spread.
Score thresholds
| Score | Meaning |
|---|---|
| 0 to 1 | Local contrast varies smoothly and forms one population, consistent with a single acquisition. |
| 2 to 3 | The contrast field shows reduced spatial coherence, a bimodal distribution, or some abrupt jumps. |
| 4 to 5 | Strong contrast discontinuities, low spatial coherence, and two contrast populations. Consistent with a composite of different sources. |
Why this matters
A spliced figure is hard to see because the eye forgives a clean cut, but the physics of image formation leaves a measurable trace at the seam. Forgery detection exploits exactly this: a foreign region inserted into an image carries the contrast and lighting of its own origin, and detecting inconsistencies in that lighting and local response exposes the composite without any reference, a principle established for splice detection by analysing where the illumination and contrast stop being consistent [1]. The smoothness M7 expects is itself a quantifiable property, the spatial autocorrelation introduced by Moran, which measures whether nearby measurements are more alike than distant ones, the defining feature of a field generated by one continuous process [2]. The two-population test uses the bimodality coefficient, whose behaviour and the canonical 5/9 threshold are documented by Pfister and colleagues, so that a single varied specimen is not mistaken for a paste-up [3]. The stakes are set by the prevalence of figure manipulation in the literature and by the guidance that adjusting contrast to obscure or join regions is misconduct [4]. M7 turns the expectation of a smooth, single-source contrast field into a test that a composite fails at its seams.
Limitations
Local contrast is driven by the specimen, so a genuine image with sharply bounded structures, such as a field that is half dense tissue and half empty resin, can show real contrast steps and a bimodal distribution without any manipulation. The jump threshold is set as a multiple of the spread of all block contrasts, so when that spread is itself large, as in a strongly bimodal image, the threshold rises and individual seams may not be counted as jumps; the autocorrelation and bimodality signals carry the detection in that case. The 16-pixel block bounds the spatial resolution, and uneven illumination or shading across a real acquisition lowers the autocorrelation legitimately. The thresholds are directional rather than exact. Whether the tonal response and local histogram stay consistent, the procedure the Office of Research Integrity applies, is indicator I9, and the spatial uniformity of the sensor noise level is indicator M6; M7 reads the spatial structure of the local-contrast field, so it corroborates those rather than repeating them.
Theoretical background
M7 rests on the spatial regularity of a single capture. Contrast at a point is determined by the local specimen structure and by the global imaging conditions, illumination intensity, focus, and detector gain, which vary slowly and continuously across the field of view. The result is that local contrast, sampled on a grid, behaves like a realisation of a smooth spatial random field: neighbouring samples are correlated, the values form a single connected distribution, and there are no step discontinuities except where the specimen itself has a sharp boundary. A composite is the superposition of two or more such fields, each with its own imaging conditions, joined along a seam that no single continuous process would produce. At the seam the contrast jumps, the spatial autocorrelation drops because neighbours across the seam are unrelated, and the pooled contrast values become bimodal, one mode per source. Measuring autocorrelation captures the smoothness, the bimodality coefficient captures the two-population structure, and the jump count localises the seam, so M7 reads three facets of the same violation of single-source spatial regularity.
References
- Johnson MK, Farid H. Exposing digital forgeries by detecting inconsistencies in lighting. Proceedings of the 7th Workshop on Multimedia and Security (MM&Sec '05). 2005:1-10. DOI: 10.1145/1073170.1073171
- Moran PAP. Notes on continuous stochastic phenomena. Biometrika. 1950;37(1-2):17-23. DOI: 10.1093/biomet/37.1-2.17
- Pfister R, Schwarz KA, Janczyk M, Dale R, Freeman JB. Good things peak in pairs: a note on the bimodality coefficient. Frontiers in Psychology. 2013;4:700. DOI: 10.3389/fpsyg.2013.00700
- Rossner M, Yamada KM. What's in a picture? The temptation of image manipulation. The Journal of Cell Biology. 2004;166(1):11-15. DOI: 10.1083/jcb.200406019