Your Ground Truth Is Running the Same Biased Estimator as Your Method: Incorporation Bias in the Geometric Evaluation of Segmentation Pipelines

Segmentation masks are routinely turned into physical quantities such as perimeter in centimetres, circularity, and radiomic shape features, which are then compared against the world. The boundary-length estimator shipped by the default stack has had a closed-form bias since 1979 and has been provably non-convergent since 2003, and the coupling of such an estimator into a synthetic reference is a known failure mode: the inverse crime. We claim none of that. We report that its standard antidote fails here. Refining the reference grid cannot separate reference from method when the shared component has a bias floor: on our test shape, binary marching squares self-converges at order $2.79$ while its true error sits at a constant $+8.20\%$. In a leaf-phenotyping pipeline of our own this hid a $+4.55\%$ perimeter error behind a reported $-0.01\%$, and a flat-mesh extractor appeared to beat a raster baseline while being nearly three times worse, a $+3.87\%$ digitisation bias cancelling a $-7.69\%$ projection bias. We derive the closed-form condition for when this happens: with a shared distortion $p$ and digitisation biases $b_A, b_B$, the ordering in absolute error inverts exactly when $(1+p)(1+\bar b) < 1$, where $\bar b = (b_A + b_B)/2$. Auditing the stack (scikit-image, OpenCV, PlantCV, HistomicsTK, PyRadiomics, IBSI), most of it is silent where the feature is defined, and the remedy it recommends is not independent either: four-direction discrete Crofton is exactly marching squares divided by Kulpa's constant on saddle-free masks. The failure is larger in three dimensions: PyRadiomics returns sphericity $0.919$ for a perfect digital sphere, at every resolution. We propose a reference-estimator rule stronger than independence alone, a three-grid test that detects the failure, and a convergent estimator that cuts our leaf error to $-0.26\%$ at comparable cost.