A feature is conditional on its inputs

The measurement chain is easiest to misunderstand at the point where it produces a value. A feature can look like a property attached to a tumour even though the calculation consumed a particular reconstruction, a particular region, a particular grid, and a particular intensity representation. A compact way to keep that dependency visible is y = f(image, mask, geometry, preprocessing).

The notation is not a claim that these are the only variables in every feature. The implementation and the estimator also matter, and the region definition may contain more structure than a binary mask. It is a mental model for asking a finite, auditable question when a value changes: which input or transformation changed, and was that change intended?

Four inputs, one conditional measurement

The image includes the acquisition and reconstruction choices that produced the sample values. The mask identifies the samples treated as the region of interest. The geometry gives those samples their physical spacing, orientation, and relationship to other objects. Preprocessing includes operations such as filtering, intensity clipping or normalization, resampling, and discretisation. Changing one of these can change the value even when the underlying biology is unchanged. That does not make the changed value meaningless; it means that it is a measurement under a different operational definition.

Voxel size is a particularly direct example. A texture matrix counts spatial relationships on a grid. A relationship sampled on a 0.7 mm grid is not the same physical relationship as one sampled on a 2 mm grid. Resampling to a declared grid can make a study’s comparison more controlled, but it does not make the feature invariant to the choice of grid. The target spacing and interpolator therefore belong in the reported measurement definition.

Segmentation supplies a second example. Moving a boundary changes which voxels enter first-order summaries and which pairs enter texture matrices. The source of the contour, its boundary rule, and any margin or perturbation are measurement inputs. A feature that changes under a plausible contour perturbation has segmentation-related uncertainty; that observation alone does not prove that the feature can or cannot serve as a biomarker. Suitability depends on the intended reference, error tolerance, and decision.

A dependence map for reporting

The causal explanation comes first; the compact map is useful when reviewing a methods section or designing a protocol:

Input or choice	What it can change	What to make visible
Acquisition and reconstruction	noise texture, resolution, and intensity pattern	protocol, scanner, reconstruction, and relevant strata
Region and segmentation	included tissue, boundary, shape, and texture pairs	region hypothesis, contour source, geometry, and boundary rule
Geometry and resampling	physical relationships and interpolation artefacts	grid, spacing, orientation, and interpolator for image and label
Intensity preprocessing	values, range, grey-level representation, and histogram	order, parameters, units, and any fitted state
Feature implementation	mathematical definition, defaults, and aggregation	software, version, effective settings, and estimator

The last row leads to the next section, but it is already important here: a software feature name is not a universal unit. The full result is the name plus the conditions under which it was calculated.

Comparing settings without pretending they are one measurement

Imagine two deliberately different protocols. One uses a 1 mm grid, a sharp reconstruction, and a fixed bin width of 25; another uses a 2 mm grid, a smoother reconstruction, and a fixed bin width of 5. Neither protocol is automatically wrong. A texture value from the first should not be pooled with a value from the second as if the two were repeated observations of one unchanged measurement. The grey-level alphabet and the spatial relationships have both changed. The appropriate comparison might instead concern robustness across the settings, or the performance of a prespecified model under a defined transport question.

This is why pinning and reporting are more useful than a slogan that every study must use the same settings. A study can intentionally vary a reconstruction or a segmentation to measure sensitivity. What it must not do is let the variation stay implicit and then attribute the resulting difference to biology without checking the measurement chain.

The dependence map is a local view of a larger system. The next section places these conditional inputs between biological reality and the clinical claim, and separates measurement validity from association, prediction, and utility.

Sources

• Zwanenburg A, Vallières M, Abdalah MA, et al. The Image Biomarker Standardisation Initiative. Radiology. 2020;295(2):328-338. doi:10.1148/radiol.2020191145, PMID 32154773.
• Pfaehler E, et al. Phys Imaging Radiat Oncol. 2021;20:69-75. doi:10.1016/j.phro.2021.10.007, PMID 34816024.
• Haarburger C, et al. Scientific Reports. 2020;10:12688. doi:10.1038/s41598-020-69534-6.