Feature families and their assumptions

Chapter 5 defined a feature as the output of an image, mask, geometry, preprocessing, and implementation contract. It followed that contract to a measurement table: rows represent observations and columns represent calculated quantities. This chapter begins with that handoff. The question is no longer only where a number came from, but what relationship each column summarizes and what assumptions are hidden in that summary.

A radiomics table can contain many names while relying on a small set of recurring ideas. A useful first classification asks three questions: what are the intensity values inside the region, what is the geometry of the region, and how are the intensity values arranged in space? The answers are the first-order, shape, and texture families. This is a conceptual map, not a claim that the table contains three independent measurements or that a family name identifies a biological process. The Image Biomarker Standardisation Initiative (IBSI) provides reference definitions for these mathematical objects, while the PyRadiomics feature documentation shows how one implementation exposes them.

First-order features: the values inside the region

First-order features summarize the distribution of voxel values selected by the mask. Mean, median, minimum, maximum, percentiles, variance, skewness, and kurtosis describe the values without considering where individual voxels are located. The same collection of values gives the same first-order summary even if those values are rearranged within a fixed mask. That makes first-order features useful for describing an intensity distribution, but it also limits what they can say: a broad distribution does not reveal whether high and low values are adjacent, separated into compartments, or arranged in a repeated pattern.

The simplicity is conditional on the image values and the region being defined. A change in reconstruction, intensity transformation, clipping, interpolation, or resampling can change the values entering the summary. A change in the mask can change which values enter it. Thus a first-order feature is not merely a property of a list of numbers; it is a summary of the values produced by the earlier measurement contract.

Discretisation can enter this family as well. In the PyRadiomics definitions, many statistics are calculated from the ROI values themselves, whereas histogram-based features such as entropy and uniformity use a discretised representation. Changing the binning rule therefore need not affect every first-order feature in the same way. The distinction is part of the operational definition, not a detail that can be inferred from the word “first-order”. The PyRadiomics customization documentation and the feature definitions should be consulted when the exact implementation semantics matter.

Shape features: morphology of the mask

Shape features summarize the geometry of the region represented by the mask. Volume, surface area, elongation, flatness, diameter, and sphericity are examples of quantities that describe the mask rather than the grey values inside it. Their immediate input is the region and its spatial geometry.

Shape is therefore intensity-independent only conditionally: if the mask and its geometry are held fixed, changing the image intensities does not directly change a shape calculation. That does not make shape independent of the full measurement chain. A segmentation may have been produced from the image, a reconstruction may influence that segmentation, and resampling or registration may alter the rasterized boundary. Voxel spacing, coordinate interpretation, surface construction, and the choice between a planar and volumetric calculation also affect what the shape value means.

This distinction prevents two opposite errors. It is wrong to describe a shape feature as an intensity statistic, but it is also wrong to treat it as an unmediated fact about the lesion. A shape value is morphology under a declared mask and geometry definition. Its biological interpretation requires another argument: a name such as volume or elongation does not by itself establish growth, invasiveness, or clinical usefulness.

Shape should not be labelled universally reproducible, just as texture should not be labelled universally unstable. Different shape definitions respond differently to boundary perturbation, resolution, and dimensionality, and their observed behavior depends on the tested pipeline. The systematic review by Pfaehler et al. and the segmentation-variability study by Haarburger et al. support examining features at the level of their definitions and perturbations rather than assigning a universal verdict to an entire family.

Texture features: spatial relationships

Texture features add spatial arrangement to the intensity information. Before a texture matrix is built, continuous intensities are mapped to a declared set of grey levels. The matrix then counts a particular kind of spatial relationship, and a feature summarizes that matrix. Consequently, a texture value depends not only on the image and mask, but also on the discretisation rule, neighbourhood definition, distance, direction, connectivity, dimensionality, and aggregation convention.

The five commonly encountered matrix families differ in the relationship they count. A GLCM, or grey-level co-occurrence matrix, counts how often a pair of grey levels occurs at a stated offset and direction. A GLCM feature therefore depends on choices such as distance, direction, symmetry, and the way several matrices are combined. A GLRLM, or grey-level run-length matrix, counts consecutive voxels of the same grey level along a declared direction; its summaries describe the distribution of runs under that directional construction.

A GLSZM, or grey-level size-zone matrix, counts connected regions of equal grey level and their sizes. The definition therefore depends on what constitutes connectivity and on whether the construction is planar or volumetric. A GLDM, or grey-level dependence matrix, counts neighbourhood dependencies for a voxel under a declared distance and dependence criterion. An NGTDM, or neighbourhood grey-tone difference matrix, compares a voxel’s grey level with the local neighbourhood average, so its result depends on the neighbourhood used to form that comparison.

These families are not five biological senses. They are five ways of encoding spatial relationships before applying mathematical summaries. Even within one family, two features can summarize different properties of the same matrix. A feature name is therefore not a diagnosis of heterogeneity and not a direct description of tissue biology. It is a compact statistic whose meaning depends on the construction that preceded it. The detailed construction of a GLCM and the role of discretisation are developed in the next section.

A fixed-input thought experiment

Consider a fixed mask and a fixed multiset of image values. In one arrangement, nearby voxels form a smooth progression; in another, the same values are interleaved throughout the region. First-order features can remain unchanged because the value distribution is unchanged. Shape features remain unchanged because the mask is unchanged. Texture matrices can change because the neighbouring pairs, runs, zones, dependencies, or neighbourhood differences have changed.

This experiment isolates the intended distinction between the families. It does not imply that a real pipeline changes only one input at a time. A new reconstruction can alter intensities and spatial patterns together. A new segmentation can alter both shape and the set of voxels available for texture. A new discretisation can change the grey-level alphabet before any texture matrix is counted. The family classification helps locate the immediate exposure, but it does not remove the dependencies among stages.

Filtered images create new feature domains

Radiomics may calculate first-order and texture features not only from the original image, but also from derived images. A Laplacian-of-Gaussian (LoG) filter acts as a band-pass transformation at a chosen scale, while a wavelet decomposition produces images corresponding to different frequency bands. Other transformations, including square, square-root, logarithmic, exponential, and gradient operations, create additional intensity domains.

A feature calculated on one of those derived images is a feature of the transformed image, not simply another copy of the feature from the original image. A first-order statistic now summarizes filter responses. A texture matrix now counts relationships between discretised filter responses. Changing the filter type, scale, band, boundary handling, or ordering can therefore change the quantity being measured.

Shape is different in this respect. It is derived from the mask and its geometry, not from the intensity image, so it is not normally recomputed for each filtered image in this extraction design. Adding filters expands the number of intensity-derived and texture candidates while leaving the mask-derived shape calculation conceptually separate. The extra columns are not automatically extra independent evidence: original and filtered images, and different bands of one decomposition, can represent related views of the same input.

Filter semantics must match when values from different implementations are compared. The precise definition of a filter, its scale or band convention, the physical grid on which it operates, and the downstream discretisation all belong to the measurement contract. This is one reason filter standardisation is addressed in IBSI 2. Version-specific defaults, enabled feature lists, and implementation pins are appropriate for a maintained companion-Web reference; the durable point is that a filtered feature is defined by its filter as well as by its family.

Dimensionality is part of the feature

Two-dimensional and three-dimensional calculations are not interchangeable display choices. A two-dimensional texture analysis may construct matrices within each slice and then aggregate the resulting values. A three-dimensional analysis can include relationships across adjacent slices in the volume. The same image, mask, and grey-level mapping can therefore produce different numbers under the two constructions.

The distinction applies to shape as well. A planar boundary and a volumetric surface describe different geometric objects. Physical spacing, slice thickness, anisotropy, resampling, and the handling of small or empty slice-level regions can affect the relationship between a nominal 2D or 3D choice and the actual measurement. A report that names a GLCM, shape feature, or texture family without stating its dimensionality leaves a feature-defining condition unresolved. For texture, IBSI documents reference constructions and aggregation schemes for planar and volumetric settings. PyRadiomics separately exposes shape and shape2D implementation classes; that software distinction should not be read as making a planar geometry equivalent to the IBSI 3D morphology workflow. Neither setting is intrinsically superior. The appropriate choice follows from the intended estimand and the image geometry.

A battery of correlated candidates

Once the families are combined, the table should be read as a set of related candidates rather than as a collection of independent discoveries. First-order features reuse the same ROI values. Shape features reuse the same mask and geometry. Texture features reuse the same discretised image and often summarize overlapping matrix information. Filtered features add related transformed views and can multiply the number of possible candidates again.

Correlation among columns is not itself a defect. Reusing the same measurement inputs, applying related transformations, or summarizing the same matrices can induce dependence or correlation among candidates, but those shared structures do not guarantee an observed correlation for every pair. The practical consequence is that the nominal width of the table does not tell you how many independent patterns it contains, and it does not justify treating every feature as a separate biological hypothesis. Feature selection, multiplicity, and model validation must account for how the candidates were generated and chosen.

The behavior of those candidates remains feature- and pipeline-dependent. Some members of one family may tolerate a declared perturbation while others do not. A family-level median or proportion can help identify where to inspect, but it cannot replace feature-level estimates under the intended test-retest, reconstruction, segmentation, or preprocessing conditions. Do not turn the family labels into the unsupported rules that shape is always reproducible or texture is always unstable. Measure the behavior of the actual definitions under the actual contract.

The measurement table is therefore most useful when every column can be traced back to its family and its assumptions: which values entered, which mask and geometry were used, how continuous intensities were discretised, whether a filter created the image domain, and whether the construction was 2D or 3D. The next section, Texture matrices from first principles, makes that reasoning concrete by starting with discretisation and building a GLCM so that a family name becomes an inspectable operation.

Sources

• Zwanenburg A, Vallières M, Abdalah MA, et al. The Image Biomarker Standardisation Initiative: standardized quantitative radiomics for high-throughput image-based phenotyping. Radiology. 2020;295(2):328-338. doi:10.1148/radiol.2020191145, PMID 32154773, and published full text at PMC7193906.
• PyRadiomics documentation - radiomic feature definitions and customizing the extraction.
• Whybra M, et al. IBSI 2. Radiology. 2024. doi:10.1148/radiol.231319.
• 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.