Chapter 34: Quantification and Radiomics
First-order statistics of ROIs/VOIs, texture (GLCM), shape features, and radiomics. Turning images into numbers. The close of the textbook.
The last topic of the image-processing part is quantification: turning an image into numbers. From an extracted region of interest (ROI, 2D) or volume of interest (VOI, 3D), it pulls out features that feed decisions about diagnosis, prognosis, and treatment response. The aim of this step is to turn the impression the eye forms into a reproducible number.
First-order statistics and histogram features
The most basic features are statistics of the pixel values themselves within the ROI. The mean CT number reflects the tissue type or the degree of contrast enhancement; the standard deviation and entropy reflect internal heterogeneity. The more mottled the inside of a tumor, the larger the standard deviation and the histogram entropy. Skewness and kurtosis capture the asymmetry and peakedness of the histogram's shape. These are first-order features determined by the histogram alone; they do not look at how the pixels are arranged (their spatial relationship).
Texture: the same mean, a different "grain"
Even with the same mean, a different arrangement of pixels gives a different "grain" (texture). A smooth region and a finely mottled region can have similar mean and standard deviation and be distinguishable only by texture. The standard way to capture this is the gray-level co-occurrence matrix (GLCM). It counts the combinations of gray levels of pixel pairs adjacent in a given direction, and derives Haralick features from that distribution.
- Contrast: the expected squared difference of adjacent pixel values. Large in a rough region.
- Homogeneity: gives large weight to pixel pairs of close value. Large in a smooth region.
- Energy and entropy: the concentration and disorder of the co-occurrence distribution.
- Correlation: the linear correlation of adjacent pixel values.
The same mean with different texture, and the radiomics pipeline. Left: even at the same mean, a smooth region and a textured region are distinguishable by texture features. Right: from an ROI, first-order, texture (GLCM), and shape features are taken, formed into a feature vector, and fed to a machine-learning model.
Simulation: place an ROI and measure
On a phantom with two regions of the same mean but different texture, place a box ROI and measure. Switch presets between the "smooth region" and the "textured region." The means are nearly the same, yet the standard deviation and the GLCM contrast and homogeneity differ clearly. Because GLCM looks at how pixels are arranged (their spatial relationship), it picks up a difference in "grain" that first-order statistics cannot. This is capturing, through texture, a difference the mean alone cannot see.
Phantom and ROI
ROI histogram
On a phantom with two regions of the same mean but different texture, place a box ROI and measure. Switching presets between the smooth and textured regions, the means are nearly identical yet the standard deviation and the GLCM contrast and homogeneity differ clearly. Because GLCM looks at how pixels are arranged, it picks up a difference in grain that first-order statistics cannot. Capturing, through texture, a difference the mean alone cannot see is the idea of radiomics.
Shape features and radiomics
The shape of a region is a feature too: area and volume, perimeter and surface area, circularity (sphericity in 3D), and compactness. Circularity is , equal to 1 for a circle and smaller the more elongated. The more irregular a tumor's outline, the more these shape features indicate "complex."
Radiomics gathers hundreds to thousands of first-order, texture, and shape features and feeds them to machine learning to predict prognosis, genotype, and treatment response. It is the same idea as quantifying dimensions and defects in the non-destructive testing of Chapter 7, extended to medical images.
The pitfalls of radiomics
Features are sensitive to acquisition settings, reconstruction method, voxel size, and how the ROI is drawn, and their values drift between scanners and sites. The number of features tends to exceed the number of cases, making overfitting and spurious correlation easy. Reproducibility and standardization (efforts like the IBSI) and validation on independent data are the keys to using radiomics clinically. Quantification is powerful, but you need to know what each number depends on, and how much.
Closing: from measurement to using the image
The textbook has come full circle. It began with a single X-ray in Chapter 1 and traced CT reconstruction: line integrals and the sinogram, simple backprojection and its blur, filtered backprojection, fan and cone beams, industrial CT, Monte Carlo photon transport, iterative reconstruction, dose and image quality, sparse views and compressed sensing, artifacts, deep learning, and spectral CT. From there it crossed worlds where the same mathematics changes form: MRI's Fourier measurement, nuclear medicine's emission counting and collimators, and in the Frontiers part, tomosynthesis, photoacoustics, electron tomography, and phase contrast. In this final image-processing part, it reached the point of displaying, cleaning, extracting, overlaying, and measuring the images so reconstructed.
The skeleton running through it all is simple. First measure something (measurement), recover an image from limited measurements (reconstruction), and put that image into a form people and machines can use (image processing). The devices, the scales, and the physical quantities measured all differ, but this three-part flow, and the tools that support it (the Fourier transform, optimization, regularization, statistical models, and learning), were shared throughout. For a reader who has confirmed all this by hand, the new devices and methods you meet next should be understandable by placing them somewhere on this map. Tomographic imaging is the work of connecting the physics of measurement through mathematics.
References
- Haralick RM, Shanmugam K, Dinstein I. Textural Features for Image Classification. IEEE Transactions on Systems, Man, and Cybernetics 3, 610–621 (1973).
- Gillies RJ, Kinahan PE, Hricak H. Radiomics: Images Are More than Pictures, They Are Data. Radiology 278, 563–577 (2016).
- Zwanenburg A et al. The Image Biomarker Standardization Initiative. Radiology 295, 328–338 (2020).
- Lambin P et al. Radiomics: extracting more information from medical images using advanced feature analysis. European Journal of Cancer 48, 441–446 (2012).