Shape Features

Mesh-based volume is computed by counting voxels within a delineated Volume of Interest (VOI) and multiplying by voxel dimensions. Approximated volume uses a marching cubes triangulation of the surface for a more precise boundary representation. Key metrics include:

• Voxel Volume (Vvoxel): The simplest count-based method, sensitive to resolution.
• Mesh Volume (Vmesh): The volume enclosed by the triangulated surface mesh, the IBSI-recommended standard.
• Major Axis Length: The longest diameter of an ellipsoid fitted to the VOI, critical for RECIST-like assessments.

Surface area quantifies the total area of the VOI's boundary, calculated via marching cubes triangulation. The Surface-to-Volume Ratio (SVR) divides surface area by volume, providing a key measure of shape complexity independent of size.

• High SVR: Indicates a spiculated, irregular, or non-spherical morphology, often associated with malignancy.
• Low SVR: Indicates a compact, spherical shape typical of benign nodules or normal anatomical structures.
• Clinical Relevance: SVR is a strong independent predictor in radiomic signatures for tumor aggressiveness and treatment response.

Sphericity measures how closely a VOI resembles a perfect sphere. It is calculated as the ratio of the surface area of a sphere with the same volume to the actual surface area of the VOI. Values range from 0 to 1, where 1 is a perfect sphere.

• Compactness 1 & 2: Alternative formulations that relate volume to surface area or the maximum enclosing sphere.
• Asphericity: The inverse concept, quantifying deviation from spherical shape.
• Engineering Note: These metrics are highly sensitive to voxel resampling and require isotropic voxels for accurate cross-scan comparisons.

The Maximum 3D Diameter is defined as the largest pairwise Euclidean distance between any two surface mesh vertices of the VOI. It represents the longest straight line that can be drawn through the object's volume.

• Feret Diameter: The 2D analog, measured on a single slice; the 3D version is more robust to slice orientation.
• Clinical Use: This metric directly correlates with the Response Evaluation Criteria in Solid Tumors (RECIST) but provides a true 3D assessment rather than a single axial measurement.
• Elongation: Derived from the ratio of the major to minor principal axes, indicating how stretched the shape is.

Flatness quantifies the relationship between the three principal axes of an ellipsoid fitted to the VOI. It is defined as the square root of the ratio of the second largest to the largest principal component.

• Elongation: The ratio of the minor to major principal axes, indicating a stretched, cigar-like shape.
• Principal Component Analysis (PCA): Used to compute the three orthogonal axes that best describe the shape's orientation and extent.
• Interpretation: A flat, discoid lesion will have low flatness, while a tubular or elongated structure will have low elongation.

The Least Axis Length is the smallest diameter of the PCA-fitted ellipsoid, representing the shortest dimension through the VOI's center of mass. The Minor Axis Length is the second-largest principal axis.

• Shape Descriptors: Together with the Major Axis, these three lengths fully describe the size and proportions of the best-fit ellipsoid.
• Clinical Application: The least axis is particularly useful for assessing tumor invasion depth and proximity to critical structures in surgical planning.
• Robustness: These metrics are generally robust to segmentation variability when the overall mass is correctly identified.