# Prefer Nested Segmentation to Compound Segmentation

## TL;DR

This paper compares compound and nested segmentation methods for dividing organ contours in radiotherapy, demonstrating that nested segmentation provides more consistent sub-segment volumes and is more suitable for importance assessment.

## Contribution

The study introduces nested segmentation as an improved method over compound segmentation for dividing organ contours, ensuring volume consistency in radiotherapy analysis.

## Key findings

- Compound segmentation leads to inconsistent sub-segment volumes.
- Nested segmentation produces more uniform sub-segment volumes.
- Nested segmentation is faster or comparable in runtime.

## Abstract

Introduction: Intra-organ radiation dose sensitivity is becoming increasingly relevant in clinical radiotherapy. One method for assessment involves partitioning delineated regions of interest and comparing the relative contributions or importance to clinical outcomes. We show that an intuitive method for dividing organ contours, compound (sub-)segmentation, can unintentionally lead to sub-segments with inconsistent volumes, which will bias relative importance assessment. An improved technique, nested segmentation, is introduced and compared. Methods: Clinical radiotherapy planning parotid contours from 510 patients were segmented. Counts of radiotherapy dose matrix voxels interior to sub-segments were used to determine the equivalency of sub-segment volumes. The distribution of voxel counts within sub-segments were compared using Kolmogorov-Smirnov tests and characterized by their dispersion. Analytical solutions for 2D/3D analogues were derived and sub-segment area/volume were compared directly. Results: Both parotid and 2D/3D region of interest analogue segmentation confirmed compound segmentation intrinsically produces sub-segments with volumes that depend on the region of interest shape and selection location. Significant volume differences were observed when sub-segmenting parotid contours into 18ths, and vanishingly small sub-segments were observed when sub-segmenting into 96ths. Central sub-segments were considerably smaller than sub-segments on the periphery. Nested segmentation did not exhibit these shortcomings and produced sub-segments with equivalent volumes when dose grid and contour collinearity was addressed, even when dividing the parotid into 96ths. Nested segmentation was always faster or equivalent in runtime to compound segmentation. Conclusions: Nested segmentation is more suited than compound segmentation for analyses requiring equal weighting of sub-segments.