# Area-preserving mapping of 3D ultrasound carotid artery images using density-equalizing reference map

## TL;DR

This paper introduces a novel area-preserving mapping technique called density-equalizing reference map (DERM) for 3D carotid artery images, enabling accurate comparison of vessel-wall thickness across patients by minimizing local geometric distortion.

## Contribution

The paper presents a new area-preserving mapping method that combines density-equalizing and reference map techniques to accurately flatten 3D carotid surfaces onto a standardized 2D domain.

## Key findings

- Reduced area distortion by over 80% compared to previous methods
- First one-to-one area-preserving map from 3D surface to non-convex 2D domain
- Effective for quantitative analysis of carotid artery features

## Abstract

Carotid atherosclerosis is a focal disease at the bifurcations of the carotid artery. To quantitatively monitor the local changes in the vessel-wall-plus-plaque thickness (VWT) and compare the VWT distributions for different patients or for the same patients at different ultrasound scanning sessions, a mapping technique is required to adjust for the geometric variability of different carotid artery models. In this work, we propose a novel method called density-equalizing reference map (DERM) for mapping 3D carotid surfaces to a standardized 2D carotid template, with an emphasis on preserving the local geometry of the carotid surface by minimizing the local area distortion. The initial map was generated by a previously described arc-length scaling (ALS) mapping method, which projects a 3D carotid surface onto a 2D non-convex L-shaped domain. A smooth and area-preserving flattened map was subsequently constructed by deforming the ALS map using the proposed algorithm that combines the density-equalizing map and the reference map techniques. This combination allows, for the first time, one-to-one mapping from a 3D surface to a standardized non-convex planar domain in an area-preserving manner. Evaluations using 20 carotid surface models show that the proposed method reduced the area distortion of the flattening maps by over 80% as compared to the ALS mapping method.