Aortic root landmark localization with optimal transport loss for heatmap regression

TL;DR

This work tackles accurate aortic root landmark localization from 3D CT to aid transcatheter aortic valve implantation planning. It introduces a one-step heatmap regression framework based on optimal transport loss, augmented by a grid-based Lipschitz penalty (GLiP) to balance stability and precision when learning from downsampled CT data. The method, implemented with a 3D U-Net and Gaussian ground-truth heatmaps for the RCC, LCC, and NCC hinge points, achieves sub-2 mm median errors and outperforms existing two-stage approaches and other loss functions. While demonstrated on a private 3D CT dataset, the approach promises robust, high-accuracy landmark localization on coarse images and potential extensions to valve sizing and other anatomical sites, with code available on GitHub. The GLiP–OT framework offers stable learning for heatmap regression and may generalize to other modalities and architectures beyond U-Net.

Abstract

Anatomical landmark localization is gaining attention to ease the burden on physicians. Focusing on aortic root landmark localization, the three hinge points of the aortic valve can reduce the burden by automatically determining the valve size required for transcatheter aortic valve implantation surgery. Existing methods for landmark prediction of the aortic root mainly use time-consuming two-step estimation methods. We propose a highly accurate one-step landmark localization method from even coarse images. The proposed method uses an optimal transport loss to break the trade-off between prediction precision and learning stability in conventional heatmap regression methods. We apply the proposed method to the 3D CT image dataset collected at Sendai Kousei Hospital and show that it significantly improves the estimation error over existing methods and other loss functions. Our code is available on GitHub.

Figures (12)

• Figure 1: Architecture of U-Net. The input is 3D-CT data, and the output is the predicted heatmaps of three landmarks. Magenta arrows denote convolution operation with kernel size 3 and ReLU activation function. Red arrows denote the max-pooling of size 2, green arrows denote the up-sampling of size 2, and blue blanked arrows denote the skip connection. Blue boxes correspond to the size of features. The width and height of the boxes are proportional to feature dimension and image size.
• Figure 2: Boxplot of test Euclid distance error of the two existing methods (Tan+19 and Noothout+20) and six loss functions (WCE, FL, MSE, L1, SL1, GLiP) with U-Net. Although the worst errors of UNet-FL (47.7 mm) and UNet-SL1 (38.5 mm) are higher than 14 mm, these points are omitted for space limitation in the figure.
• Figure 3: Boxplot of the test average projection distance error between the ground truth and predicted landmarks.
• Figure 4: Boxplot of the test angle error between the ground truth and predicted planes. The worst error of Noohtout+20 and UNet-SL1 is higher than 15.
• Figure 5: Boxplot of test Euclid distance error for optimal transport loss with/without the penalty term of GLiP. Plane means the average projection distance.