基于欧拉特征变换的二维切片重建三维图像的拓扑损失法
Euler Characteristic Transform Based Topological Loss for Reconstructing 3D Images from Single 2D Slices
摘要：
重建三维图像的计算机视觉任务，即，从单个2D图像切片中提取形状是极具挑战性的，在有限数据的情况下更是如此。深度学习模型通常会优化几何损失函数，这可能会导致重建效果不佳，因为它们忽略了形状的结构属性。为了解决这个问题，我们提出了一种新的拓扑损失函数的基础上的欧拉特征变换。这种损失可以被用作一种归纳偏差，以帮助优化任何神经网络，在有限数据的情况下进行更好的重建。我们通过将其纳入SHAPR（一种最先进的形状重建模型）来展示所提出的损失函数的有效性，并在两个基准数据集上进行测试，即，红细胞和细胞核数据集。我们还展示了一个有利的性质，即内射性，并讨论了基于欧拉特征变换的拓扑损失函数的稳定性。
英文摘要：
The computer vision task of reconstructing 3D images, i.e., shapes, from their single 2D image slices is extremely challenging, more so in the regime of limited data. Deep learning models typically optimize geometric loss functions, which may lead to poor reconstructions as they ignore the structural properties of the shape. To tackle this, we propose a novel topological loss function based on the Euler Characteristic Transform. This loss can be used as an inductive bias to aid the optimization of any neural network toward better reconstructions in the regime of limited data. We show the effectiveness of the proposed loss function by incorporating it into SHAPR, a state-of-the-art shape reconstruction model, and test it on two benchmark datasets, viz., Red Blood Cells and Nuclei datasets. We also show a favourable property, namely injectivity and discuss the stability of the topological loss function based on the Euler Characteristic Transform.
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