Shape Metric

Shape metrics quantify the similarity or dissimilarity between geometric objects, a crucial task in various fields from computer vision to neuroscience. Current research focuses on developing robust and efficient shape metrics, particularly for high-dimensional data and neural network representations, addressing challenges like computational cost and statistical uncertainty in limited data regimes. This includes developing novel distance functions like symmetric Chamfer distance to improve accuracy in 3D reconstruction and exploring the relationships between different shape metrics, such as the connection between Bures distance and shape distances. Improved shape metrics enhance the accuracy and interpretability of analyses across diverse applications, including image processing, data visualization, and the analysis of neural network representations.