Pengfei He

Hongyuan Zhang, Ching-Wei Wang, Hikam Muzakky et al.

Localization of the craniofacial landmarks from lateral cephalograms is a fundamental task in cephalometric analysis. The automation of the corresponding tasks has thus been the subject of intense research over the past decades. In this paper, we introduce the "Cephalometric Landmark Detection (CL-Detection)" dataset, which is the largest publicly available and comprehensive dataset for cephalometric landmark detection. This multi-center and multi-vendor dataset includes 600 lateral X-ray images with 38 landmarks acquired with different equipment from three medical centers. The overarching objective of this paper is to measure how far state-of-the-art deep learning methods can go for cephalometric landmark detection. Following the 2023 MICCAI CL-Detection Challenge, we report the results of the top ten research groups using deep learning methods. Results show that the best methods closely approximate the expert analysis, achieving a mean detection rate of 75.719% and a mean radial error of 1.518 mm. While there is room for improvement, these findings undeniably open the door to highly accurate and fully automatic location of craniofacial landmarks. We also identify scenarios for which deep learning methods are still failing. Both the dataset and detailed results are publicly available online, while the platform will remain open for the community to benchmark future algorithm developments at https://cl-detection2023.grand-challenge.org/.

Nicolas Garcia Trillos, Pengfei He, Chenghui Li

In this work we study statistical properties of graph-based algorithms for multi-manifold clustering (MMC). In MMC the goal is to retrieve the multi-manifold structure underlying a given Euclidean data set when this one is assumed to be obtained by sampling a distribution on a union of manifolds $\mathcal{M} = \mathcal{M}_1 \cup\dots \cup \mathcal{M}_N$ that may intersect with each other and that may have different dimensions. We investigate sufficient conditions that similarity graphs on data sets must satisfy in order for their corresponding graph Laplacians to capture the right geometric information to solve the MMC problem. Precisely, we provide high probability error bounds for the spectral approximation of a tensorized Laplacian on $\mathcal{M}$ with a suitable graph Laplacian built from the observations; the recovered tensorized Laplacian contains all geometric information of all the individual underlying manifolds. We provide an example of a family of similarity graphs, which we call annular proximity graphs with angle constraints, satisfying these sufficient conditions. We contrast our family of graphs with other constructions in the literature based on the alignment of tangent planes. Extensive numerical experiments expand the insights that our theory provides on the MMC problem.