A semi-supervised learning approach for automated 3D cephalometric landmark identification using computed tomography.

Identification of 3D cephalometric landmarks that serve as proxy to the shape of human skull is the fundamental step in cephalometric analysis. Since manual landmarking from 3D computed tomography (CT) images is a cumbersome task even for the trained experts, automatic 3D landmark detection system is in a great need. Recently, automatic landmarking of 2D cephalograms using deep learning (DL) has achieved great success, but 3D landmarking for more than 80 landmarks has not yet reached a satisfactory level, because of the factors hindering machine learning such as the high dimensionality of the input data and limited amount of training data due to the ethical restrictions on the use of medical data. This paper presents a semi-supervised DL method for 3D landmarking that takes advantage of anonymized landmark dataset with paired CT data being removed. The proposed method first detects a small number of easy-to-find reference landmarks, then uses them to provide a rough estimation of the all landmarks by utilizing the low dimensional representation learned by variational autoencoder (VAE). The anonymized landmark dataset is used for training the VAE. Finally, coarse-to-fine detection is applied to the small bounding box provided by rough estimation, using separate strategies suitable for the mandible and the cranium. For mandibular landmarks, patch-based 3D CNN is applied to the segmented image of the mandible (separated from the maxilla), in order to capture 3D morphological features of mandible associated with the landmarks. We detect 6 landmarks around the condyle all at once rather than one by one, because they are closely related to each other. For cranial landmarks, we again use the VAE-based latent representation for more accurate annotation. In our experiment, the proposed method achieved a mean detection error of 2.88 mm for 90 landmarks using only 15 paired training data.

Deep learning-based solvability of underdetermined inverse problems in medical imaging.

Recently, with the significant developments in deep learning techniques, solving underdetermined inverse problems has become one of the major concerns in the medical imaging domain, where underdetermined problems are motivated by the willingness to provide high resolution medical images with as little data as possible, by optimizing data collection in terms of minimal acquisition time, cost-effectiveness, and low invasiveness. Typical examples include undersampled magnetic resonance imaging(MRI), interior tomography, and sparse-view computed tomography(CT), where deep learning techniques have achieved excellent performances. However, there is a lack of mathematical analysis of why the deep learning method is performing well. This study aims to explain about learning the causal relationship regarding the structure of the training data suitable for deep learning, to solve highly underdetermined problems. We present a particular low-dimensional solution model to highlight the advantage of deep learning methods over conventional methods, where two approaches use the prior information of the solution in a completely different way. We also analyze whether deep learning methods can learn the desired reconstruction map from training data in the three models (undersampled MRI, sparse-view CT, interior tomography). This paper also discusses the nonlinearity structure of underdetermined linear systems and conditions of learning (called M-RIP condition).