Automatic segmentation of magnetic resonance (MR) images is crucial for morphological evaluation of the pediatric musculoskeletal system in clinical practice. However, the accuracy and generalization performance of individual segmentation models are limited due to the restricted amount of annotated pediatric data. Hence, we propose to train a segmentation model on multiple datasets, arising from different parts of the anatomy, in a multi-task and multi-domain learning framework. This approach allows to overcome the inherent scarcity of pediatric data while benefiting from a more robust shared representation. The proposed segmentation network comprises shared convolutional filters, domain-specific batch normalization parameters that compute the respective dataset statistics and a domain-specific segmentation layer. Furthermore, a supervised contrastive regularization is integrated to further improve generalization capabilities, by promoting intra-domain similarity and impose inter-domain margins in embedded space. We evaluate our contributions on two pediatric imaging datasets of the ankle and shoulder joints for bone segmentation. Results demonstrate that the proposed model outperforms state-of-the-art approaches.

The scope of this paper is the guaranteed fitting of specified types of quadratic surfaces to scattered 3D point clouds. Since we chose quadrics to account for articular surfaces of various shapes in medical images, the models thus estimated usefully extract global symmetry-related intrinsic features in human joints: centers, axes, extremal curvatures. The unified type-enforcing method is based on a constrained weighted least-squares minimization of algebraic residuals which uses a robust and bias- corrected metric. Provided that at most one quadratic constraint is involved, every step produces closed-form eigenvector solutions. In this framework, guaranteeing the occurrence of 3D primitives of certain types among this eigendecomposition is not a straightforward transcription of the priorly handled 2D case. To explore possibilities, we re-exploit a mapping to a 2D space called the quadric shape map (QSM) where the influence of any constraint on shape and type can in fact be studied visually. As a result, we provide a new enforceable quadratic constraint that practically ensures types such as hyperboloids, which helps characterize saddle-like articular surfaces. Application to a database shows how this guarantee is needed to coherently extract the center and axes of the ankle joint.

Presents a geometric model to be used as a framework for the description and analysis of three-dimensional (3-D) elongated shapes. Elongated shapes can be decomposed into two different parts: a 3-D curve (the central axis) and a 3-D surface (the straight surface). The central axis is described in terms of curvature and torsion. A novel concept of torsion image is introduced which allows the user to study the torsion of some relevant 3-D structures such as the medulla of long bones, without computing the third derivative. The description of the straight surface is based on an ordered set of Fourier Descriptors (FDs), each set representing a 2-D slice of the structure. These descriptors possess completeness, continuity, and stability properties, and some geometrical invariancies. A polar diagram is built which contains the anatomical information of the straight surface and can be used as a tool for the analysis and discrimination of 3-D structures. A technique for the reconstruction of the 3-D surface from the model's two components is presented. Various applications to the analysis of long bone structures, such as the ulna and radius, are derived from the model, namely, data compression, comparison of 3-D shapes, segmentation into 3-D primitives, and torsion and curvature analysis. The relevance of the method to morphometry and to clinical applications is discussed.