Computed tomography (CT) and magnetic resonance imaging (MRI) scanners measure three-dimensional (3D) images of patients. However, only low-dimensional local twodimensional (2D) images may be obtained during surgery or radiotherapy. Although computer vision techniques have shown that 3D shapes can be estimated from multiple 2D images, shape reconstruction from a single 2D image such as an endoscopic image or an X-ray image remains a challenge. In this study, we propose X-ray2Shape, which permits a deep learning-based 3D organ mesh to be reconstructed from a single 2D projection image. The method learns the mesh deformation from a mean template and deep features computed from the individual projection images. Experiments with organ meshes and digitally reconstructed radiograph (DRR) images of abdominal regions were performed to confirm the estimation performance of the methods.

This paper is concerned with a formation shaping problem for point agents in a two-dimensional space, where control avoids the possibility of reflection ambiguities. One solution for this type of problems was given first for three or four agents by considering a potential function which consists of both the distance error and the signed area terms. Then, by exploiting a hierarchical control strategy with such potential functions, the method was extended to any number of agents recently. However, a specific gain on the signed area term must be employed there, and it does not guarantee the global convergence. To overcome this issue, this paper provides a necessary and sufficient condition for the global convergence, subject to the constraint that the desired formation consists of isosceles triangles only. This clarifies the admissible range of the gain on the signed area for this case. In addition, as for formations consisting of arbitrary triangles, it is shown when high gain on the signed area is admissible for global convergence.

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