Towards multiple 3D bone surface identification and reconstruction using few 2D X-ray images for intraoperative applications

This article discusses a possible method to use a small number, e.g. 5, of conventional 2D X-ray images to reconstruct multiple 3D bone surfaces intraoperatively. Each bone’s edge contours in X-ray images are automatically identified. Sparse 3D landmark points of each bone are automatically reconstructed by pairing the 2D X-ray images. The reconstructed landmark point distribution on a surface is approximately optimal covering main characteristics of the surface. A statistical shape model, dense point distribution model (DPDM), is then used to fit the reconstructed optimal landmarks vertices to reconstruct a full surface of each bone separately. The reconstructed surfaces can then be visualised and manipulated by surgeons or used by surgical robotic systems

Unsupervised Generative Modeling Using Matrix Product States

Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum physics, we propose a generative model using matrix product states, which is a tensor network originally proposed for describing (particularly one-dimensional) entangled quantum states. Our model enjoys efficient learning analogous to the density matrix renormalization group method, which allows dynamically adjusting dimensions of the tensors and offers an efficient direct sampling approach for generative tasks. We apply our method to generative modeling of several standard datasets including the Bars and Stripes, random binary patterns and the MNIST handwritten digits to illustrate the abilities, features and drawbacks of our model over popular generative models such as Hopfield model, Boltzmann machines and generative adversarial networks. Our work sheds light on many interesting directions of future exploration on the development of quantum-inspired algorithms for unsupervised machine learning, which are promisingly possible to be realized on quantum devices.Comment: 11 pages, 12 figures (not including the TNs) GitHub Page: https://congzlwag.github.io/UnsupGenModbyMPS