NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Go

We present NeuroMorph, a new neural network architecture that takes as input two 3D shapes and produces in one go, i.e. in a single feed forward pass, a smooth interpolation and point-to-point correspondences between them. The interpolation, expressed as a deformation field, changes the pose of the source shape to resemble the target, but leaves the object identity unchanged. NeuroMorph uses an elegant architecture combining graph convolutions with global feature pooling to extract local features. During training, the model is incentivized to create realistic deformations by approximating geodesics on the underlying shape space manifold. This strong geometric prior allows to train our model end-to-end and in a fully unsupervised manner without requiring any manual correspondence annotations. NeuroMorph works well for a large variety of input shapes, including non-isometric pairs from different object categories. It obtains state-of-the-art results for both shape correspondence and interpolation tasks, matching or surpassing the performance of recent unsupervised and supervised methods on multiple benchmarks.Comment: Published at the IEEE/CVF Conference on Computer Vision and Pattern Recognition 202

Projection-based Topology Optimization Method for Linear and Nonlinear Design

Lighter designs are desirable in many industrial applications and structural optimization is an effective way to generate lightweight structures. Topology optimization is an important tool for investigating the optimal design of engineering structures. Although continuum topology optimization method has already achieved remarkable progress in recent years, there still exist several challenges for conventional density-based method such as manufacturability. Additive manufacturing (AM) is a rapidly developing technology by which the design can achieve more freedom. However, it does not mean that the optimized design generated by topology optimization algorithm can be directly manufactured without any geometry post-processing. Besides AM techniques, the traditional manufacturing methods of machining and casting are also popular in recent years, because the majority of engineering parts are manufactured through these methods. It is difficult for conventional density-based method to account for these manufacturing constraints. The projection-based topology optimization approach is a new trend in this field to properly restrict the optimal solutions by implementing geometric constraints. The nature of projection method is to apply new design variables projected in a pseudo-density domain to find the optimal solutions. In this dissertation, several advanced projection-based topology optimization schemes are proposed to resolve linear and nonlinear design problems and demonstrated through numerical examples. In chapter 2 and 3, a new projection technique is proposed to resolve nonlinear topology optimization problems with large deformation. Chapter 4 describes a novel design method, which combines the TPMS (Triply periodic minimal surface) formulation with standard projection-based method to design functionally graded TPMS lattice. In chapter 5, a projection-based method is combined with moving particles for reverse shape compensation for additive manufacturing technique. Chapter 6 describes a density‐based boundary evolving algorithm based on projection function for continuum‐based topology optimization. In the chapter 7, a novel projection-based method for structural design considering restrictions of multi-axis machining processes is proposed