Assembling parts into an object is a combinatorial problem that arises in a variety of contexts in the real world and involves numerous applications in science and engineering. Previous related work tackles limited cases with identical unit parts or jigsaw-style parts of textured shapes, which greatly mitigate combinatorial challenges of the problem. In this work, we introduce the more challenging problem of shape assembly, which involves textureless fragments of arbitrary shapes with indistinctive junctions, and then propose a learning-based approach to solving it. We demonstrate the effectiveness on shape assembly tasks with various scenarios, including the ones with abnormal fragments (e.g., missing and distorted), the different number of fragments, and different rotation discretization.

翻译：将部件组合成一个物体是一个组合问题,在现实世界的多种情况下产生,涉及科学和工程方面的多种应用。以往的相关工作处理的有限案例有相同的单元部分或纹质形状的拼图式部分,这大大减轻了问题的组合性挑战。在这项工作中,我们引入了更具有挑战性的形状组合问题,它涉及任意形状的无纹理碎片和不清晰的交接点,然后提出一种基于学习的解决方案。我们展示了形状组合任务在各种情景下的有效性,包括异常碎片(如缺失和扭曲)、不同碎片数量和不同交替离散的情况。