Many innovative applications require establishing correspondences among 3D geometric objects. However, the countless possible deformations of smooth surfaces make shape matching a challenging task. Finding an embedding to represent the different shapes in high-dimensional space where the matching is easier to solve is a well-trodden path that has given many outstanding solutions. Recently, a new trend has shown advantages in learning such representations. This novel idea motivated us to investigate which properties differentiate these data-driven embeddings and which ones promote state-of-the-art results. In this study, we analyze, for the first time, properties that arise in data-driven learned embedding and their relation to the shape-matching task. Our discoveries highlight the close link between matching and smoothness, which naturally emerge from training. Also, we demonstrate the relation between the orthogonality of the embedding and the bijectivity of the correspondence. Our experiments show exciting results, overcoming well-established alternatives and shedding a different light on relevant contexts and properties for learned embeddings.
翻译:许多创新应用都需要在 3D 几何天体中建立对应。 然而, 光滑表面的无数可能的变形使得形状与一项挑战性任务相匹配。 找到一个嵌入以代表高维空间中不同形状, 匹配比较容易解决的形状, 是一条非常坚固的路径。 最近, 一个新的趋势在学习这种表达方式方面显示出优势。 这个新想法促使我们调查这些数据驱动的嵌入和那些促进最先进结果的属性。 在这项研究中, 我们首次分析了数据驱动的学习嵌入及其与形状匹配任务的关系中产生的属性。 我们的发现凸显了匹配与平滑之间的密切联系, 后者自然从培训中产生。 另外, 我们还展示了嵌入和对应的两面性之间的关系。 我们的实验展示了令人振奋的结果, 克服了完善的替代方法,并对相关背景和特性进行了不同的透视, 以便学习嵌入。