We provide a novel new approach for aligning geometric models using a dual graph structure where local features are mapping probabilities. Alignment of non-rigid structures is one of the most challenging computer vision tasks due to the high number of unknowns needed to model the correspondence. We have seen a leap forward using DNN models in template alignment and functional maps, but those methods fail for inter-class alignment where nonisometric deformations exist. Here we propose to rethink this task and use unrolling concepts on a dual graph structure - one for a forward map and one for a backward map, where the features are pulled back matching probabilities from the target into the source. We report state of the art results on stretchable domains alignment in a rapid and stable solution for meshes and cloud of points.

翻译：我们提供了一个新的方法,用一个双图表结构来调整几何模型,其中地方特征是绘制概率的。非硬体结构的对齐是最具挑战性的计算机愿景任务之一,因为建模通信需要大量未知因素。我们已经看到在模板对齐和功能地图中使用DNN模型向前飞跃,但在存在非单向畸形的地方,这些方法在等级间对齐方面失败。我们在这里提议重新思考这项任务,在双图表结构上使用松动概念----一个是前方地图,一个是后方地图,将功能从目标中拉回到源头,匹配概率。我们报告可伸缩域对齐的艺术结果,为介质和点云提供快速稳定的解决方案。