Deep functional maps for simultaneously computing direct and symmetric correspondences of 3D shapes

We introduce a novel method of isometric correspondences for 3D shapes, designed to address the problem of multiple solutions associated with deep functional maps when matching shapes with left-to-right reflectional intrinsic symmetries. Unlike the existing methods that only find the direct correspondences using single Siamese network, our proposed method is able to detect both the direct and symmetric correspondences among shapes simultaneously. Furthermore, our method detects the reflectional intrinsic symmetry of each shape. Key to our method is the using of two Siamese networks that learn consistent direct descriptors and their symmetric ones, combined with carefully designed regularized functional maps and supervised loss. This leads to the first deep functional map capable of both producing two high-quality correspondences of shapes and detecting the left-to-right reflectional intrinsic symmetry of each shape. Extensive experiments demonstrate that the proposed method obtains more accurate results than state-of-the-art methods for shape correspondences and reflectional intrinsic symmetries detection.