GenCorres: Consistent Shape Matching via Coupled Implicit-Explicit Shape Generative Models

TL;DR

GenCorres tackles unsupervised joint shape matching by learning a coupled implicit and mesh shape generator to fit a collection of unorganized shapes. It uses Stage I to build a dense, regularized implicit shape space with ARAP/ACAP-based geo-regularization and cycle-consistency, Stage II to initialize an explicit mesh generator via latent-space interpolation and template registration, and Stage III to refine the mesh generator with Chamfer-based alignment and deformation priors. The approach unifies joint and pairwise matching, enabling dense, consistent correspondences across a large synthetic shape space and delivering a compact encoding of correspondences. Experimental results on DFAUST, FAUST, and SMAL demonstrate state-of-the-art performance in both shape generation quality and joint/pairwise matching, while ablations highlight the importance of geo-regularization, cycle-consistency, and the explicit generator for robust correspondences.

Abstract

This paper introduces GenCorres, a novel unsupervised joint shape matching (JSM) approach. Our key idea is to learn a mesh generator to fit an unorganized deformable shape collection while constraining deformations between adjacent synthetic shapes to preserve geometric structures such as local rigidity and local conformality. GenCorres presents three appealing advantages over existing JSM techniques. First, GenCorres performs JSM among a synthetic shape collection whose size is much bigger than the input shapes and fully leverages the datadriven power of JSM. Second, GenCorres unifies consistent shape matching and pairwise matching (i.e., by enforcing deformation priors between adjacent synthetic shapes). Third, the generator provides a concise encoding of consistent shape correspondences. However, learning a mesh generator from an unorganized shape collection is challenging, requiring a good initialization. GenCorres addresses this issue by learning an implicit generator from the input shapes, which provides intermediate shapes between two arbitrary shapes. We introduce a novel approach for computing correspondences between adjacent implicit surfaces, which we use to regularize the implicit generator. Synthetic shapes of the implicit generator then guide initial fittings (i.e., via template-based deformation) for learning the mesh generator. Experimental results show that GenCorres considerably outperforms state-of-the-art JSM techniques. The synthetic shapes of GenCorres also achieve salient performance gains against state-of-the-art deformable shape generators.

Figures (10)

• Figure 1: GenCorres performs consistent shape matching by learning a coupled implicit and mesh (explicit) generator to fit a shape collection without pre-defined correspondences. (Left) Interpolation between a pair of shape in the shape space. Constraining deformations between adjacent synthetic shapes with the regularization loss improves the shape space. (Right) The mesh generator provides consistent correspondences between pairs of shapes.
• Figure 2: GenCorres has three stages. The first stage learns an implicit shape generator to fit the input shapes. The training loss regularizes the induced correspondences between adjacent implicit shapes of the generator. The second stage uses the implicit generator to initialize a mesh generator through latent space interpolation and template matching. The third stage then refines the mesh generator with ACAP energy.
• Figure 3: (Left) Effects of the geometric deformation regularization loss $r_{\textup{geo}}(f^{\phi})$. We compute 30 interpolated shapes between a source shape (a) and a target shape (b) via linear interpolation between their latent codes. All the interpolated shapes are visualized in the same coordinate system. (c) Interpolation results without $r_{\textup{geo}}(f^{\phi})$. (d) With $r_{\textup{geo}}(f^{\phi})$. (Right) Effects of the cycle-consistency regularization loss $r_{\textup{cyc}}(f^{\phi})$. We color-code errors of propagated correspondences through a path of intermediate shapes between each source-target shape pair. The error is visualized on the target mesh. (e) Without $r_{\textup{cyc}}(f^{\phi})$. (f) With $r_{\textup{cyc}}(f^{\phi})$.
• Figure 4: The mesh generator improves the inter-shape correspondences by learning better shape generation. (a) the deformed template from stage II. (b) the shape generated by the mesh generator. (c) the input raw mesh.
• Figure 5: The comparison of shape interpolation between SALD atzmon_2021_sald and our method on the DFAUST dataset. (a) source shape. (b) target shape. (c) interpolation results of SALD. (d) our results.