Shape-of-You: Fused Gromov-Wasserstein Optimal Transport for Semantic Correspondence in-the-Wild

Semantic correspondence is essential for handling diverse in-the-wild images lacking explicit correspondence annotations. While recent 2D foundation models offer powerful features, adapting them for unsupervised learning via nearest-neighbor pseudo-labels has key limitations: it operates locally, ignoring structural relationships, and consequently its reliance on 2D appearance fails to resolve geometric ambiguities arising from symmetries or repetitive features. In this work, we address this by reformulating pseudo-label generation as a Fused Gromov-Wasserstein (FGW) problem, which jointly optimizes inter-feature similarity and intra-structural consistency. Our framework, Shape-of-You (SoY), leverages a 3D foundation model to define this intra-structure in the geometric space, resolving abovementioned ambiguity. However, since FGW is a computationally prohibitive quadratic problem, we approximate it through anchor-based linearization. The resulting probabilistic transport plan provides a structurally consistent but noisy supervisory signal. Thus, we introduce a soft-target loss dynamically blending guidance from this plan with network predictions to build a learning framework robust to this noise. SoY achieves state-of-the-art performance on SPair-71k and AP-10k datasets, establishing a new benchmark in semantic correspondence without explicit geometric annotations. Code is available at Shape-of-You.

Structure-from-Sherds++: Robust Incremental 3D Reassembly of Axially Symmetric Pots from Unordered and Mixed Fragment Collections

Reassembling multiple axially symmetric pots from fragmentary sherds is crucial for cultural heritage preservation, yet it poses significant challenges due to thin and sharp fracture surfaces that generate numerous false positive matches and hinder large-scale puzzle solving. Existing global approaches, which optimize all potential fragment pairs simultaneously or data-driven models, are prone to local minima and face scalability issues when multiple pots are intermixed. Motivated by Structure-from-Motion (SfM) for 3D reconstruction from multiple images, we propose an efficient reassembly method for axially symmetric pots based on iterative registration of one sherd at a time, called Structure-from-Sherds++ (SfS++). Our method extends beyond simple replication of incremental SfM and leverages multi-graph beam search to explore multiple registration paths. This allows us to effectively filter out indistinguishable false matches and simultaneously reconstruct multiple pots without requiring prior information such as base or the number of mixed objects. Our approach achieves 87% reassembly accuracy on a dataset of 142 real fragments from 10 different pots, outperforming other methods in handling complex fracture patterns with mixed datasets and achieving state-of-the-art performance. Code and results can be found in our project page https://sj-yoo.info/sfs/.