# Canonical Surface Mapping via Geometric Cycle Consistency

## TL;DR

This paper introduces a novel geometric cycle consistency approach for Canonical Surface Mapping that enables training models to predict dense correspondences between images and 3D models without extensive manual annotations.

## Contribution

The paper proposes a cycle consistency loss for CSM, allowing training with only foreground masks, enabling scalable learning across diverse classes without dense supervision.

## Key findings

- Achieves dense correspondence prediction without manual keypoint annotations
- Outperforms methods requiring more supervision in correspondence tasks
- Enables scalable CSM across multiple object categories

## Abstract

We explore the task of Canonical Surface Mapping (CSM). Specifically, given an image, we learn to map pixels on the object to their corresponding locations on an abstract 3D model of the category. But how do we learn such a mapping? A supervised approach would require extensive manual labeling which is not scalable beyond a few hand-picked categories. Our key insight is that the CSM task (pixel to 3D), when combined with 3D projection (3D to pixel), completes a cycle. Hence, we can exploit a geometric cycle consistency loss, thereby allowing us to forgo the dense manual supervision. Our approach allows us to train a CSM model for a diverse set of classes, without sparse or dense keypoint annotation, by leveraging only foreground mask labels for training. We show that our predictions also allow us to infer dense correspondence between two images, and compare the performance of our approach against several methods that predict correspondence by leveraging varying amount of supervision.