π^3: Scalable Permutation-Equivariant Visual Geometry Learning
We introduce pi^3, a feed-forward neural network that offers a novel
approach to visual geometry reconstruction, breaking the reliance on a
conventional fixed reference view. Previous methods often anchor their
reconstructions to a designated viewpoint, an inductive bias that can lead to
instability and failures if the reference is suboptimal. In contrast, pi^3
employs a fully permutation-equivariant architecture to predict
affine-invariant camera poses and scale-invariant local point maps without any
reference frames. This design makes our model inherently robust to input
ordering and highly scalable. These advantages enable our simple and bias-free
approach to achieve state-of-the-art performance on a wide range of tasks,
including camera pose estimation, monocular/video depth estimation, and dense
point map reconstruction. Code and models are publicly available.
6879b78a21b37e676c8e40b1
Yifan Wang
6879b78a21b37e676c8e40b2
Jianjun Zhou
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Haoyi Zhu
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Wenzheng Chang
6879b78a21b37e676c8e40b5
Yang Zhou
6879b78a21b37e676c8e40b6
Zizun Li
6879b78a21b37e676c8e40b7
Junyi Chen
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Jiangmiao Pang
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Chunhua Shen
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Tong He
admin_assigned
2025-07-18T12:44:26.300Z
6747ede3a9c72aebe1322382
https://cdn-avatars.huggingface.co/v1/production/uploads/no-auth/inILqQ05sESbYLdsEldJ_.png
Tong He
user
tonghe90
π^3: Scalable Permutation-Equivariant Visual Geometry Learning
We introduce pi^3, a feed-forward neural network that offers a novel
approach to visual geometry reconstruction, breaking the reliance on a
conventional fixed reference view. Previous methods often anchor their
reconstructions to a designated viewpoint, an inductive bias that can lead to
instability and failures if the reference is suboptimal. In contrast, pi^3
employs a fully permutation-equivariant architecture to predict
affine-invariant camera poses and scale-invariant local point maps without any
reference frames. This design makes our model inherently robust to input
ordering and highly scalable. These advantages enable our simple and bias-free
approach to achieve state-of-the-art performance on a wide range of tasks,
including camera pose estimation, monocular/video depth estimation, and dense
point map reconstruction. Code and models are publicly available.
A permutation-equivariant neural network, $\pi^3$, reconstructs visual geometry without a fixed reference view, achieving state-of-the-art performance in camera pose estimation, depth estimation, and point map reconstruction.
feed-forward neural network permutation-equivariant architecture affine-invariant scale-invariant camera pose estimation monocular depth estimation video depth estimation dense point map reconstruction