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Peize Liu

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Published work

3 published item(s)

preprint2026arXiv

H-OmniStereo: Zero-Shot Omnidirectional Stereo Matching with Heading-Aligned Normal Priors

Stereo matching on top-bottom equirectangular images provides an effective framework for full-surround perception, as vertically aligned epipolar lines enable the use of advanced perspective stereo architectures that are largely driven by large-scale datasets and monocular priors. However, the performance of such adaptations is severely limited by the scarcity of omnidirectional stereo datasets and the degradation of perspective monocular priors under spherical distortions. To address these challenges, we propose H-OmniStereo, a zero-shot omnidirectional stereo matching framework. First, we construct high-quality synthetic dataset comprising over 2.8 million top-bottom equirectangular stereo pairs to scale up training. Second, we introduce an equirectangular monocular normal estimator, specifically operating in a heading-aligned coordinate system. Beyond providing distortion-robust and cross-view-consistent geometric priors for establishing reliable correspondences in stereo matching, this design boosts training efficiency and accommodates train-test FoV mismatches. Extensive experiments show that our approach achieves higher accuracy than existing methods on out-of-domain datasets and successfully generalizes to real-world consumer camera setups using a single model. The model and dataset will be released at https://github.com/JIANG-CX/H-OmniStereo.

preprint2026arXiv

Stability Conditions and Moduli Spaces on Kuznetsov Component of Cubic Fivefolds

We study the Kuznetsov component of cubic fivefolds via their quadric fibration model, and construct a family of Serre-invariant Bridgeland stability conditions on it. For every primitive numerical class, we prove that the associated Bridgeland moduli space contains a non-empty smooth locus, on which the restriction to a general hyperplane section preserves stability. As a consequence, we obtain Lagrangian immersions into hyper-Kähler varieties arising as moduli spaces on the Kuznetsov component of cubic fourfolds, generalizing a geometric construction of Illiev-Manivel, which realizes the Fano surface of planes of the cubic fivefold as a Lagrangian subvariety in a hyper-Kähler fourfold.

preprint2022arXiv

Deformation Quantisation via Kontsevich Formality Theorem

This dissertation is an exposition of Kontsevich's proof of the formality theorem and the classification of deformation quantisation on a Poisson manifold. We begin with an account of the physical background and introduce the Weyl-Moyal product as the first example. Then we develop the deformation theory via differential graded Lie algebras and $\mathrm{L}_\infty$-algebras, which allows us to reformulate the classification of deformation quantisation as the existence of a $\mathrm{L}_\infty$-quasi-isomorphism between two differential graded Lie algebras, known as the formality theorem. Next we present Kontsevich's proof of the formality theorem in $\mathbb{R}^d$ and his construction of the star product. We conclude with a brief discussion of the globalisation of Kontsevich star product on Poisson manifolds.