arXiv subjects
Publications and source records attributed to Junyan Cao.
This article is motivated by the OpenAI manuscripts "Minimal metrics and interior injectivity for nef adjoints" and "Log abundance in characteristic zero". We establish a jet comparison for metrics with minimal singularities and use it to prove a dlt-type extension theorem. Combined with geometric arguments from the latter manuscript, this yields an alternative analytic proof of its Theorem~3.1.
We introduce and study a new numerical invariant of big line bundles on normal complex projective varieties, defined in terms of the total Betti number of hypersurfaces associated with high tensor powers of the line bundle. We prove that this invariant is birational and provides an upper bound for the volume of the line bundle. When the big line bundle admits a rational Zariski decomposition, we show that the invariant coincides with the volume. In particular, this holds when the line bundle is ample or is defined on a projective surface. We also investigate the analogous problem in the real algebraic setting, proving the existence of real algebraic hypersurfaces associated with high tensor powers of a big line bundle whose real vanishing loci have arbitrarily large total Betti numbers.
We address a question of Campana by giving a criterion for when nilpotent local systems on quasi-projective varieties have 2-step nilpotent monodromy. As an application, we prove that the monodromy group of any complex local system on smooth complex quasi-projective variety that is special in the sense of Campana or $h$-special (e.g. containg a Zariski dense entire curve), is virtually 2-step nilpotent. This result sharply refines a theorem of Cadorel, Yamanoi, and the second author. To establish this result, we develop a deformation theory for certain local systems on quasi-compact Kähler manifolds by constructing universal deformations for such local systems.
In this paper, we prove that if $E$ is a pseudo-effective sheaf with vanishing first Chern class on a klt compact Kähler space $X$, then, after passing to a finite quasi-étale cover, the reflexive pullback of $E$ is locally free and flat. This extends the flatness criterion of Höring--Peternell, originally established for projective varieties, to the Kähler setting. The proof relies on two main ingredients, both of which are new even in the projective case. The first is a flatness theorem for stable sheaves: we show that a slope-stable pseudo-effective sheaf with vanishing first Chern class is Hermitian flat. This is obtained by combining Hermitian--Einstein theory with the subharmonicity properties of direct image sheaves. The second is a singular Kähler analogue of Simpson's flatness theorem for extensions of locally free Hermitian flat sheaves.
In this paper, we review the NTIRE 2026 challenge on single-image reflection removal (SIRR) in the wild. SIRR is a fundamental task in image restoration. Despite progress in academic research, most methods are tested on synthetic images or limited real-world images, creating a gap in real-world applications. In this challenge, we provide participants with the OpenRR-5k dataset. This dataset requires participants to process real-world images covering a range of reflection scenarios and intensities, aiming to generate clean images without reflections. The challenge attracted more than 100 registrations, with eleven of them participating in the final testing phase. The top-ranked methods advanced the state-of-the-art reflection removal performance and earned unanimous recognition from five experts in the field. The proposed OpenRR-5k dataset is available at https://huggingface.co/datasets/qiuzhangTiTi/OpenRR-5k, and the homepage of this challenge is at https://github.com/caijie0620/OpenRR-5k.
In this survey, we review recent developments in extending Hodge theory to differential forms with values in bundles equipped with singular metrics, based on joint work with Ya Deng, Christopher D. Hacon, and Mihai Păun.
In this article, we pursue two main objectives. The first is to show that the fundamental results of Green-Lazarsfeld (1987, 1991) on generic vanishing theorems, and works of Budur-Wang (2015, 2020) on cohomology jumping loci, can be established within a unified framework based on suitable versions of the $\partial\bar{\partial}$-lemma. Our second-and primary-goal is to develop the technical tools required for this approach, namely an $L^2$-Hodge theory for the cohomology of rank-one local systems on quasi-compact Kähler manifolds. Further developments concerning higher-rank local systems, as well as several geometric applications, will be presented in a companion paper and are briefly outlined in the introduction.
In this note, motivated by the recent preprint of W. Ou, we pursue three main objectives. The first is to make progress towards the positivity of the relative canonical bundle in the Kähler setting. In the second part, we provide a proof of Ou's algebraicity criterion. Finally, based on the two previous parts, we slightly extend his uniruledness criterion.
Let $X$ be a compact complex manifold such that its canonical bundle $K_X$ is numerically trivial. Assume additionally that $X$ is Moishezon or $X$ is Fujiki with dimension at most four. Using the MMP and classical results in foliation theory, we prove a Beauville-Bogomolov type decomposition theorem for $X$. We deduce that holomorphic geometric structures of affine type on $X$ are in fact locally homogeneous away from an analytic subset of complex codimension at least two, and that they cannot be rigid unless $X$ is an étale quotient of a compact complex torus. Moreover, we establish a characterization of torus quotients using the vanishing of the first two Chern classes which is valid for any compact complex $n$-folds of algebraic dimension at least $n-1$. Finally, we show that a compact complex manifold with trivial canonical bundle bearing a rigid geometric structure must have infinite fundamental group if either $X$ is Fujiki, $X$ is a threefold, or $X$ is of algebraic dimension at most one.
Image harmonization aims to adjust the foreground illumination in a composite image to make it harmonious. The existing harmonization methods can only produce one deterministic result for a composite image, ignoring that a composite image could have multiple plausible harmonization results due to multiple plausible reflectances. In this work, we first propose a reflectance-guided harmonization network, which can achieve better performance with the guidance of ground-truth foreground reflectance. Then, we also design a diverse reflectance generation network to predict multiple plausible foreground reflectances, leading to multiple plausible harmonization results. The extensive experiments on the benchmark datasets demonstrate the effectiveness of our method.
In this article we pursue the following main goals. In the first place, we establish the existence of "estimable" Hermite--Einstein metrics for stable reflexive coherent sheaves on compact normal Kähler spaces. If moreover the background variety has klt singularities, we obtain a much more precise result.
Image composition refers to inserting a foreground object into a background image to obtain a composite image. In this work, we focus on generating plausible shadows for the inserted foreground object to make the composite image more realistic. To supplement the existing small-scale dataset, we create a large-scale dataset called RdSOBA with rendering techniques. Moreover, we design a two-stage network named DMASNet with decomposed mask prediction and attentive shadow filling. Specifically, in the first stage, we decompose shadow mask prediction into box prediction and shape prediction. In the second stage, we attend to reference background shadow pixels to fill the foreground shadow. Abundant experiments prove that our DMASNet achieves better visual effects and generalizes well to real composite images.
Given a composite image with photographic object and painterly background, painterly image harmonization targets at stylizing the composite object to be compatible with the background. Despite the competitive performance of existing painterly harmonization works, they did not fully leverage the painterly objects in artistic paintings. In this work, we explore learning from painterly objects for painterly image harmonization. In particular, we learn a mapping from background style and object information to object style based on painterly objects in artistic paintings. With the learnt mapping, we can hallucinate the target style of composite object, which is used to harmonize encoder feature maps to produce the harmonized image. Extensive experiments on the benchmark dataset demonstrate the effectiveness of our proposed method.
Painterly image harmonization aims to harmonize a photographic foreground object on the painterly background. Different from previous auto-encoder based harmonization networks, we develop a progressive multi-stage harmonization network, which harmonizes the composite foreground from low-level styles (e.g., color, simple texture) to high-level styles (e.g., complex texture). Our network has better interpretability and harmonization performance. Moreover, we design an early-exit strategy to automatically decide the proper stage to exit, which can skip the unnecessary and even harmful late stages. Extensive experiments on the benchmark dataset demonstrate the effectiveness of our progressive harmonization network.
Image compositing plays a vital role in photo editing. After inserting a foreground object into another background image, the composite image may look unnatural and inharmonious. When the foreground is photorealistic and the background is an artistic painting, painterly image harmonization aims to transfer the style of background painting to the foreground object, which is a challenging task due to the large domain gap between foreground and background. In this work, we employ adversarial learning to bridge the domain gap between foreground feature map and background feature map. Specifically, we design a dual-encoder generator, in which the residual encoder produces the residual features added to the foreground feature map from main encoder. Then, a pixel-wise discriminator plays against the generator, encouraging the refined foreground feature map to be indistinguishable from background feature map. Extensive experiments demonstrate that our method could achieve more harmonious and visually appealing results than previous methods.
Painterly image harmonization aims to insert photographic objects into paintings and obtain artistically coherent composite images. Previous methods for this task mainly rely on inference optimization or generative adversarial network, but they are either very time-consuming or struggling at fine control of the foreground objects (e.g., texture and content details). To address these issues, we propose a novel Painterly Harmonization stable Diffusion model (PHDiffusion), which includes a lightweight adaptive encoder and a Dual Encoder Fusion (DEF) module. Specifically, the adaptive encoder and the DEF module first stylize foreground features within each encoder. Then, the stylized foreground features from both encoders are combined to guide the harmonization process. During training, besides the noise loss in diffusion model, we additionally employ content loss and two style losses, i.e., AdaIN style loss and contrastive style loss, aiming to balance the trade-off between style migration and content preservation. Compared with the state-of-the-art models from related fields, our PHDiffusion can stylize the foreground more sufficiently and simultaneously retain finer content. Our code and model are available at https://github.com/bcmi/PHDiffusion-Painterly-Image-Harmonization.
Given a composite image, image harmonization aims to adjust the foreground illumination to be consistent with background. Previous methods have explored transforming foreground features to achieve competitive performance. In this work, we show that using global information to guide foreground feature transformation could achieve significant improvement. Besides, we propose to transfer the foreground-background relation from real images to composite images, which can provide intermediate supervision for the transformed encoder features. Additionally, considering the drawbacks of existing harmonization datasets, we also contribute a ccHarmony dataset which simulates the natural illumination variation. Extensive experiments on iHarmony4 and our contributed dataset demonstrate the superiority of our method. Our ccHarmony dataset is released at https://github.com/bcmi/Image-Harmonization-Dataset-ccHarmony.
The goal of image harmonization is adjusting the foreground appearance in a composite image to make the whole image harmonious. To construct paired training images, existing datasets adopt different ways to adjust the illumination statistics of foregrounds of real images to produce synthetic composite images. However, different datasets have considerable domain gap and the performances on small-scale datasets are limited by insufficient training data. In this work, we explore learnable augmentation to enrich the illumination diversity of small-scale datasets for better harmonization performance. In particular, our designed SYthetic COmposite Network (SycoNet) takes in a real image with foreground mask and a random vector to learn suitable color transformation, which is applied to the foreground of this real image to produce a synthetic composite image. Comprehensive experiments demonstrate the effectiveness of our proposed learnable augmentation for image harmonization. The code of SycoNet is released at https://github.com/bcmi/SycoNet-Adaptive-Image-Harmonization.