276 research outputs found

    Web Page Classification and Hierarchy Adaptation

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    Uniqueness and value distribution of differences of entire functions

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    AbstractWe consider the existence of transcendental entire solutions of certain type of non-linear difference equations. As an application, we investigate the value distribution of difference polynomials of entire functions. In particular, we are interested in the existence of zeros of fn(z)(λfm(z+c)+ÎŒfm(z))−a, where f is an entire function, n, m are two integers such that nâ©Ÿm>0, and λ, ÎŒ are non-zero complex numbers. We also obtain a uniqueness result in the case where shifts of two entire functions share a small function

    SeamlessNeRF: Stitching Part NeRFs with Gradient Propagation

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    Neural Radiance Fields (NeRFs) have emerged as promising digital mediums of 3D objects and scenes, sparking a surge in research to extend the editing capabilities in this domain. The task of seamless editing and merging of multiple NeRFs, resembling the ``Poisson blending'' in 2D image editing, remains a critical operation that is under-explored by existing work. To fill this gap, we propose SeamlessNeRF, a novel approach for seamless appearance blending of multiple NeRFs. In specific, we aim to optimize the appearance of a target radiance field in order to harmonize its merge with a source field. We propose a well-tailored optimization procedure for blending, which is constrained by 1) pinning the radiance color in the intersecting boundary area between the source and target fields and 2) maintaining the original gradient of the target. Extensive experiments validate that our approach can effectively propagate the source appearance from the boundary area to the entire target field through the gradients. To the best of our knowledge, SeamlessNeRF is the first work that introduces gradient-guided appearance editing to radiance fields, offering solutions for seamless stitching of 3D objects represented in NeRFs.Comment: To appear in SIGGRAPH Asia 2023. Project website is accessible at https://sites.google.com/view/seamlessner

    RecolorNeRF: Layer Decomposed Radiance Fields for Efficient Color Editing of 3D Scenes

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    Radiance fields have gradually become a main representation of media. Although its appearance editing has been studied, how to achieve view-consistent recoloring in an efficient manner is still under explored. We present RecolorNeRF, a novel user-friendly color editing approach for the neural radiance fields. Our key idea is to decompose the scene into a set of pure-colored layers, forming a palette. By this means, color manipulation can be conducted by altering the color components of the palette directly. To support efficient palette-based editing, the color of each layer needs to be as representative as possible. In the end, the problem is formulated as an optimization problem, where the layers and their blending weights are jointly optimized with the NeRF itself. Extensive experiments show that our jointly-optimized layer decomposition can be used against multiple backbones and produce photo-realistic recolored novel-view renderings. We demonstrate that RecolorNeRF outperforms baseline methods both quantitatively and qualitatively for color editing even in complex real-world scenes.Comment: To appear in ACM Multimedia 2023. Project website is accessible at https://sites.google.com/view/recolorner
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