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arXiv 2307.08652cs.GR
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Search Me Knot, Render Me Knot:三维中纽结的嵌入搜索与可微渲染

Search Me Knot, Render Me Knot: Embedding Search and Differentiable Rendering of Knots in 3D

Aalok Gangopadhyay, Paras Gupta, Tarun Sharma, Prajwal Singh, Shanmuganathan Raman

AI总结:

本文研究基于三维纽结的逆向感知艺术,提出可逆神经网络参数化的纽结嵌入与可微渲染框架,并通过物理约束损失实现单/多视图目标优化及真实3D打印验证。

摘要:

我们提出了基于纽结的逆向感知艺术问题。给定多张目标图像及其对应的视角配置,目标是找到一种基于三维纽结的管状结构,使其在从指定视角配置观察时,外观与目标图像相似。为解决该问题,我们首先设计了一种可微渲染算法,用于在任意透视相机配置下渲染嵌入三维空间的管状纽结。利用该可微渲染算法,我们在纽结配置空间中进行搜索,以找到理想的纽结嵌入。我们通过所需模板纽结的同胚来表示纽结嵌入,其中这些同胚由可逆神经网络的权重参数化。我们的方法是完全可微的,因此可以使用基于梯度的优化为所需感知艺术找到理想的三维管状结构。我们提出了若干损失函数来施加额外的物理约束,强制管道不存在自交、位于空间中的预定义区域内、满足管道材料的物理弯曲极限,并且材料成本处于指定预算之内。结果表明,我们的纽结表示具有很强的表达能力,即使在单视图和多视图约束下面对具有挑战性的目标图像,也能给出令人印象深刻的结果。通过大量消融研究,我们证明所提出的每一个损失函数都能有效确保物理可实现性。我们构建了一个真实世界的三维打印对象,以展示本方法的实际效用。据我们所知,我们是首个提出用于基于纽结的逆向感知艺术的完全可微优化框架的工作。

英文摘要:

We introduce the problem of knot-based inverse perceptual art. Given multiple target images and their corresponding viewing configurations, the objective is to find a 3D knot-based tubular structure whose appearance resembles the target images when viewed from the specified viewing configurations. To solve this problem, we first design a differentiable rendering algorithm for rendering tubular knots embedded in 3D for arbitrary perspective camera configurations. Utilizing this differentiable rendering algorithm, we search over the space of knot configurations to find the ideal knot embedding. We represent the knot embeddings via homeomorphisms of the desired template knot, where the homeomorphisms are parametrized by the weights of an invertible neural network. Our approach is fully differentiable, making it possible to find the ideal 3D tubular structure for the desired perceptual art using gradient-based optimization. We propose several loss functions that impose additional physical constraints, enforcing that the tube is free of self-intersection, lies within a predefined region in space, satisfies the physical bending limits of the tube material and the material cost is within a specified budget. We demonstrate through results that our knot representation is highly expressive and gives impressive results even for challenging target images in both single view as well as multiple view constraints. Through extensive ablation study we show that each of the proposed loss function is effective in ensuring physical realizability. We construct a real world 3D-printed object to demonstrate the practical utility of our approach. To the best of our knowledge, we are the first to propose a fully differentiable optimization framework for knot-based inverse perceptual art.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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