Search Me Knot, Render Me Knot: Embedding Search and Differentiable Rendering of Knots in 3D
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Date
2024
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and John Wiley & Sons Ltd.
Abstract
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 weights of an invertible neural network parametrize the homeomorphisms. 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 and multiple-view constraints. Through extensive ablation study, we show that each proposed loss function effectively ensures physical realizability. We construct a real-world 3D-printed object to demonstrate the practical utility of our approach.
Description
CCS Concepts: Computing methodologies → Computer graphics; Rendering
@article{10.1111:cgf.15138,
journal = {Computer Graphics Forum},
title = {{Search Me Knot, Render Me Knot: Embedding Search and Differentiable Rendering of Knots in 3D}},
author = {Gangopadhyay, Aalok and Gupta, Paras and Sharma, Tarun and Singh, Prajwal and Raman, Shanmuganathan},
year = {2024},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.15138}
}