Instant transport maps on 2D grids

Nader, Georges; Guennebaud, Gaël

doi:10.1145/3272127.3275091

Cited by 10 publications

(28 citation statements)

References 33 publications

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“…In [32] a GPU-based approach for solving the OMT optimization problem was suggested and applied to high-frequency grayscale images. Elsewhere [26] the authors introduced a new solver for computing an approximated OMT that is derivative free and converges within a few iterations. This method is topologyaware and preserves sharp features during metamorphosis but does not support texture or color transformations.…”

Section: 2mentioning

confidence: 99%

Automatically Controlled Morphing of 2D Shapes with Textures

Tereshin¹,

Adzhiev²,

Fryazinov³

et al. 2020

SIAM J. Imaging Sci.

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This paper deals with 2D image transformations from a perspective of a 3D heterogeneous shape modeling and computer animation. Shape and image morphing techniques have attracted a lot of attention in artistic design, computer animation, and interactive and streaming applications. We present a novel method for morphing between two topologically arbitrary 2D shapes with sophisticated textures (raster color attributes) using a metamorphosis technique called space-time blending (STB) coupled with space-time transfinite interpolation. The method allows for a smooth transition between source and target objects by generating in-between shapes and associated textures without setting any correspondences between boundary points or features. The method requires no preprocessing and can be applied in 2D animation when position and topology of source and target objects are significantly different. With the conversion of given 2D shapes to signed distance fields, we have detected a number of problems with directly applying STB to them. We propose a set of novel and mathematically substantiated techniques, providing automatic control of the morphing process with STB and an algorithm of applying those techniques in combination. We illustrate our method with applications in 2D animation and interactive applications.

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Section: 2mentioning

confidence: 99%

Automatically Controlled Morphing of 2D Shapes with Textures

Tereshin¹,

Adzhiev²,

Fryazinov³

et al. 2020

SIAM J. Imaging Sci.

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“…Directly solving this linear program can be very costly, and has only been typically done for histograms of up to a few tens of thousands of bins [Bonneel et al 2011]. Faster alternate approaches have tried to tackle particular cases, such as semi-discrete formulations [Gu et al 2013;Kitagawa et al 2016;Lévy 2015;Mérigot 2011] for matching weighted point sets to continuous densities via geometric constructions, or formulations to match 2-d continuous distributions to uniform continuous distributions [Nader and Guennebaud 2018]. Other approaches approximate the problem, such as entropy-regularized optimal transport, which results in blurred transport plan but is extremely fast to compute, especially when data lie on a grid [Solomon et al 2015].…”

Section: Prior Workmentioning

confidence: 99%

“…Optimal transport is a popular mathematical framework for manipulating positive measures, and in particular, in most cases studied so far, probability measures. It has become widespread in computer graphics [Bonneel et al 2011;Nader and Guennebaud 2018;Solomon et al 2015] and machine learning [Arjovsky et al 2017;Deshpande et al 2018;Kolouri et al 2018] for its ability to compare histograms or to produce compelling interpolations between probability distributions. Within this framework, transporting a histogram f towards another д is often seen as moving a pile of sand shaped by the graph of f towards a hole shaped by д at minimal cost.…”

Section: Introductionmentioning

confidence: 99%

“…Stopping the motion of the sand at some intermediate time defines a measure in-between f and д, a concept called displacement interpolation, or, when dealing with more than two input measures, Wasserstein barycenter. This computationally difficult problem has received recent attention, with fast solutions for various specific cases when the size of the hole matches that of the pile of sand, the so-called balanced optimal transport problem [Bonneel et al 2015;Kitagawa et al 2016;Nader and Guennebaud 2018;Solomon et al 2015].…”

Section: Introductionmentioning

confidence: 99%

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Bonneel

Cœurjolly

2019

ACM Trans. Graph.

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Optimal transport research has surged in the last decade with wide applications in computer graphics. In most cases, however, it has focused on the special case of the so-called "balanced" optimal transport problem, that is, the problem of optimally matching positive measures of equal total mass. While this approach is suitable for handling probability distributions as their total mass is always equal to one, it precludes other applications manipulating disparate measures. Our paper proposes a fast approach to the optimal transport of constant distributions supported on point sets of different cardinality via one-dimensional slices. This leads to one-dimensional partial assignment problems akin to alignment problems encountered in genomics or text comparison. Contrary to one-dimensional balanced optimal transport that leads to a trivial linear-time algorithm, such partial optimal transport, even in 1-d, has not seen any closed-form solution nor very efficient algorithms to date. We provide the first efficient 1-d partial optimal transport solver. Along with a quasilinear time problem decomposition algorithm, it solves 1-d assignment problems consisting of up to millions of Dirac distributions within fractions of a second in parallel. We handle higher dimensional problems via a slicing approach, and further extend the popular iterative closest point algorithm using optimal transport - an algorithm we call Fast Iterative Sliced Transport. We illustrate our method on computer graphics applications such a color transfer and point cloud registration.

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“…Real-time 2D shape interpolation offered by optimal mass transport [4] could solve the discontinuous shadow animation problem. However, this is limited by texture resolution where artists strive for infinite resolution vector quality [102,103].…”

Section: Introductionmentioning

confidence: 99%

Art-Directed Composition in Dynamic Real Scenes

Petikam¹

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<p>Art direction is crucial for films and games to maintain a cohesive visual style. This involves carefully controlling visual elements like lighting and colour to unify the director's vision of a story. With today's computer graphics (CG) technology 3D animated films and games have become increasingly photorealistic. Unfortunately, art direction using CG tools remains laborious. Since realistic lighting can go against artistic intentions, art direction is almost impossible to preserve in real-time and interactive applications. New live applications like augmented and mixed reality (AR and MR) now demand automatically art-directed compositing in unpredictably changing real-world lighting. </p> <p>This thesis addresses the problem of dynamically art-directed 3D composition into real scenes. Realism is a basic component of art direction, so we begin by optimising scene geometry capture in realistic composites. We find low perceptual thresholds to retain perceived seamlessness with respect to optimised real-scene fidelity. We then propose new techniques for automatically preserving art-directed appearance and shading for virtual 3D characters. Our methods allow artists to specify their intended appearance for different lighting conditions. Unlike with previous work, artists can direct and animate stylistic edits to automatically adapt to changing real-world environments. We achieve this with a new framework for look development and art direction using a novel latent space of varied lighting conditions. For more dynamic stylised lighting, we also propose a new framework for art-directing stylised shadows using novel parametric shadow editing primitives. This is a first approach that preserves art direction and stylisation under varied lighting in AR/MR.</p>

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Instant transport maps on 2D grids

Cited by 10 publications

References 33 publications

Automatically Controlled Morphing of 2D Shapes with Textures

Automatically Controlled Morphing of 2D Shapes with Textures

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Art-Directed Composition in Dynamic Real Scenes

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