Fast Multigrid Optimal Mass Transport for Image Registration and Morphing

Rehman, Tauseef Ur; Pryor, Gallagher; Tannenbaum, Allen

doi:10.5244/c.21.11

Cited by 7 publications

(5 citation statements)

References 11 publications

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“…This method can only handle interpolation between blocks of pure color. 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.…”

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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“…The significant contributions in mathematical foundations of the optimal transport problem together with recent advancements in numerical methods [36], [15], [14], [114], [160] have spurred the recent development of numerous data analysis techniques for modern estimation and detection (e.g. classification) problems.…”

Section: A Brief Historical Notementioning

confidence: 99%

Transport-based analysis, modeling, and learning from signal and data distributions

Kolouri¹,

Park²,

Thorpe³

et al. 2016

Preprint

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Transport-based techniques for signal and data analysis have received increased attention recently. Given their abilities to provide accurate generative models for signal intensities and other data distributions, they have been used in a variety of applications including content-based retrieval, cancer detection, image super-resolution, and statistical machine learning, to name a few, and shown to produce state of the art in several applications. Moreover, the geometric characteristics of transport-related metrics have inspired new kinds of algorithms for interpreting the meaning of data distributions. Here we provide an overview of the mathematical underpinnings of mass transport-related methods, including numerical implementation, as well as a review, with demonstrations, of several applications. Software accompanying this tutorial is available at [134].

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“…Our interest is in developing methods that can be applied to continuous domains: we generate continuous interpolated distributions from a pair of continuous input distributions. While there exists limited work on Eulerian approaches for displacement interpolation in continuous domains solving PDEs, these methods require dense grids that rapidly become impractical in higher dimensions, and are limited to quadratic ground distances in a Euclidean space [Rehman et al 2009;Rehman et al 2007]. These methods do not work on non uniformly spaced scattered data typically obtained from measurements.…”

Section: Introductionmentioning

confidence: 99%

Displacement interpolation using Lagrangian mass transport

et al. 2011

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. Naive linear interpolation generates an unrealistic double highlight (c). Since we used a parametric BRDF model, we can compute the ground-truth in-between BRDF by interpolating the parameters (d). Our approach has no knowledge of the parametric BRDF representation but is nonetheless able to produce a similar output (e). AbstractInterpolation between pairs of values, typically vectors, is a fundamental operation in many computer graphics applications. In some cases simple linear interpolation yields meaningful results without requiring domain knowledge. However, interpolation between pairs of distributions or pairs of functions often demands more care because features may exhibit translational motion between exemplars. This property is not captured by linear interpolation. This paper develops the use of displacement interpolation for this class of problem, which provides a generic method for interpolating between distributions or functions based on advection instead of blending. The functions can be non-uniformly sampled, high-dimensional, and defined on non-Euclidean manifolds, e.g., spheres and tori. Our method decomposes distributions or functions into sums of radial basis functions (RBFs). We solve a mass transport problem to pair the RBFs and apply partial transport to obtain the interpolated function. We describe practical methods for computing the RBF decomposition and solving the transport problem. We demonstrate the interpolation approach on synthetic examples, BRDFs, color distributions, environment maps, stipple patterns, and value functions.

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Fast Multigrid Optimal Mass Transport for Image Registration and Morphing

Cited by 7 publications

References 11 publications

Automatically Controlled Morphing of 2D Shapes with Textures

Automatically Controlled Morphing of 2D Shapes with Textures

Transport-based analysis, modeling, and learning from signal and data distributions

Displacement interpolation using Lagrangian mass transport

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