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Method for obtaining optimal transmission mapping in high-dimensional area and related product

A transmission mapping and intra-area technology, which is applied in the field of obtaining optimal transmission mapping in high-dimensional areas, can solve problems such as difficult to effectively calculate high-dimensional OT, and achieve reduced computational complexity, high computational efficiency, and strong versatility Effect

Pending Publication Date: 2022-08-02
DALIAN UNIV OF TECH
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Problems solved by technology

It can be seen that the existing algorithms are difficult to efficiently calculate the high-dimensional OT problem

Method used

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  • Method for obtaining optimal transmission mapping in high-dimensional area and related product
  • Method for obtaining optimal transmission mapping in high-dimensional area and related product
  • Method for obtaining optimal transmission mapping in high-dimensional area and related product

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Embodiment Construction

[0026] The technical solutions in the embodiments of the present disclosure will be clearly and completely described below with reference to the accompanying drawings. It should be understood that the embodiments described in this specification are only some of the embodiments provided by the present disclosure for the purpose of facilitating the clear understanding of the solution and complying with legal requirements, and not all embodiments of the present disclosure can be implemented. Based on the embodiments disclosed in this specification, all other embodiments obtained by those skilled in the art without creative efforts shall fall within the protection scope of the present disclosure.

[0027] figure 1 is an exemplary flowchart illustrating a method 100 for obtaining an optimal transport map in a high-dimensional region according to an embodiment of the present disclosure. Based on the description below, those skilled in the art will understand that the method 100 her...

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Abstract

The invention relates to a method for acquiring optimal transmission mapping in a high-dimensional region and a related product. The method is executed by a computing device, and comprises the following steps: acquiring a source density of a high-dimensional region and a target density of a target region in the high-dimensional region; determining a discrete Mongolian-Ampere equation associated with optimal transmission mapping based on the source density and the target density, wherein the discrete Mongolian-Ampere equation comprises a Brenier potential energy function; constructing a linear constant coefficient ellipse partial differential equation according to the discrete Monte day-Ampere equation; solving the linear constant coefficient elliptic partial differential equation by using fast Fourier transform to determine the Brenier potential energy function; and obtaining the optimal transmission mapping from the source density to the target density based on the Brenier potential energy function. By using the scheme of the invention, the optimal transmission mapping in the high-dimensional region can be quickly and accurately obtained.

Description

technical field [0001] The present disclosure generally relates to the field of optimal transmission technology. More specifically, the present disclosure relates to a method, apparatus, and computer-readable storage medium for obtaining an optimal transport map in a high-dimensional region. Background technique [0002] In recent years, optimal transmission has developed rapidly and is widely used in fields such as vision, deep learning, and medical images. According to the research, Optimal transportation ("OT") mapping is the most economical way to transform one probability measure to another, and the total transportation cost is regarded as the Wasserstein difference between the two probability measures. distance. Thus, OT mapping can be used to measure differences between probability distributions and for virtual magnifying glasses, image registration, and the like. [0003] In practical applications, the OT mapping whose cost function is the square of the Euclidean ...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06T11/00G06F17/13G06F17/14
CPCG06T11/003G06F17/142G06F17/13
Inventor 雷娜
Owner DALIAN UNIV OF TECH
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