Two-dimensional scalar field data visualization method and system based on colormap optimization

Patent metadata

Field	Value
Publication number	US-11790484-B2
Application number	US-201917257906-A
Country	US
Kind code	B2
Filing date	Nov 6, 2019
Priority date	May 21, 2019
Publication date	Oct 17, 2023
Grant date	Oct 17, 2023

Abstract

A two-dimensional scalar field data visualization method and system based on colormap optimization including: receiving initial colormap and two-dimensional scalar field input data; calculating key colors in the initial colormap, and setting the key colors as control points; calculating a linear interpolation between pairwise control points using a piecewise linear function, generating and mapping a colormap to the two-dimensional scalar field data; establishing an energy optimization equation for control point coordinate positions and the mapped two-dimensional scalar field data, where the coordinate positions are numerical values between 0 and 1 obtained by normalizing index values in the colormap corresponding to the control points; and solving the energy optimization equation to obtain a control point coordinate position, generating a new colormap using the piecewise linear function and optimized control point coordinate position, and mapping the new colormap to the two-dimensional scalar field data, to obtain a final visualization result.

First claim

What is claimed is:

1. A two-dimensional scalar field data visualization method based on colormap optimization, comprising:
receiving an initial colormap and two-dimensional scalar field data that are input;

calculating key colors in the initial colormap, and setting those key colors as control points;
calculating a linear interpolation between pairwise control points by using a piecewise linear function, to generate a colormap, and mapping the colormap to the two-dimensional scalar field data;
establishing an energy optimization equation for coordinate positions of the control points and the two-dimensional scalar field data for which mapping is performed, wherein the coordinate positions of the control points are numerical values between 0 and 1 obtained by normalizing index values in the colormap corresponding to the control points; and
solving the energy optimization equation to obtain an optimized coordinate position of the control point, generating a new colormap by using the piecewise linear function and the optimized coordinate position of the control point, and mapping the new colormap to the two-dimensional scalar field data, to obtain a final visualization result.

2. The method according to claim 1 , wherein the calculating key colors in the initial colormap, and setting the key colors as control points specifically comprises the following steps:
setting a cluster quantity K, and calculating the key colors in the initial colormap by using a clustering algorithm; and using the key colors as the control points, each of the control points comprising the coordinate position of the control point on the initial colormap and a color corresponding to the control point.

3. The method according to claim 1 , wherein the calculating a linear interpolation between pairwise control points by using a piecewise linear function, to generate a colormap, and mapping the colormap to the two-dimensional scalar field data specifically comprises the following steps:
c = c i + 1 - c i p i + 1 - p i × ( p - p i ) + c i , p i <p<p i+1 ;  (2), wherein

p represents a coordinate position of a control point; and c represents a color of the control point;
applying the piecewise linear function to any two adjacent control points, to generate a new colormap comprising a plurality of colors; establishing a mapping relationship between colors and data by using a color mapping process ξ in the new colormap during subsequent application, thereby generating data to which the color is mapped, wherein the color mapping process is expressed by f(x; p ), p representing the position of the control point, and x representing a value of a data point; and
normalizing, by using a maximum and minimum normalization method, any two-dimensional scalar field data to a parameter space of 0 to 1, and establishing a mapping relationship between the colors and the coordinate positions of the control points by using formula (2).

4. The method according to claim 3 , wherein the color mapping process ξ is as follows: assuming that C is used to represent a colormap comprising n colors, wherein C={C 1 , C 2 , . . . , C n }, T={T 1 , T 2 , . . . , T n }, 0≤T≤1 being used to represent numerical values of the two-dimensional scalar field data normalized to 0-1 that are arranged in ascending order, and C being assigned to an element with a same subscript in T.

5. The method according to claim 1 , wherein in specific steps of the establishing an energy optimization equation for coordinate positions of the control points,
the energy optimization equation comprises a weighted sum of a boundary term, a contrast term, and a fidelity term;
arg E ( x; p )=α B ( x; p )+β F ( x; p )+γ V ( x; p );  (3), where

x is the two-dimensional scalar field data for which mapping is performed, p is a to-be-optimized position of the control point, and α, β, and γ are weight parameters; E(x; p ) represents the energy optimization equation; B(x; p ) represents the boundary term; F(x; p ) represents the fidelity term; and V(x; p ) represents the contrast term.

6. The method according to claim 5 , wherein the solving the energy optimization equation to obtain an optimized coordinate position of the control point specifically comprises the following steps:
performing sequential quadratic programming to solve the optimization function arg E(x; p ) iteratively, by using the coordinate position of the control point as a variable for optimization solution;
calculating the boundary term, wherein a function of the boundary term is to guarantee that boundary distribution of color mapping data is consistent with a hidden boundary structure of the two-dimensional scalar field data, and a boundary of the two-dimensional scalar field data refers to a change between different values;
calculating the fidelity term, wherein a function of the fidelity term is to guarantee a minimum difference between an optimized colormap and an initial colormap;
calculating a foreground-background contrast term, wherein a function of the contrast term is to guarantee a maximum contrast between a foreground color and a background color of the color mapping data, to enhance identifiability of the foreground data,
thereby obtaining the optimized coordinate position of the control point.

7. The method according to claim 5 , wherein the boundary term is defined as:
B ( x; p )=−Σ i M q ( x i )*Σ j∈Ω ∥f ( x i ; p )− f ( x j ; p )∥ 2 ;  (4), where

B(x; p ) represents the boundary term; and q(x i ) represents a marginal likelihood function of the data point x i ; assuming that i is a label of any data point in the two-dimensional scalar field data, x i represents a numerical value of the data point; Ω represents a neighbor point of the current data point i, and M represents all data points in the two-dimensional scalar field; f(x i ; p ) represents mapping of a parameter value to a color value, for the data point x i and a set p of control point positions, a color mapping equation can be used to obtain a corresponding color value of the data point x i ; and ∥⋅∥ represents a Euclidean distance; and
the fidelity term is defined as:

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Assignees

• Univ Shandong

Inventors

• Zeng Qiong
• Wang Yunhai
• Tu changhe
• Cao Yi
• Viola Ivan

Classifications

• G06T11/10

  Texturing; Colouring; Generation of textures or colours (retouching, inpainting or scratch removal G06T5/77) · CPC title

• G06T11/26 Primary

  Drawing of charts or graphs · CPC title

• G06T3/4007 Primary

  based on interpolation, e.g. bilinear interpolation (image demosaicing G06T3/4015; edge-driven or edge-based scaling G06T3/403) · CPC title

• G06T7/90

  Determination of colour characteristics · CPC title

• G06T2207/10024

  Color image · CPC title