CN106529169A - Fuzzy set visualization method and application thereof to aspect of medical data visualization - Google Patents

Abstract

The invention discloses a fuzzy set visualization method. It includes: step 1, mapping each element in the fuzzy set and the center of the set to a point with color and transparency, and initializing its geometric position; step 2, optimizing the position of the element point and the center point of the set; step 3, using The optimized element points and the collection center point and the boundary of the display medium are constrained, and the Delaunay triangular mesh is used to divide the discrete triangular mesh through these points; step 4, calculate the color and transparency distribution of each vertex of the triangular mesh, And color it according to the calculation result. The invention also discloses the application of the method in medical data visualization. Compared with the prior art, the present invention can make full use of geometry, color and transparency information, and display the information in the fuzzy set more clearly and intuitively in the form of diagrams.

Description

Fuzzy Set Visualization Method and Its Application in Medical Data Visualization

technical field

The invention relates to a fuzzy set visualization method and its application in medical data visualization.

Background technique

Due to the complexity of human body systems and unavoidable errors in medical testing equipment, medical data often contain certain uncertainties. The traditional medical data presentation methods focus more on deterministic data. In consultation, telemedicine, and patient communication, it is easy to cause misunderstanding to express uncertain medical data in the form of a definite chart, which hinders the objectivity of diagnosis and communication in medical treatment. cause unnecessary trouble. Therefore, it is necessary to visualize these uncertain medical data.

According to the characteristics of uncertainty data, [A.M.MacEachren, R.E.Roth, J.F.O'Brien, B.Li, D.Swingley and M.Gahegan, Visual Semiotics & Uncertainty Visualization: An Empirical Study, IEEE Transactions on Visualization and Computer Graphics 18,12( 2012), 2496-2505] summarized some principles and ideas for visualizing uncertainty. Scholars proposed visual fuzzy numbers [M.Correll and M.Gleicher, Error Bars Considered Harmful: Exploring Alternate Encodings for Mean and Error, IEEE Transactions on Visualization and Computer Graphics, 20,12(2014), 2142-2151][A.R.Buck and J.M. Keller, Visualizing Uncertainty with Fuzzy Rose Diagrams, Proceedings of IEEE Symposium on Computational Intelligence for Engineering Solutions (CIES), (2014), 30-36.], Fuzzy Relations [B.Zier and A.Inoue, Fuzzy Relational Visualization for Decision Support, Proceedings of the Twenty-Second Midwest Artificial Intelligence and Cognitive Science Conference, (2011), 8-15] and fuzzy graphs [H.Guo, J.Huang and D.H.Laidlaw, Representing Uncertainty in Graph Edges: An Evaluation of PairedVisual Variables, IEEE Transactions on Visualization and Computer Graphics, 21, 10(2015), 1173-1186]. As a typical type of data with uncertainty, this patent will discuss the visualization method of fuzzy sets.

The belonging relationship of the elements to the set in the traditional set is a right and wrong relationship, and the fuzzy set uses a continuous variable from 0 to 1 to define the degree of belonging of the elements to the set, which is called the belonging function. Such a simple generalization allows fuzzy sets to contain more subordinate information, thus bringing many applications in engineering, management, and medicine to fuzzy sets. Since fuzzy sets are composed of pairs of elements and their belonging functions, the traditional method of storing and displaying fuzzy sets is a simple list or list of these pairs, which lacks intuition. Especially when the amount of data increases, it is not easy for users to find key information from the full-screen data, such as which of any two elements has a greater degree of belonging to the set, and whether there are many elements with a degree of belonging to the set greater than 0.5, etc. Wait.

The existing fuzzy set visualization method [Y.Park, J.Park, Disk diagram: An interactive visualization technique of fuzzy set operations for the analysis of fuzzydata, Information Visualization 9,3(2010), 220-232] uses a circular diagram, This visualization method is not suitable for fuzzy sets with multiple membership functions of 1, and it is prone to occlusion when the number of elements increases and the membership function values are similar.

Contents of the invention

The technical problem to be solved by the present invention is to overcome the deficiencies of the existing fuzzy set visualization technology, and provide a fuzzy set visualization method, which can make full use of geometry, color and transparency information, and make the information in the fuzzy set more clear and intuitive in the form of diagrams displayed.

The present invention specifically adopts the following technical solutions to solve the above technical problems:

A fuzzy set visualization method, comprising the following steps:

Step 1. Map each element in the fuzzy set and the center of the set to a point with color and transparency, and initialize its geometric position:

Firstly, the collection centers are evenly distributed on the display medium, and the average distance between the collection centers is determined; using the average distance as a reference, the elements in each collection are distributed around the collection center, so that the distance between the element point and the collection center point The distance of is negatively linearly related to the membership function of the element to the set;

Step 2. Optimize the position of the element point and the center point of the set:

Define two types of ideal distances: one is the distance from the element point to the center point of the set, and its ideal distance is r(1-u _A (x)), where r is the radius of set A, and u _A (x) is the pair set of element x The membership function of A; one is the minimum ideal distance between element points, which is determined by the user according to the geometric size of the display medium; the spring-mass model is established, and the two types of distance are modeled as the ideal length of the spring, and the element points are Model the center of the mass as a mass point, fix the mass point close to the center of the display medium, and use the spring-mass model for physical simulation to find the position of the mass point under static conditions as the position of the optimized element point and the center of the set;

Step 3. Constraints on the optimized element points, set center points, and the boundaries of the display medium, using Delaunay triangular mesh division, to establish a discrete triangular mesh passing through these points;

Step 4. Calculate the color and transparency distribution of each vertex of the triangular mesh, and color according to the calculation result: draw a layer for each fuzzy set, set all vertices of the same layer to the same color, and set different colors to different layers ; For each layer, calculate the transparency of the vertices of the triangular mesh and draw the layer, and finally superimpose the layers to obtain a visualization scheme; where the transparency calculation method of the vertices of the triangular mesh is specifically: define the transparency of the center point c of the set as 0 , the transparency of element point x is 1-u _A (x), where u _A (x) is the membership function of element x to set A, if u _A (x) is not equal to 1, extrapolate the line from c to x to find Point y=c+(cx)/(1-u _A (x)), and the transparency at point y is set to 1; finally, the transparency at the center point, element point, and extrapolation point of the set is used as the boundary condition, in the triangle Solve second-order harmonic equations on the mesh to obtain the transparency of the remaining triangular mesh vertices.

Further, when initializing the geometric positions of the center point of the set and the element point, if an element belongs to multiple sets, the initial positions of the different sets are averaged as its initial position.

In order to help users better perceive the specific belonging function, further, the method further includes:

Step 5. Add transparency contours to the obtained visualization scheme.

The fuzzy set visualization method of the present invention can be widely used in the visualization processing of data containing uncertainty in many fields such as astronomy, meteorology, machine identification, remote sensing measurement, etc., for example:

The application of the method in medical data visualization firstly abstracts the medical data containing uncertainty, abstracts the uncertainty into a set language according to the error or possibility, and abstracts the subordinate probability to quantify the uncertainty, thus forming One or more fuzzy sets; and then use the method described in any of the above technical solutions to perform visual processing on the one or more fuzzy sets.

Compared with the prior art, the present invention has the following beneficial effects:

The present invention effectively improves the succinctness, intuition, recognizability and aesthetics of information display including uncertainty, thereby being more user-friendly;

Compared with the existing fuzzy set visualization method based on the circular graph, the present invention extends the circular boundary of the circular graph to the free curve boundary, and extends the pure color of the circular graph to the display of different colors and transparency, making full use of the display medium The geometry, color and transparency channels can express information more accurately and comprehensively.

Description of drawings

Fig. 1 is the basic schematic diagram of the inventive method;

Fig. 2 is the result example that utilizes the method of the present invention to carry out visual processing to simple fuzzy set;

Fig. 3 is the result example that utilizes the method of the present invention to carry out visual processing to table 1 medical data;

Figure 4 shows the user survey results of the three visualization schemes.

detailed description

The technical scheme of the present invention is described in detail below in conjunction with accompanying drawing:

As shown in Figure 1, the present invention firstly abstracts uncertain medical data (or other uncertain data) into a fuzzy set, and then uses the background color, vertex and The transparency of the background is displayed, where the transparency distribution of the displayed background is indicated by the isoline of transparency.

Fig. 2 shows a result of visualizing a simple fuzzy set with the method of the present invention. In the fuzzy set with three elements in this figure, the set is represented by red (not shown in the figure), the center of the set is represented by a + font point, the element is represented by a black point, and the belonging function of the element to the set is represented by transparency (shown in the form of transparency contours in the figure). A high transparency corresponds to a low membership function, a completely opaque area indicates a membership function of 1, and a completely transparent area indicates a membership function of 0.

In order to facilitate the public's understanding, the technical solution of the present invention will be described in detail below with a specific embodiment.

The processing object in this embodiment is a group of medical data containing uncertainty, and the visualization processing process of the present invention is specifically as follows:

Step 1. Abstract the medical data containing uncertainty, abstract the uncertainty into a set language according to the error or possibility, and abstract the subordinate probability to quantify the uncertainty, thus forming one or more fuzzy sets:

The medical data is abstracted as a fuzzy set, which is abstracted into element x and set A according to the subordination relationship in the medical data, and the probability of uncertainty is given in the form of the membership function u _A (x).

Step 2. Map each element in the fuzzy set and the center of the set to a point with color and transparency, and initialize its geometric position:

In the position initialization, firstly, the collection centers are evenly distributed on the display media such as screen or paper, and the average distance between the collection centers is determined, and half of this distance is set as the ideal collection radius r; the average distance is For reference, the elements in each set are distributed around the center of the set, so that the distance between the element point and the center point of the set is negatively linearly related to the membership function of the element to the set. For example, at the time of initialization, the center of the collection is taken as the origin, and the polar coordinate system is used. If the collection A has n elements, the position of the i-th element x _i corresponds to a length of (1-u _A ( _xi ))r, The position where the angle is 2πi/n. If an element belongs to multiple sets, the initial positions set by the different sets it belongs to are averaged as its initial position.

Step 3, optimize the position of element point and set center point:

Define two types of ideal distances: one is the distance from the element point to the center point of the set, and the ideal distance is r(1-u _A (x)), where r is the ideal radius of the set A, and u _A (x) is the element x The membership function for the set A; one is the minimum ideal distance between element points, which is determined by the user according to the geometric size of the display medium, and can generally be set to 0.25r. Establish a spring-mass model, model these two types of distances as the ideal length of the spring, model the element point and the center of the collection as a mass point, set the stiffness coefficient of the spring to 1, fix the mass point close to the center of the display medium, and use the spring -Mass point physics simulation (this is prior art, details can be found in literature [T.Liu, AWBargteil, JFO'Brien and L.Kavan, Fast simulation of mass-spring systems, ACM Transactions on Graphics 32,6(2013), 209 :1-209:7.]) to find the position of the mass point in the static situation, as the position of the element point and the center of the set after optimization. In the simulation, we also set the shortest distance between element points, generally set to 0.05r. When the spring length between element points is less than the defined shortest distance, the spring stiffness coefficients with too short length will be enlarged by 2 times to re-run the spring-mass physical simulation, and repeat this process until the distance between all element points is greater than the specified the shortest distance.

Step 4. Constraints on the optimized element points, set center points, and display medium boundaries, use Delaunay triangular meshing (for details, please refer to the literature [J.R.Shewchuk, Triangle: Engineering a 2DQuality Mesh Generator and Delaunay Triangulator, Lecture Notes in ComputerScience, 1148(1996), 203-222]), a discrete triangular mesh through these points is constructed for plotting the data plots.

Step 5. Calculate the color and transparency distribution of each vertex of the triangular mesh, and perform coloring according to the calculation result:

Define the transparency of the center point c of the set as 0, and the transparency of the element point x as 1-u _A (x), where u _A (x) is the membership function of the element x to the set A. At the same time, if u _A (x) is not equal to 1, extrapolate the line from c to x to find the point y=c+(cx)/(1-u _A (x)), and set the transparency at point y to 1. Finally, the second-order harmonic equation is solved on the triangular grid with the transparency of the set center point, element point, and extrapolation point as boundary conditions (see literature [A.Jacobson, I.Baran, J.Popovi′c, O. Sorkine, Bounded biharmonic weights for real-time deformation, ACM Transactions on Graphics 30, 4(2011), 78:1-78:8]), to obtain the transparency of the vertices of the rest of the triangular mesh. If multiple fuzzy sets are displayed at the same time, a layer is drawn for each fuzzy set, all vertices of the same layer are set to the same color, different layers are set to different colors, and finally the layers are superimposed to obtain the final visualization scheme.

Users can quickly perceive the fuzzy set and degree of belonging through the color and transparency information of the element points on the drawn visual diagram. At the same time, users can quickly find out which element points have similar degree of belonging and which element points belong to High degree, which elements have low degree of attribution, and so on. In order to help users better perceive the specific belonging function, the present invention can further calculate the isoline of transparency and superimpose it on the visual diagram to help display the value of the belonging function. When calculating the contour line, you only need to traverse all triangles. If the transparency of two vertices on the traversed triangle is higher and lower than the value of the contour line, use linear interpolation to add a vertex on the contour line segment. If there are two such line segment vertices on a triangle, connect these two vertices as a segment in the contour line. Obtain all these line segments after traversing all triangles, superimpose and draw on the visualization diagram to obtain a visualization diagram with isolines.

Figure 3 illustrates an example of simultaneously visualizing a set of patient recovery data. Firstly, the data given in Table 1 is modeled as the fuzzy membership of a given group of patients to the set of recovered patients, and the degree of recovery is modeled as the membership function of the above fuzzy set, and then the steps described above are followed Generate a visual diagram, as shown in Figure 3 (the color information in the figure is not shown, and the transparency is displayed in the form of contour lines). The user interactively specifies the superimposed contour of u _A (x)=0.5. In FIG. 3 , it can be conveniently and intuitively seen the groups whose recovery degree of the patients is greater than 50%.

Table 1

In order to verify the effect of the present invention, the method of the present invention is compared with the prior art by taking the visualization of fuzzy childhood diseases as an example. Table 2 lists the data of fuzzy childhood diseases, and gives the probabilities corresponding to different diseases for different symptoms.

Table 2

upper respiratory infection pneumonia hand, foot and mouth disease fever 80% 15% 1% cough 50% 30% 0% sore throat 20% 10% 10% Vomit 30% 20% 5% rash 20% 1% 20%

First, according to the previous steps, respectively, for the fuzzy sets corresponding to the three diseases, use red, green, and blue colors to represent the three fuzzy sets. After completing the layout optimization, calculate their visualization layers respectively, and finally superimpose the three images. layer to obtain the visualization processing result of the present invention. Through this result, users can intuitively observe some information contained in the data, such as the phenomenon that cough symptoms may correspond to upper respiratory tract infection and pneumonia but not to hand, foot and mouth disease. "Cough" is close to "upper respiratory infection" in the green area and "pneumonia" in the blue area, but far away from "hand, foot and mouth disease" in the red area; for example, it can be directly observed that the element point corresponding to the symptom rash falls in the green area "Upper Respiratory Tract Infection" and the red "Hand, Foot and Mouth Disease" area are adjacent to the border and farther away from the blue "Upper Respiratory Tract Infection" area, from which the user can perceive that symptoms Rash is more likely to correspond to the upper respiratory tract than pneumonia Infection and hand, foot and mouth disease are two diseases, and the probability of confirming upper respiratory tract infection and hand, foot and mouth disease from symptomatic rash is not high.

Then by displaying the original data table (Table 2) and the circular diagram used to visualize the fuzzy set (using the literature [Y.Park, J.Park, Disk diagram: An interactive visualization technique of fuzzyset operations for the analysis of fuzzy data, Information Visualization 9,3(2010), 220-232] the data in Table 2 are processed and obtained) and the visualization results generated by the present invention, the statistics of the surveyed users on the visualization scheme in the amount of information, simplicity, recognizability, intuitive The results are shown in Figure 4, where scores from 0 to 10 represent poor to very good. It can be seen from the investigation results that the present invention sacrifices a small amount of information and improves the simplicity, intuitiveness, recognizability and aesthetics of information display, thereby being more user-friendly. The amount of information sacrificed mainly comes from the limited ability of human eyes to quantify transparency. According to user needs, the method of superimposing contours in the present invention can be used to more accurately quantify the belonging function, thereby alleviating this problem. On the other hand, compared with the circular graph, the present invention extends the circular boundary of the circular graph to the free curve boundary, and extends the pure color of the circular graph to the display of different colors and transparency, making full use of the geometry and transparency of the display medium. The color and transparency channels are more popular with users in all aspects.

Claims (4)

1. A fuzzy set visualization method, comprising the following steps: Step 1. Map each element in the fuzzy set and the center of the set to a point with color and transparency, and initialize its geometric position: Firstly, the collection centers are evenly distributed on the display medium, and the average distance between the collection centers is determined; using the average distance as a reference, the elements in each collection are distributed around the collection center, so that the distance between the element point and the collection center point The distance of is negatively linearly related to the membership function of the element to the set; Step 2. Optimize the position of the element point and the center point of the set: Define two types of ideal distances: one is the distance from the element point to the center point of the set, and its ideal distance is r(1-u _A (x)), where r is the radius of set A, and u _A (x) is the pair set of element x The membership function of A; one is the minimum ideal distance between element points, which is determined by the user according to the geometric size of the display medium; the spring-mass model is established, and the two types of distance are modeled as the ideal length of the spring, and the element points are Model the center of the mass as a mass point, fix the mass point close to the center of the display medium, and use the spring-mass model for physical simulation to find the position of the mass point under static conditions as the position of the optimized element point and the center of the set; Step 3. Constraints on the optimized element points, set center points, and the boundaries of the display medium, using Delaunay triangular mesh division, to establish a discrete triangular mesh passing through these points; Step 4. Calculate the color and transparency distribution of each vertex of the triangular mesh, and perform coloring according to the calculation result: Draw a layer for each fuzzy set, set all vertices of the same layer to the same color, and set different colors for different layers; for each layer, calculate the transparency of the vertices of the triangular mesh and draw the layer, and finally superimpose The layer obtains the visualization scheme; wherein, the transparency calculation method of the vertices of the triangular mesh is as follows: define the transparency of the set center point c as 0, and the transparency of the element point x as 1-u _A (x), where u _A (x) is The membership function of element x to set A, if u _A (x) is not equal to 1, extrapolate the line from c to x to find point y=c+(cx)/(1-u _A (x)), and point y Set the transparency at 1; finally, using the transparency at the set center point, element point, and extrapolation point as boundary conditions, solve the second-order harmonic equation on the triangular mesh to obtain the transparency of the other vertices of the triangular mesh. 2. The method according to claim 1, wherein, when initializing the geometric positions of the set central point and the element point, if an element belongs to multiple sets, the initial positions under different sets are averaged as its initial position. 3. The method of claim 1, further comprising: Step 5. Add transparency contours to the obtained visualization scheme. 4. The application of the method according to any one of claims 1 to 3 in the visualization of medical data, first abstract the medical data containing uncertainty, abstract the uncertainty into a set language according to the error or possibility, and abstract The membership probability is obtained to quantify the uncertainty, thereby forming one or more fuzzy sets; and then the one or more fuzzy sets are visualized using the method according to any one of claims 1-3.