CN108596997A - A kind of corona darkens the dynamic and visual method of image statistics feature - Google Patents

Abstract

The invention discloses a kind of dynamic and visual methods that corona darkens image statistics feature, including step：The image that constant duration in EventSelect time of origin section is darkened according to a corona forms image sequence；The statistical nature of sequence of computed images：Angle average variance and angle one dimensional image entropy；Establish two kinds of features to colour sequential Linear Mapping；Two groups of donuts are drawn respectively, each annulus corresponds to the characteristic value at a time point, for each annulus by waiting big annular block to form, the color of each annular block represents the size of the darkening image fan regional characteristic value at corresponding time point by the Linear Mapping acquisition established.The present invention will effectively darken image statistics characteristic reaction and position occurs in the Opacitization, by the time attribute for representing feature with donut, three-dimensional feature is mapped into two-dimensional space, changes with time to darkening image statistics feature in the Opacitization generation position and carries out dynamic tracing.

Description

A kind of corona darkens the dynamic and visual method of image statistics feature

Technical field

The present invention relates to information visualization field, espespecially a kind of corona darkens the dynamic and visual side of image statistics feature Method.

Background technology

The sun is in universe and the earth is at a distance of a nearest fixed star, when breaking out violent solar activity on the sun (such as：Day Crown substance slinging) when, earth magnetosphere and ionization are moved in electromagnetic radiation, energetic charged particles subflow and the high speed plasma disturbed and confused like the clouds of enhancing Layer, is hindering and damaging spacecraft and satellite just at phenomena such as causing the geomagnetic storm of terrestrial space, ionospheric storm, aurora when serious Often work, leads to the consequences such as power grid excess load, communicating interrupt on the earth.There is scientist to point out, some natures occurred in recent years Disaster, such as earthquake, volcano eruption, tsunami, it is all related with the aggravation of solar activity.It can be seen that solar activity is not only possible It threatens to the safety of terrestrial space environment, it is also possible to which massive losses are brought to the production and living of the mankind.From 60 years 20th century Since generation, countries in the world constantly emit scientific satellite and to solar activity observe and study comprehensively, to realize to space weather Prediction, reduce the adverse effect brought of pace weather weather.

Coronal mass ejection (CME) is that most frequent, most grand extensive activity phenomenon is broken out in solar activity, to CME It is the basis predicted space weather to carry out research.Often with other physics mistakes such as corona darkenings in the onset process of CME The generation of journey, carrying out research to these attendant phenomenons helps further to study CME, and then empty for forecast space weather, reduction Between the adverse effect of weather bring help.

In the attendant phenomenon of CME, corona the Opacitization and its tightness degree highest.Corona the Opacitization refers in low day In the certain area of crown, the decrease phenomenon of radiation light intensity within a certain period of time on white light, extreme ultraviolet and Soft X-Ray Region.Make For the initial important features of CME, corona darkens the research hotspot for having become Solar Physics field.In the important research of one of which Appearance is to study generation, differentiation and the propagation law of corona the Opacitization.

In recent years, with the fast development of computer realm, more and more technologies can be used for grinding for corona darkening Study carefully.Visualization technique will be difficult to the data conversion directly displayed at lively intuitive using computer graphics and image processing techniques Expression-form, auxiliary people from mass data enhance and find data in hide feature and rule, acquisition more more have Knowledge.Visualization technique has been widely used in the every field such as medical treatment, geography, finance, commercial affairs, plays more and more important Effect, also receive more and more attention.

At present to there are mainly two types of the research methods of corona the Opacitization feature evolution rule：It is a kind of to utilize scientific visualization Technology analyzes dark region internal structure, another to be analyzed using the conventional statistics such as line chart figure darkening feature.It passes Three time of the Opacitization, position and feature dimensions are not combined analysis by the method for visualizing of system, are only individually divided Analyse the two dimensional character of position and feature or time and feature composition.The present invention is proposed for the information for darkening image statistics feature Method for visualizing, binding time dimension occur position displaying in corona the Opacitization and darken the change of image statistics feature at any time Change.It is intuitively analyzed darkening image statistics feature, shows the dynamic change for darkening feature in the Opacitization evolution process, It helps to carry out more comprehensive research and analysis to the Opacitization.

Invention content

Darkening characteristic analysis method in view of present corona can not be characteristic value, position in corona the Opacitization evolution process It changes with time while showing, the purpose of the present invention is to propose to a kind of by the Opacitization image statistics feature at any time Change and the method for visualizing that position is shown occurs in the Opacitization.

Realize that the technical solution of the object of the invention is as follows：

A kind of corona darkens the dynamic and visual method of image statistics feature, including：

Step 1：Event is darkened for a corona, selects its time of origin section (t_start,t_end) interior time interval be k n A time point t={ t₁,t₂,…,t_n, select n width a × b image composition image sequence I corresponding with t_s={ I₁,I₂,…,I_n}； Wherein, a × b indicates the size of image, the i-th width image I_iCorresponding time point t_i, 1≤i≤n；

Step 2：Sequence of computed images I_sAngle be averaged sequential varianceIncluding：

Step 2.1：Sequential variance is defined as the variance calculated based on time-division difference diagram；Time-division difference diagram refers to image sequence In, use t_i+1Time point image subtracts t_iThe obtained difference image of time point image；Image I is calculated first_iSequential variance square Battle array V^RD(t_i), including：

1) image I is calculated_iMiddle coordinate is the sequential variance V of the pixel of (x, y)^RD(x,y,t_i),

Wherein, 1≤x≤a, 1≤y≤b, i ＜ n；P(x,y,t_i) indicate image I_iMiddle coordinate is the picture of the pixel of (x, y) Element value,It is P (x, y, t_i) and P (x, y, t_i+1) mean value；

2) traversal image I_i, calculate the sequential variance V for owning (x, y)^RD(x,y,t_i), composition image I_iSequential variance square Battle array V^RD(t_i)；

Step 2.2：Calculate image I_iAngle be averaged sequential varianceImage I_iThe angle sequential variance that is averaged it is fixed Justice is image I_iIn it is all in fan-shaped window window_j ^R,θInterior coordinate points (^x, y) sequential variance V^RD(x,y,t_i) be averaged Value；Wherein, θ represents the central angle size of fan-shaped window, and R represents the radius of fan-shaped window, and it is jth that j, which represents current fan-shaped window, A sector window；Including：

1) from image I_i0 ° of position in Sino-Japan face region, this day face surface start, and calculate fan-shaped window window_J=1 ^R,θ Interior average sequential variance yieldsFan-shaped window window_J=1 ^R,θAngular bisector l_J=1With I_i0 ° of position in Sino-Japan face region Set coincidence；

2) by window_J=1 ^R,θAs sliding window, angle [alpha] is rotated clockwise, obtains the 2nd fan-shaped window window_J=2 ^R,θ, calculate window_J=2 ^R,θInterior average sequential variance yieldsWherein, 0≤α≤360 °, 360 ° of α=0 % are Angle [alpha] can be divided exactly by 360 °；Be rotated by 360 ° successively/α angle [alpha] and calculate after, obtain image I_iAngle be averaged sequential variance

Step 2.3：Traverse image sequence I_s, image sequence I is calculated_sAngle be averaged sequential variance

Step 3：Sequence of computed images I_sAngle one dimensional image entropy E, including：

Step 3.1：Calculate image I_iAngle one dimensional image entropy E (t_i), including：

1) by I_iAccording toBe converted to the gray level image that gray value is 0~255 I_i'；

2) from image I_i' 0 ° of position in Sino-Japan face region starts, calculate fan-shaped window window_J=1 ^R,θInterior angle is one-dimensional Image entropy E_j(t_i),

Wherein, p_j,mRepresent window_j ^R,θInterior pixel value is that the pixel quantity of m accounts for window_j ^R,θInterior pixel sum Ratio；

3) by window_J=1 ^R,θAs sliding window, angle [alpha] is rotated clockwise, obtains the 2nd fan-shaped window window_J=2 ^R,θ, calculate window_J=2 ^R,θInterior angular image entropy E₂(t_i)；Wherein, 0≤α≤360 °, 360 ° of α=0 % are angle Degree α can be divided exactly by 360 °；Be rotated by 360 ° successively/α angle [alpha] and calculate after, obtain image I_iAngular image entropy E (t_i)={ E₁ (t_i), E₂(t_i) ..., E_360°/α(t_i)}；

Step 3.2：Traverse image sequence I_s, image sequence I is calculated_sAngle one dimensional image entropy E={ E (t₁), E (t₂) ..., E (t_n)}；

Step 4：Establish image sequence I_sAngle be averaged sequential varianceTo RGB color range L T.LT.LT color₁, color₂,…,color_cThe Linear Mapping f of ＞_v-cSo that

Step 5：Establish image sequence I_sAngle one dimensional image entropy E to RGB color range L T.LT.LT color₁,color₂,…, color_cThe Linear Mapping f of ＞_e-cSo that f_e-c(min (E))=color₁, f_e-c(max (E))=color_c；

Step 6：Draw the donut ring that radius is r × i^v={ ring^v ₁,ring^v ₂,…,ring^v _n-1, wherein r is Positive integer, visual image sequence I_sAngle be averaged sequential varianceIncluding：

Step 6.1：Since 0 ° of position, that is, position directly above, along clockwise direction, the annular that central angle is α is drawn successively Block block^v _i,j={ block^v _i,1,block^v _i,2,…,block^v _i,360°/α, j represents j-th of annular block；When j=360 °/ To get to ring when α^v _i；

Step 6.2：Annular block block^v _i,jColor by mappingIt obtains；

Step 6.3：It draws n-1 donut successively inside-out according to the method described above, obtains image sequence I_sAngle The average sequential variance of degreeVisualization result；

Step 7：Draw the donut ring that radius is r × i^e={ ring^e ₁,ring^e ₂,…,ring^e _n, wherein r is Positive integer, visual image sequence I_sAngle one dimensional image entropy E；Including：

Step 7.1：Since 0 ° of position, that is, position directly above, along clockwise direction, the annular that central angle is α is drawn successively Block block^e _i,j={ block^e _i,1,block^e _i,2,…,block^e _i,360°/α, j represents j-th of annular block；When j=360 °/ To get to ring when α^e _i；

Step 7.2：Annular block block^e _i,jColor by map f_e-c(E_j(t_i)),t_i=i is obtained；

Step 7.3：It draws n donut successively inside-out according to the method described above, obtains image sequence I_sAngle The visualization result of one dimensional image entropy E.

Compared with prior art, the positive effect of the present invention is：Traditional method for visualizing not by the Opacitization when Between, three dimensions in position and feature combine analysis, only independent analysis position and feature or time and feature composition Two dimensional character.The present invention proposes that, for the information visualization methods for darkening image statistics feature, binding time dimension is dark in corona Change phenomenon generation position displaying darkening image statistics feature to change with time.Intuitively divided darkening image statistics feature Analysis shows the dynamic change that feature is darkened in the Opacitization evolution process, helps to carry out more comprehensive research to the Opacitization And analysis.

Description of the drawings

Fig. 1 is the Sino-Japan face region of image, fan-shaped window schematic diagram.

Fig. 2 is annulus schematic diagram.

Position view occurs for Fig. 3 experimental data middile corona the Opacitizations.

Fig. 4 is the present invention in experimental data set upper angle average variance effect of visualization figure.

Fig. 5 is the present invention in experimental data set upper angle one dimensional image entropy effect of visualization figure.

Limitation in view of Figure of description to colour expression, spy are explained as follows：

In Fig. 4, color mapping f_v-cIt willIt is mapped to color ＜ color₁,color₂,color₃＞.

In Fig. 5, color mapping f_e-cE is mapped to color ＜ color₁,color₂,color₃＞.

Specific implementation mode

The specific implementation mode of the present invention is further detailed below.

A kind of corona darkens the dynamic and visual method of image statistics feature, completes the corona the Opacitization on day face and occurs The dynamic change that position is changed over time to darkening characteristics of image, includes the following steps：

Step 1：Event is darkened for a corona, selects its time of origin section (t_start,t_end) interior time interval be k n A time point t={ t₁,t₂,…,t_n, select n width a × b image composition image sequence I corresponding with t_s={ I₁,I₂,…,I_n, Wherein, a × b indicates the size of image, i-th, (1≤i≤n) width image I_iCorresponding time point t_i。

Step 2：Sequence of computed images I_sAngle be averaged sequential variance

Step 2.1：Sequential variance is defined as the variance calculated based on time-division difference diagram.Time-division difference diagram refers to image sequence In, with the obtained difference image of t+1 time chart image subtraction t moment images.Calculate image I_iSequential variance matrix V^RD(t_i) It is as follows：

1) image I is calculated_iMiddle coordinate is (x, y), the sequential variance V of the pixel of (1≤x≤a, 1≤y≤b)^RD(x,y, t_i), calculation formula is as follows：

Wherein, P (x, y, t_i) indicate image I_iMiddle coordinate is the pixel value of the pixel of (x, y),Be P (x, y, t_i) and P (x, y, t_i+1) mean value, that is,

2) traversal image I_i, calculate the sequential variance V for owning (x, y)^RD(x,y,t_i), composition image I_iSequential variance square Battle array V^RD(t_i)。

Step 2.2：Calculate image I_iAngle be averaged sequential varianceImage I_iThe angle sequential variance that is averaged it is fixed Justice is image I_iIn it is all in fan-shaped window window_j ^R,θThe sequential variance V of interior coordinate points (x, y)^RD(x,y,t_i) be averaged Value, calculation formula are as follows：

Wherein, θ represents the central angle size of fan-shaped window, and R represents the radius of fan-shaped window, and j represents current fan-shaped window It is j-th of fan-shaped window, | window_j ^R,θ| indicate window_j ^R,θThe number of middle coordinate points.It is as follows：

1) from image I_i0 ° of position (day face surface) in Sino-Japan face region starts, and calculates fan-shaped window window_J=1 ^R,θIt is interior Average sequential variance yields(t_i), fan-shaped window window_J=1 ^R,θAngular bisector l_J=1, with I_i0 ° of position in Sino-Japan face region Set coincidence.

2) by window_J=1 ^R,θAs sliding window, α is rotated clockwise, (0≤α≤360, α | 360) angle obtains the 2nd A sector window window_J=2 ^R,θ, calculate window_J=2 ^R,θInterior average sequential variance yieldsRotate 360/ α angle [alpha] Afterwards, image I is calculated_iAngle be averaged sequential variance

Step 2.3：Traverse image sequence I_s, image I is calculated_sAngle be averaged sequential variance

Step 3：Sequence of computed images I_sAngle one dimensional image entropy E.

Step 3.1：Calculate image I_iAngle one dimensional image entropy E (t_i).It is as follows：

1) by I_iAccording toBe converted to the gray level image that gray value is 0~255 I_i'。

2) from image I_i' 0 ° of position (day face right over) in Sino-Japan face region starts, calculate fan-shaped window window_J=1 ^R,θ Interior angle one dimensional image entropy E_j(t_i), calculation formula is as follows：

Wherein, p_j,_mRepresent window_j ^R,θInterior pixel value is that the pixel quantity of m accounts for window_j ^R,θInterior pixel sum Ratio, calculation formula are as follows：

3) by window_J=1 ^R,θAs sliding window, α is rotated clockwise, (0≤α≤360, α | 360) angle obtains the 2nd A sector window window_J=2 ^R,θ, calculate window_J=2 ^R,θInterior angular image entropy E₂(t_i).After rotating 360/ α angle [alpha], meter Calculation obtains image I_iAngular image entropy E (t_i)={ E₁(t_i), E₂(t_i) ..., E_360/α(t_i)}。

Step 3.2：Traverse image sequence I_s, image I is calculated_sAngular image entropy E={ E (t₁), E (t₂) ..., E (t_n)}。

Step 4：Establish image sequence I_sAngle be averaged sequential varianceTo RGB color range L T.LT.LT color₁, color₂,…,color_cThe Linear Mapping f of ＞_v-cSo that

Step 5：Establish image sequence I_sAngle one dimensional image entropy E to RGB color range L T.LT.LT color₁,color₂,…, color_cThe Linear Mapping f of ＞_e-cSo that f_e-c(min (E))=color₁, f_e-c(max (E))=color_c。

Step 6：Draw the donut ring that radius is r × i^v={ ring^v ₁,ring^v ₂,…,ring^v _n-1, whereinVisual image sequence I_sAngle be averaged sequential varianceIt is as follows：

Step 6.1：Since 0 ° (position directly above), along clockwise direction, the annular block that central angle is α is drawn successively block^v _i,j={ block^v _i,1,block^v _i,2,…,block^v _i,360/α, j represents j-th of annular block, when j=360/ α, obtains ring^v _i。

Step 6.2：Annular block block^v _i,jColor by mappingIt obtains.

Step 6.3：It draws n-1 donut successively inside-out, obtains image sequence I_sAngle be averaged sequential side DifferenceVisualization result.

Step 7：Draw the donut ring that radius is r × i^e={ ring^e ₁,ring^e ₂,…,ring^e _n, whereinVisual image sequence I_sAngle one dimensional image entropy E.It is as follows：

Step 7.1：Since 0 ° (position directly above), along clockwise direction, the annular block that central angle is α is drawn successively block^e _i,j={ block^e _i,1,blocke_i,2,…,block^e _i,360/α, j represents j-th of annular block, when j=360/ α, obtains To ring^e _i。

Step 7.2：Annular block block^e _i, the color of j is by mapping f_e-c(E_j(t_i)),(t_i=i) it obtains.

Step 7.3：It draws n-1 donut successively inside-out, obtains image sequence I_sAngle one dimensional image entropy E Visualization result.

The present invention devises a kind of for the information visualization methods for darkening image statistics feature, binding time dimension, meter The angle sequential variance and angle one dimensional image entropy for darkening image are calculated, position occurs in corona the Opacitization using visualization technique Displaying darkens image statistics feature and changes with time.It is intuitively analyzed darkening image statistics feature, it is existing to show darkening Dynamic change as darkening feature in evolution process helps to carry out more comprehensive research and analysis to the Opacitization.

To verify effectiveness of the invention, it is the most real that selection is happened at a corona the Opacitization on May 12nd, 1997 Object is tested, from EIT Data web siteshttps://umbra.nascom.nasa.gov/eit/eit-catalog.htmlIt obtains 12 days 04 May in 1997:34UT~07:N=10 width images during 34UT form image sequence.

The angle average variance of sequence of computed images, fan-shaped window window_j ^R,θR and image are Sino-Japan in (as shown in Figure 1) The same size of face zone radius, fan-shaped window central angle θ=5 °, rotates clockwise angle [alpha]=1 °.

The one dimensional image entropy of sequence of computed images, fan-shaped window window_j ^R,θMiddle R is as the Sino-Japan face zone radius of image Size, fan-shaped window central angle θ=5 °, rotates clockwise angle [alpha]=1 °.

Image sequence angle average variance is established to colour sequential ＜ color₁,color₂,color₃The Linear Mapping of ＞.

Image sequence angle one dimensional image entropy is established to colour sequential ＜ color₁,color₂,color₃The linear of ＞ is reflected It penetrates.

Drafting radius be r × i, 9 donuts (method for drafting is as shown in Figure 2) of (r=10, i=(1,2 ..., 9)), The angle average variance of visual image sequence, experimental result are as shown in Figure 4.

Drafting radius is r × i, 10 donuts (method for drafting such as Fig. 2 institutes of (r=10, i=(1,2 ..., 10)) Show), the angle one dimensional image entropy of visual image sequence, experimental result is as shown in Figure 5.

Claims (1)

1. a kind of corona darkens the dynamic and visual method of image statistics feature, which is characterized in that including：

Step 1：Event is darkened for a corona, selects its time of origin section (t_start,t_end) interior time interval is when being n of k Between point t={ t₁,t₂,…,t_n, select n width a × b image composition image sequence I corresponding with t_s={ I₁,I₂,…,I_n}；Its In, a × b indicates the size of image, the i-th width image I_iCorresponding time point t_i, 1≤i≤n；

Step 2：Sequence of computed images I_sAngle be averaged sequential varianceIncluding：

Step 2.1：Sequential variance is defined as the variance calculated based on time-division difference diagram；Time-division difference diagram refers in image sequence, Use t_i+1Time point image subtracts t_iThe obtained difference image of time point image；Image I is calculated first_iSequential variance matrix V^RD(t_i), including：

1) image I is calculated_iMiddle coordinate is the sequential variance V of the pixel of (x, y)^RD(x,y,t_i),

Wherein, 1≤x≤a, 1≤y≤b, i ＜ n；P(x,y,t_i) indicate image I_iMiddle coordinate is the pixel of the pixel of (x, y) Value,It is P (x, y, t_i) and P (x, y, t_i+1) mean value；

2) traversal image I_i, calculate the sequential variance V for owning (x, y)^RD(x,y,t_i), composition image I_iSequential variance matrix V^RD (t_i)；

Step 2.2：Calculate image I_iAngle be averaged sequential varianceImage I_iThe angle sequential variance that is averaged be defined as Image I_iIn it is all in fan-shaped window window_j ^R,θThe sequential variance V of interior coordinate points (x, y)^RD(x,y,t_i) average value；

Wherein, θ represents the central angle size of fan-shaped window, and R represents the radius of fan-shaped window, and it is jth that j, which represents current fan-shaped window, A sector window；Including：

1) from image I_i0 ° of position in Sino-Japan face region, this day face surface start, and calculate fan-shaped window window_J=1 ^R,θInterior Average sequential variance yieldsFan-shaped window window_J=1 ^R,θAngular bisector l_J=1With I_i0 ° of position weight in Sino-Japan face region It closes；

2) by window_J=1 ^R,θAs sliding window, angle [alpha] is rotated clockwise, obtains the 2nd fan-shaped window window_J=2 ^R,θ, meter Calculate window_J=2 ^R,θInterior average sequential variance yieldsWherein, 0≤α≤360 °, 360 ° of α=0 % are that angle [alpha] can be by 360 ° Divide exactly；Be rotated by 360 ° successively/α angle [alpha] and calculate after, obtain image I_iAngle be averaged sequential variance

Step 2.3：Traverse image sequence I_s, image sequence I is calculated_sAngle be averaged sequential variance

Step 3：Sequence of computed images I_sAngle one dimensional image entropy E, including：

Step 3.1：Calculate image I_iAngle one dimensional image entropy E (t_i), including：

1) by I_iAccording toBe converted to the gray level image I that gray value is 0~255_i'；

2) from image I_i' 0 ° of position in Sino-Japan face region starts, calculate fan-shaped window window_J=1 ^R,θInterior angle one dimensional image Entropy E_j(t_i),

Wherein, p_j,mRepresent window_j ^R,θInterior pixel value is that the pixel quantity of m accounts for window_j ^R,θThe ratio of interior pixel sum；

3) by window_J=1 ^R,θAs sliding window, angle [alpha] is rotated clockwise, obtains the 2nd fan-shaped window window_J=2 ^R,θ, meter Calculate window_J=2 ^R,θInterior angular image entropy E₂(t_i)；Wherein, 0≤α≤360 °, 360 ° of α=0 % are that angle [alpha] can be whole by 360 ° It removes；Be rotated by 360 ° successively/α angle [alpha] and calculate after, obtain image I_iAngular image entropy E (t_i)={ E₁(t_i), E₂ (t_i) ..., E_360°/α(t_i)}；

Step 3.2：Traverse image sequence I_s, image sequence I is calculated_sAngle one dimensional image entropy E={ E (t₁), E (t₂) ..., E (t_n)}；

Step 4：Establish image sequence I_sAngle be averaged sequential varianceTo RGB color range L T.LT.LT color₁,color₂,…, color_cThe Linear Mapping f of ＞_v-cSo that

Step 5：Establish image sequence I_sAngle one dimensional image entropy E to RGB color range L T.LT.LT color₁,color₂,…,color_c The Linear Mapping f of ＞_e-cSo that f_e-c(min (E))=color₁, f_e-c(max (E))=color_c；

Step 6：Draw the donut that radius is r × iWherein r is positive integer, Visual image sequence I_sAngle be averaged sequential varianceIncluding：

Step 6.1：Since 0 ° of position, that is, position directly above, along clockwise direction, the annular block that central angle is α is drawn successivelyJ represents j-th of annular block；As j=360 °/α to get To ring^v _i；

Step 6.2：Annular block block^v _i,jColor by mappingIt obtains；

Step 6.3：It draws n-1 donut successively inside-out according to the method described above, obtains image sequence I_sAngle it is average Sequential varianceVisualization result；

Step 7：Draw the donut ring that radius is r × i^e={ ring^e ₁,ring^e ₂,…,ring^e _n, wherein r is just whole Number, visual image sequence I_sAngle one dimensional image entropy E；Including：

Step 7.1：Since 0 ° of position, that is, position directly above, along clockwise direction, the annular block that central angle is α is drawn successively block^e _i,j={ block^e _i,1,block^e _i,2,…,block^e _i,360°/α, j represents j-th of annular block；As j=360 °/α, Obtain ring^e _i；

Step 7.2：Annular block block^e _i,jColor by map f_e-c(E_j(t_i)),t_i=i is obtained；

Step 7.3：It draws n donut successively inside-out according to the method described above, obtains image sequence I_sThe one-dimensional figure of angle As the visualization result of entropy E.