CN107358634A - The color rendering intent and device of a kind of fractal pattern - Google Patents
The color rendering intent and device of a kind of fractal pattern Download PDFInfo
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Abstract
The present invention relates to the color rendering intent and device of a kind of fractal pattern, iterated function system theory is combined with HMM, the color of fractal pattern is regarded as an observable external presentation, it is determined by a series of hiding unobservable states, utilize the color change of Markov sequence control fractal pattern, realize the Color control of fractal pattern, method is simple, overcome the limitation of conventional iterative function system, establish the stochastic model of more flexibility and practicality, pass through the coloring rule in layout drawing process, any regulation and control that pattern color is realized in disturbance are carried out to transition probability matrix, Fractal Artistic Patterns of the substantial amounts of color rich in change can be quickly generated.
Description
Technical field
The present invention relates to fractal pattern technical field, the color rendering intent and device of more particularly to a kind of fractal pattern.
Background technology
Point shape cross discipline emerging as one meets the demand of variety of arts, fractal pattern by geometrical aesthetic with
Vision shape combines together.Fractal geometry utilizes its distinctive self-similarity, can construct it is ever-changing and with appoint
Anticipate high-resolution art pattern.Fractal Art is art and the merging point of science, is the perfect unity of mathematics and aesthetic,
It is that certain that generated by computer numerical value calculation has the figure of scientific meaning and esthetic sentiment, and fractal pattern changes
Property, contingency and its it is not repeated make Fractal Art application it is more and more extensive.
Iterated function system (Iterated Function System, IFS) is a kind of classical fractal pattern generation skill
Art, it can generate rich and changeful fractal pattern, and its theoretical and method is widely studied and is applied to numerous necks
Among domain.But IFS methods only considered the shape moulding of point shape, lack Color Expression element.
The content of the invention
For this reason, it may be necessary to provide the color rendering intent and device of a kind of fractal pattern, it can solve the problem that IFS systems lack color
Expressive element, any regulation and control of fractal pattern color are realized, Fractal Art figure of the substantial amounts of color rich in change can be quickly generated
Case.
To achieve the above object, a kind of color rendering intent of fractal pattern is inventor provided, is comprised the following steps：
Pass through N number of affine transformation ω of hidden Markov chain value IFS systemsiForm affine transformation v ariety { X；ω1,
ω2,…,ωN, and set up the transition probability matrix P=(p of affine transformation v arietyij)N×N,1≤i,j≤N；
Setpoint color value matrix (cjk)N×MWith color probability matrix (qjk)N×M；
One affine transformation ω is randomly choosed according to transition probability matrix Pi(1≤i≤N), and affine transformation is calculated
Point ωi(x), x ∈ X (1≤i≤N) coordinate；
A kind of color is randomly choosed from color value matrix according to color probability matrix；
Drawn a little on the coordinate of affine transformation point is calculated using the color of selection；
Picture point is carried out according to setting iterations, exports the fractal pattern finally coloured.
Further optimization, " setpoint color value matrix and the color probability matrix " includes：
Setpoint color value matrix (cjk)N×M,1≤j≤N,1≤k≤M；
Set probability-distribution function F (x) ＞ 0；
Initialize color probability matrix (qjk)N×M,1≤j≤N,1≤k≤M；
To matrix color probability matrix (qjk)N×M, 1≤j≤N, 1≤k≤M row probability distribution is normalized,
Obtain color probability matrix Q=(qjk)N×M,1≤j≤N,1≤k≤M。
Further optimization, in addition to：
From affine transformation v ariety { X；ω1,ω2,…,ωNIn select some affine transformations, decomposed step by step according to conversion formula
Obtain decomposing code
The colour model of each subgraph is established according to decomposition code
According to the colour model of each subgraphLocal Subgraphs are exported one by one
Picture
Further optimization, the conversion formula are：
Further optimization, in addition to：
Other Local Subgraphs pictures not decomposed are exported one by one.
Inventor additionally provides a kind of color rendering device of fractal pattern of another technical scheme, including model establishes list
Member, coordinate calculating unit, color selecting unit and pattern picture dot element；
The model is established unit and is used for by N number of affine transformation ω of hidden Markov chain value IFS systemsiComposition is imitative
Penetrate transformation family { X；ω1,ω2,…,ωN, and set up the transition probability matrix P=(p of affine transformation v arietyij)N×N,1≤i,j≤N；
Setpoint color value matrix (cjk)N×MWith color probability matrix (qjk)N×M；
The coordinate calculating unit is used to randomly choose an affine transformation ω according to transition probability matrix Pi(1≤i≤
N), and it is calculated affine transformation point ωi(x), x ∈ X (1≤i≤N) coordinate；
The color selecting unit is used to randomly choose a kind of color from color value matrix according to color probability matrix；
The pattern picture dot element is used to draw a little on the coordinate of affine transformation point is calculated using the color of selection；And
Picture point is carried out according to setting iterations, exports the fractal pattern finally coloured.
Further optimization, the model are established unit and are additionally operable to：
Setpoint color value matrix (cjk)N×M,1≤j≤N,1≤k≤M；
Set probability-distribution function F (x) ＞ 0；
Initialize color probability matrix (qjk)N×M,1≤j≤N,1≤k≤M；
To matrix color probability matrix (qjk)N×M, 1≤j≤N, 1≤k≤M row probability distribution is normalized,
Obtain color probability matrix Q=(qjk)N×M,1≤j≤N,1≤k≤M。
Further optimization, in addition to resolving cell, the resolving cell are used for from affine transformation v ariety { X；ω1,ω2,…,
ωNIn select some affine transformations, decompose to obtain step by step according to conversion formula and decompose code
The model establishes the colour model that unit is additionally operable to establish each subgraph according to decomposition code
The pattern picture dot element is additionally operable to the colour model according to each subgraph
Local Subgraphs picture is exported one by one
Further optimization, the conversion formula are：
Further optimization, the pattern picture dot element are additionally operable to export other Local Subgraphs pictures not decomposed one by one.
Prior art is different from, iterated function system theory is combined by above-mentioned technical proposal with HMM,
The color of fractal pattern is regarded as an observable external presentation, it is true by a series of hiding unobservable state institutes
It is fixed, the color change of fractal pattern is controlled using Markov sequence, realizes the Color control of fractal pattern, method is simple, gram
The limitation of conventional iterative function system is taken, the stochastic model of more flexibility and practicality is established, is painted by layout
Coloring rule during system, any regulation and control that pattern color is realized in disturbance are carried out to transition probability matrix, can be quickly generated big
Fractal Artistic Patterns of the color of amount rich in change.
Brief description of the drawings
Fig. 1 is a kind of flow principle schematic of the color rendering intent of fractal pattern described in specific embodiment 1；
Fig. 2 is a kind of flow principle schematic of the color rendering intent of fractal pattern described in specific embodiment 2；
Fig. 3 is a kind of principle schematic diagram of the color rendering device of fractal pattern described in specific embodiment 3.
Embodiment
To describe the technology contents of technical scheme, construction feature, the objects and the effects in detail, below in conjunction with specific reality
Apply example and coordinate accompanying drawing to be explained in detail.
Referring to Fig. 1, embodiment 1, a kind of color rendering intent of fractal pattern, comprise the following steps：
Step S110：Pass through N number of affine transformation ω of hidden Markov chain value IFS systemsiForm affine transformation v ariety { X；
ω1,ω2,…,ωN, and set up the transition probability matrix P=(p of affine transformation v arietyij)N×N,1≤i,j≤N。
N number of affine transformation ω of hidden Markov chain value IFS systemsiState set { the X of composition；ω1,ω2,…,ωN,
Observable sequence value is affine transformation point ωi(x), x ∈ X (i=1,2 ..., N) observed result.If P=(pij)N×N,1
≤ i, j≤N be hidden Markov chain state transition probability matrix, its element pijRepresent from state ωiIt is transferred to state ωj's
Transition probability, have：pij=P (Sn=ωj|Sn-1=ωi), 1≤i, j≤N, meet
Step S120：Setpoint color value matrix (cjk)N×MWith color probability matrix (qjk)N×M。
Q=(qjk)N×M, 1≤j≤N, 1≤k≤M expressions are in state ωjWhen produce observation vk∈{Om:M=1,2 ...,
M } discrete probabilistic value (be referred to as observation probability) composition matrix, have:qjk=P (Om=vk|Sn=ωj),1≤j≤N,1≤k
≤ M, meetIf v1Represent colour 1, observation probability qj1Represent.v2Represent colour
2, observation probability qj2Represent...., vMRepresent colour M, observation probability qjMRepresent, setting Q=(qjk)N×M,1≤j≤N,1
≤ k≤M is color probability matrix, and each affine transformation sequence of points has the alternative color of M kinds on the image so generated
Value (M size can be set as needed).Color value is with one and color probability matrix (qjk)N×MIt is an equal amount of
Matrix (cjk)N×MRepresent, wherein, obtain color cjkProbable value be qjk。
Step S130：One affine transformation ω is randomly choosed according to transition probability matrix Pi(1≤i≤N), and be calculated
Affine transformation point ωi(x), x ∈ X (1≤i≤N) coordinate；Hidden Markov chain can regard the fortune on fractal space as
It is dynamic, since an original state, affine transformation state ω is randomly chosen according to certain probabilityi(i=1,2 ..., N) in
Some, and randomly generate an affine transformation point ωi(x), x ∈ X (i=1,2 ..., N).
Step S140：A kind of color is randomly choosed from color value matrix according to color probability matrix；Due to obtaining color
cjkProbable value be qjk, so as to according to color probability matrix (qjk)N×MFrom color value matrix (cjk)N×MIn randomly select one kind
Color.
Step S150：Drawn a little on the coordinate of affine transformation point is calculated using the color of selection；
Step S160：Picture point is carried out according to setting iterations, exports the fractal pattern finally coloured.
Iterated function system theory is combined with HMM, the color of fractal pattern regard as one it is considerable
The external presentation surveyed, it is determined by a series of hiding unobservable states, and graftal is controlled using Markov sequence
The color change of case, the Color control of fractal pattern is realized, method is simple, overcomes the limitation of conventional iterative function system, builds
The more stochastic model of flexibility and practicality is found, by the coloring rule in layout drawing process, to transition probability
Matrix carries out any regulation and control that pattern color is realized in disturbance, can quickly generate Fractal Art figure of the substantial amounts of color rich in change
Case.
Wherein, in step 120, including：
Setpoint color value matrix (cjk)N×M,1≤j≤N,1≤k≤M；
Set probability-distribution function F (x) ＞ 0；
Initialize color probability matrix (qjk)N×M,1≤j≤N,1≤k≤M；
To matrix color probability matrix (qjk)N×M, 1≤j≤N, 1≤k≤M row probability distribution is normalized,
Obtain color probability matrix Q=(qjk)N×M,1≤j≤N,1≤k≤M。
Probability (the q of all coloursjk)N×MDetermined at random by the distribution function for obeying a certain type.This application number
The probability distribution that mathematic(al) function determines, has very strong controllability and flexibility.Choose appropriate distribution function F (x) (F (x) ＞
0) color probability matrix (q, is initializedjk)N×M, 1≤j≤N, 1≤k≤M, and to matrix color probability matrix (qjk)N×M,1≤j
≤ N, 1≤k≤M row probability distribution are normalized：
It can be obtained by color probability matrix Q=(qjk)N×M,1≤j≤N,1≤k≤M。
Referring to Fig. 2, another embodiment 2, a kind of color rendering intent of fractal pattern, comprise the following steps：
Step S210：Pass through N number of affine transformation ω of hidden Markov chain value IFS systemsiForm affine transformation v ariety { X；
ω1,ω2,…,ωN, and set up the transition probability matrix P=(p of affine transformation v arietyij)N×N,1≤i,j≤N。
Step S220：From affine transformation v ariety { X；ω1,ω2,…,ωNIn select some affine transformations, according to conversion formula
Decompose step by step and obtain decomposing code
Step S230：Setpoint color value matrix (cjk)N×MWith color probability matrix (qjk)N×M；
Step S240：According to decomposition codeEstablish the colour model of each subgraph
Step S250：According to transition probability matrix P=(pij)N×N, 1≤i, j≤N are from colour modelOne affine transformation of middle random selection, and the seat of affine transformation point is calculated
Mark；
Step S260：Drawn a little on the coordinate of affine transformation point is calculated using the color of selection；
Step S270：Picture point is carried out according to setting iterations, exports the Local Subgraphs picture finally coloured
Step S280：According to the colour model of each subgraphIt is defeated one by one
Go out local subgraph
Using the decomposition theorem of affine transformation, by the way that IFS system decompositions are generated into multiple separate subsystems, so as to
The IFS for obtaining Local Subgraphs picture decomposes code, then carries out color to each subsystem image respectively and render, finally by each of image
Local Subgraphs picture is sequentially output, and pieces the fractal pattern to form view picture together.Based on image local independent operation, only to a certain of image
The implementation of Local Subgraphs picture is handled, other Local Subgraphs pictures without influencing whether image.Can be to the difference part of fractal pattern
Implement corresponding colouration scheme, to construct fractal pattern of the color character more rich in change.
The decomposition theorem of affine transformation：If ω1,ω2,…,ωNIt is fractal pattern f IFS codes,It is ωiIt is inverse, it is fixed
Adopted operatorForThenJ=1,2 ..., N is subgraph ωi(f) IFS codes.
Subgraph ωi(f) conversion formula of transformation matrix is：
Further, it is understood that there may be undecomposed Local Subgraphs picture, then export other Local Subgraphs not decomposed one by one
Picture.
Referring to Fig. 3, embodiment 3, a kind of color rendering device of fractal pattern, including model establish unit 310, coordinate
Computing unit 320, color selecting unit 330 and pattern picture dot element 340.
The model is established unit 310 and is used for by N number of affine transformation ω of hidden Markov chain value IFS systemsiGroup
Into affine transformation v ariety { X；ω1,ω2,…,ωN, and set up the transition probability matrix P=(p of affine transformation v arietyij)N×N,1≤i,j
≤N；Setpoint color value matrix (cjk)N×MWith color probability matrix (qjk)N×M；Hidden Markov chain value IFS systems it is N number of
Affine transformation ωiState set { the X of composition；ω1,ω2,…,ωN, observable sequence value is affine transformation point ωi(x),
X ∈ X (i=1,2 ..., N) observed result.If P=(pij)N×N, 1≤i, j≤N are that the state transfer of hidden Markov chain is general
Rate matrix, its element pijRepresent from state ωiIt is transferred to state ωjTransition probability, have：pij=P (Sn=ωj|Sn-1=
ωi), 1≤i, j≤N, meetI=1,2 ..., N.Q=(qjk)N×M, 1≤j≤N, 1≤k≤M represent to exist
State ωjWhen produce observation vk∈{Om:M=1,2 ..., M } discrete probabilistic value (be referred to as observation probability) composition matrix,
Have:qjk=P (Om=vk|Sn=ωj), 1≤j≤N, 1≤k≤M, meetJ=1,2 ..., N；If v1
Represent colour 1, observation probability qj1Represent.v2Represent colour 2, observation probability qj2Represent...., vMRepresent colour M, observation
Probability qjMRepresent, setting Q=(qjk)N×M, 1≤j≤N, 1≤k≤M are color probability matrix, every on the image so generated
Individual affine transformation sequence of points has the alternative color value of M kinds (M size can be set as needed).Color value is
With one and color probability matrix (qjk)N×MAn equal amount of matrix (cjk)N×MRepresent, wherein, obtain color cjkProbable value
For qjk。
The coordinate calculating unit 320 is used to randomly choose an affine transformation ω according to transition probability matrix Pi(1≤i
≤ N), and affine transformation point ω is calculatedi(x), x ∈ X (1≤i≤N) coordinate；Hidden Markov chain can be regarded as
Motion on fractal space, since an original state, affine transformation state ω is randomly chosen according to certain probabilityi(i=
1,2 ..., N) in some, and randomly generate an affine transformation point ωi(x), x ∈ X (i=1,2 ..., N).
The color selecting unit 330 is used to randomly choose a kind of face from color value matrix according to color probability matrix
Color；Due to obtaining color cjkProbable value be qjk, so as to according to color probability matrix (qjk)N×MFrom color value matrix
(cjk)N×MIn randomly select a kind of color.
The pattern picture dot element 340 is used to draw on the coordinate of affine transformation point is calculated using the color of selection
Point；And picture point is carried out according to setting iterations, export the fractal pattern finally coloured.
Iterated function system theory is combined with HMM, the color of fractal pattern regard as one it is considerable
The external presentation surveyed, it is determined by a series of hiding unobservable states, and graftal is controlled using Markov sequence
The color change of case, the Color control of fractal pattern is realized, method is simple, overcomes the limitation of conventional iterative function system, builds
The more stochastic model of flexibility and practicality is found, by the coloring rule in layout drawing process, to transition probability
Matrix carries out any regulation and control that pattern color is realized in disturbance, can quickly generate Fractal Art figure of the substantial amounts of color rich in change
Case.
Wherein, the model is established unit 310 and is additionally operable to：
Setpoint color value matrix (cjk)N×M,1≤j≤N,1≤k≤M；
Set probability-distribution function F (x) ＞ 0；
Initialize color probability matrix (qjk)N×M,1≤j≤N,1≤k≤M；
To matrix color probability matrix (qjk)N×M, 1≤j≤N, 1≤k≤M row probability distribution is normalized,
Obtain color probability matrix Q=(qjk)N×M,1≤j≤N,1≤k≤M。
Probability (the q of all coloursjk)N×MDetermined at random by the distribution function for obeying a certain type.This application number
The probability distribution that mathematic(al) function determines, has very strong controllability and flexibility.Choose appropriate distribution function F (x) (F (x) ＞
0) color probability matrix (q, is initializedjk)N×M, 1≤j≤N, 1≤k≤M, and to matrix color probability matrix (qjk)N×M,1≤j
≤ N, 1≤k≤M row probability distribution are normalized：
It can be obtained by color probability matrix Q=(qjk)N×M,1≤j≤N,1≤k≤M。
Wherein, in addition to resolving cell 311, the resolving cell 311 are used for from affine transformation v ariety { X；ω1,ω2,…,
ωNIn select some affine transformations, decompose to obtain step by step according to conversion formula and decompose code
The model establishes the colour model that unit 310 is additionally operable to establish each subgraph according to decomposition code
The pattern picture dot element 340 is additionally operable to the colour model according to each subgraph
Local Subgraphs picture is exported one by one
Using the decomposition theorem of affine transformation, by the way that IFS system decompositions are generated into multiple separate subsystems, so as to
The IFS for obtaining Local Subgraphs picture decomposes code, then carries out color to each subsystem image respectively and render, finally by each of image
Local Subgraphs picture is sequentially output, and pieces the fractal pattern to form view picture together.Based on image local independent operation, only to a certain of image
The implementation of Local Subgraphs picture is handled, other Local Subgraphs pictures without influencing whether image.Can be to the difference part of fractal pattern
Implement corresponding colouration scheme, to construct fractal pattern of the color character more rich in change.
The decomposition theorem of affine transformation：If ω1,ω2,…,ωNIt is the IFS codes of fractal pattern,It is ωiIt is inverse, it is fixed
Adopted operatorForThenJ=1,2 ..., N is subgraph ωi(f) IFS codes.
Subgraph ωi(f) conversion formula of transformation matrix is：
Further, it is understood that there may be undecomposed Local Subgraphs picture, the pattern picture dot element are additionally operable to export not entering one by one
Other Local Subgraphs pictures that row decomposes.
Although the various embodiments described above are described, those skilled in the art once know basic wound
The property made concept, then other change and modification can be made to these embodiments, so embodiments of the invention are the foregoing is only,
Not thereby the scope of patent protection of the present invention, every equivalent structure made using description of the invention and accompanying drawing content are limited
Or equivalent flow conversion, or other related technical areas are directly or indirectly used in, similarly it is included in the patent of the present invention
Within protection domain.
Claims (10)
1. the color rendering intent of a kind of fractal pattern, it is characterised in that comprise the following steps：
Pass through N number of affine transformation ω of hidden Markov chain value IFS systemsiForm affine transformation v ariety { X；ω1,ω2,…,
ωN, and set up the transition probability matrix P=(p of affine transformation v arietyij)N×N,1≤i,j≤N；
Setpoint color value matrix (cjk)N×MWith color probability matrix (qjk)N×M；
One affine transformation ω is randomly choosed according to transition probability matrix Pi(1≤i≤N), and affine transformation point ω is calculatedi
(x), x ∈ X (1≤i≤N) coordinate；
A kind of color is randomly choosed from color value matrix according to color probability matrix；
Drawn a little on the coordinate of affine transformation point is calculated using the color of selection；
Picture point is carried out according to setting iterations, exports the fractal pattern finally coloured.
2. the color rendering intent of fractal pattern according to claim 1, it is characterised in that " the setpoint color value square
Battle array and color probability matrix " includes：
Setpoint color value matrix (cjk)N×M,1≤j≤N,1≤k≤M；
Set probability-distribution function F (x) ＞ 0；
Initialize color probability matrix (qjk)N×M,1≤j≤N,1≤k≤M；
To matrix color probability matrix (qjk)N×M, 1≤j≤N, 1≤k≤M row probability distribution is normalized, and obtains face
Color probability matrix Q=(qjk)N×M,1≤j≤N,1≤k≤M。
3. the color rendering intent of fractal pattern according to claim 1, it is characterised in that also include：
From affine transformation v ariety { X；ω1,ω2,…,ωNIn select some affine transformations, decompose to obtain step by step according to conversion formula
Decompose code
The colour model of each subgraph is established according to decomposition code
According to the colour model of each subgraphLocal Subgraphs picture is exported one by one
4. the color rendering intent of fractal pattern according to claim 3, it is characterised in that the conversion formula is
5. the color rendering intent of fractal pattern according to claim 3, it is characterised in that also include：
Other Local Subgraphs pictures not decomposed are exported one by one.
6. the color rendering device of a kind of fractal pattern, it is characterised in that establish unit, coordinate calculating unit, face including model
Color selecting unit and pattern picture dot element；
The model is established unit and is used for by N number of affine transformation ω of hidden Markov chain value IFS systemsiForm affine change
Change race { X；ω1,ω2,…,ωN, and set up the transition probability matrix P=(p of affine transformation v arietyij)N×N,1≤i,j≤N；Setting
Color value matrix (cjk)N×MWith color probability matrix (qjk)N×M；
The coordinate calculating unit is used to randomly choose an affine transformation ω according to transition probability matrix Pi(1≤i≤N), and count
Calculation obtains affine transformation point ωi(x), x ∈ X (1≤i≤N) coordinate；
The color selecting unit is used to randomly choose a kind of color from color value matrix according to color probability matrix；
The pattern picture dot element is used to draw a little on the coordinate of affine transformation point is calculated using the color of selection；And according to
Setting iterations carries out picture point, exports the fractal pattern finally coloured.
7. the color rendering device of fractal pattern according to claim 6, it is characterised in that the model is established unit and also used
In：
Setpoint color value matrix (cjk)N×M,1≤j≤N,1≤k≤M；
Set probability-distribution function F (x) ＞ 0；
Initialize color probability matrix (qjk)N×M,1≤j≤N,1≤k≤M；
To matrix color probability matrix (qjk)N×M, 1≤j≤N, 1≤k≤M row probability distribution is normalized, and obtains face
Color probability matrix Q=(qjk)N×M,1≤j≤N,1≤k≤M。
8. the color rendering device of fractal pattern according to claim 6, it is characterised in that described also including resolving cell
Resolving cell is used for from affine transformation v ariety { X；ω1,ω2,…,ωNIn select some affine transformations, according to conversion formula step by step
Decomposition obtains decomposing code
The model establishes the colour model that unit is additionally operable to establish each subgraph according to decomposition code
The pattern picture dot element is additionally operable to the colour model according to each subgraph
Local Subgraphs picture is exported one by one
9. the color rendering device of fractal pattern according to claim 8, it is characterised in that the conversion formula is：
10. the color rendering device of fractal pattern according to claim 8, it is characterised in that the pattern picture dot element is also
For exporting other Local Subgraphs pictures not decomposed one by one.
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| LILIANG ZHANG: ""Generation of IFS Fractal Images Based on Hidden Markov Model "", 《TRANSACTIONS ON EDUTAINMENT VIII》 * |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| TWI717797B (en) * | 2019-08-05 | 2021-02-01 | 曹文峰 | Totem forming system, method, equipment, product and computer readable storage device |
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