CN102075664B - Method and system for constructing non-progressive screen dots - Google Patents

Method and system for constructing non-progressive screen dots Download PDF

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Publication number
CN102075664B
CN102075664B CN 200910238724 CN200910238724A CN102075664B CN 102075664 B CN102075664 B CN 102075664B CN 200910238724 CN200910238724 CN 200910238724 CN 200910238724 A CN200910238724 A CN 200910238724A CN 102075664 B CN102075664 B CN 102075664B
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progressive
site
function
lattice point
net hanging
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CN102075664A (en
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李平立
贾文华
邱翔宇
袁梦尤
龚健
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Peking University
Founder International Beijing Co Ltd
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Founder International Beijing Co Ltd
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Abstract

The invention relates to a method and system for constructing non-progressive screen dots, belonging to the field of printing and publishing. Multiple layers of annularly embedded non-progressive screen dots are generated through a defined function cluster F, a direct network-hanging method or screen dot optimizing method by using collimation errors that deep color is easy to invade light color on the vision of the human body on the basis of network hanging of the non-progressive screen dots. By adopting the method and the system disclosed by the invention, the printing effect is bright, the progressive effect is smooth and thin, and the new screen dot greatly reduces the continuous area of ink, therefore, the ink consumption is greatly lowered, the printing cost is saved and the environment is protected.

Description

A kind of method and system of constructing non-progressive site
Technical field
The invention belongs to the publication and printing field, be specifically related to a kind of method and system of constructing non-progressive site.
Background technology
Normal employing CMYK4 look chromatography in the colored printing relies on green grass or young crops, fuchsin, Huang, black 4 kinds of pigment double exposures to produce coloured image.These 4 kinds of basic colors are by presenting at most 8 kinds of colors after making up: red, green, blue, green grass or young crops, fuchsin, Huang, black, white, and the number of color that a width of cloth coloured image comprises is considerably beyond 8 kinds.Be 4 gray-scale maps with continuous tone by the Color Separation color correction being become 4 color shade figure, the image after the color separation, in the printing of 4 looks, can only use a kind of printing ink when printing, and the concentration of printing ink remain unchanged at every turn.In order when printing, to obtain continuous tone, need to carry out linked network to gray-scale map and process.Linked network also is screening, exactly the picture breakdown of continuous tone is become the process of site.Image behind the screening is with the size of site and the depth level of the actual look of density reflection image.
Based on people's visual effect, when from a close-ups image, site and space on every side thereof create the vacation picture of continuous tone, and larger site seems that secretly, less site seems bright; Dense zone, site seems that secretly sparse zone, site seems bright.
Continuous lifting along with technology such as the improvement of printing sheets evenness, paper printing ink characterization of adsorption, printing equipment precision is greatly improved to the site processing accuracy at present.The site of at present simple net form, its site is originally as solid, and the site is larger, and the ink thickness of its accumulation is higher.
Printing requires not only to provide the precision of printing to the raising of picture required precision, can reduce printing ink use amount, more environmental protection simultaneously.
In the site generation technique of mentioning in existing document or the system, technology or the method for non-progressive site do not appear constructing for progressive site.
Summary of the invention
For problems of the prior art, the purpose of this invention is to provide a kind of method and system of constructing non-progressive site by progressive site, the method and system can be on the bases of existing progressive site generation, by defined function bunch F, in its site scope, construct nested ring-type site, namely strengthening on the more bright basis of visual color, reduce the printing ink constructional surface, thus decrease ink consumption amount.
The object of the present invention is achieved like this, and a kind of method of constructing non-progressive site may further comprise the steps:
Step 1 is at first determined progressive lattice point net hanging zone, then obtains in the progressive lattice point net hanging zone gradual change ratio along progressive direction;
Step 2, whether judgement, if so, then changes step 3 over to and begin to construct non-progressive site, otherwise processing finishes greater than the threshold value of setting along progressive direction gradual change ratio;
Step 3 is constructed non-progressive site, by defined function bunch F, in the scope of progressive site, constructs nested ring-type site.
Further, in the step 3, construct non-progressive site by direct net suspension mode, concrete grammar is:
Construct non-progressive lattice point net hanging function Ψ by function bunch F and progressive lattice point net hanging function phi Φ, F(P) generate non-progressive site, described non-progressive lattice point net hanging function Ψ Φ, F(P)={ Ψ Φ, F(P) Ij, described Ψ Φ, F(P) IjBe direct linked network function, Ψ Φ, F(P) Ij=∑ K=0 N-1(1) kΦ (F k(P)) Ij, wherein, F k(P) Ij=F k(P Ij).
Perhaps, in the step 3, construct non-progressive site by the site optimal way, concrete grammar is:
At first directly generate progressive site according to progressive lattice point net hanging function phi, then generate new site according to function bunch F, and carry out the XOR stack in progressive site, to generate new non-progressive site.
Further, when carrying out the XOR stack, the zone of two images, size, gradual change direction and linked network angle are consistent.
Further, described function bunch F={F 0, F 1..., F N-1, n is the integer greater than 1, F 0, F 1..., F N-1Be the domain of definition for [0,1], codomain are the continuous function of [0,1], satisfy F 0(x) 〉=F 1(x) 〉=... 〉=F N-1And ∑ (x), K=0 N-1(1) kF k(x)=x, wherein 0≤x≤1;
Described progressive lattice point net hanging function phi is defined as follows: for certain discrete space Ω=(i, j) | 0≤i<Width, 0≤j<Height}, the gray level image space that defines on it is I G={ Ω → [0,1] }, the bianry image space is I 2={ Ω → { if 0,1}} is gray level image P, P ' ∈ I G, and for any i, there is P in j Ij≤ P ' Ij, then be defined as P≤P ', progressive lattice point net hanging function phi: I G→ I 2, satisfy Φ (P)≤Φ (P ');
Described gray level image P=∑ Ijα (P Ij), α (P Ij) be that coordinate is the brightness of the pixel of (i, j) among the gray level image P.
Further, the threshold value described in the step 2 is [α (P I ' j ')-α (P Ij)]/α (P I ' j '), it is worth more than or equal to 25%, less than or equal to 1, wherein, P I ' j' be high-high brightness pixel among the gray level image P, P IjBe least bright pixels point among the gray level image P.
Further, function bunch F supports recursive call, namely generate once new site on basis, progressive site, foundation once new site generates the secondary site again, so until the site printing ink that function bunch F generates stop than surpassing limit value, then oppositely the XOR stack generates non-progressive site, i.e. secondary site and a site XOR, and a final site and progressive site XOR generate non-progressive site.
A kind of system that constructs non-progressive site comprises with lower module:
Progressive site constructing module be used for to be determined progressive lattice point net hanging zone, then obtains in the progressive lattice point net hanging zone gradual change ratio along progressive direction;
The threshold decision module, be used for to judge gradual change along progressive direction than whether greater than the threshold value of setting;
Non-progressive site constructing module is used for constructing non-progressive site in gradual change than greater than the threshold value set the time, by defined function bunch F, in the scope of progressive site, constructs nested ring-type site.
Effect of the present invention is: the present invention carries out linked network by defined function bunch F, perhaps progressive site is optimized, and generates the new nested site of annular multilayer, and new site has following significant effect:
1) show money or valuables one carries unintentionally by increasing in the site, strengthened the vivid effect of picture, and image is finer and smoother level and smooth;
2) new dot shape has reduced continuous area, and the use amount to printing ink in concrete printing reduces;
3) site ring-type interval region can be adjusted flexibly according to characteristics such as printing ink and paper in new site, can extensively adapt to the demand of multiple paper and printing ink.
Why the present invention has above-mentioned remarkable result, its reason is: the present invention only processes the processing that has increased function bunch F to original linked network, processing mode is simple, do not affect the settings such as net form in processing of original linked network, net angle, be easy to original linked network is processed the improvement of upgrading, should use very simple.And above-mentioned function bunch F is the processing function through a large amount of practice test accumulation, can effectively strengthen the vivid effect of picture, and image is finer and smoother level and smooth, and printing ink saving amount is remarkable.Along with printing more high accuracy, the demand for development such as environmental protection more, this technology will become the main flow site constructing technology in the following printing to the transformation of original screening technology.
Description of drawings
Fig. 1 is the method flow schematic diagram of the non-progressive site of structure in the embodiment of the invention;
Fig. 2 is circular shaped lattice point size and ink thickness contrast schematic diagram;
Fig. 3 is continuous-tone image;
Fig. 4 is image after the pure cylinder point linked network;
Fig. 5 is image after the circular ring net dot image linked network.
Embodiment
The invention will be further described below in conjunction with specification drawings and specific embodiments.
A kind of system that constructs non-progressive site comprises with lower module:
Progressive site constructing module be used for to be determined progressive lattice point net hanging zone, then obtains in the progressive lattice point net hanging zone gradual change ratio along progressive direction;
The threshold decision module, be used for to judge gradual change along progressive direction than whether greater than the threshold value of setting;
Non-progressive site constructing module is used for constructing non-progressive site than greater than the threshold value set the time in gradual change.
In the present embodiment, also be provided with following submodule in the constructing module of described non-progressive site:
Construct the submodule of non-progressive site by direct net suspension mode, concrete grammar is: construct non-progressive lattice point net hanging function Ψ by function bunch F and progressive lattice point net hanging function phi Φ, F(P) generate non-progressive site, described non-progressive lattice point net hanging function Ψ Φ, F(P)={ Ψ Φ, F(P) Ij, described Ψ Φ, F(P) IjBe direct linked network function, Ψ Φ, F(P) Ij=∑ K=0 N-1(1) kΦ (F k(P)) Ij, wherein, F k(P) Ij=F k(P Ij);
Construct the submodule of non-progressive site by the site optimal way, concrete grammar is: at first directly generate progressive site according to progressive lattice point net hanging function phi, then generate new site according to function bunch F, and carry out the XOR stack in progressive site, to generate new non-progressive site.
Embodiment one:
Present embodiment illustrates than the circular shaped lattice point as 100% to generate gradual change, and its flow process is according to shown in Figure 1, and a kind of method of constructing non-progressive site may further comprise the steps:
At first determine progressive lattice point net hanging zone (step S11), obtain that the gradual change ratio along progressive direction is 100% in the progressive lattice point net hanging zone, wherein said gradual change ratio along progressive direction refers to along ratio minimum on the progressive direction and that maximum printing ink compares, wherein said printing ink is than namely with the percentage of region, site inked areas and white space, gradual change is specifically more different with paper because of printing ink than size, generally according to printing parameters such as printing ink and paper empirical value is set in the practice, be generally more than or equal to 25%, less than or equal to 1.
Step S12 judges that gradual change than whether greater than threshold value, if so, then meets the structural environment that carries out non-gradual change site.In general, described threshold value is [α (P I ' j ')-α (P Ij)]/α (P I ' j '), it is worth more than or equal to 25%, less than or equal to 1, wherein, P I ' j 'Be high-high brightness pixel among the gray level image P, P IjBe least bright pixels point among the gray level image P.
In the present embodiment, gradual change in the progressive lattice point net hanging zone is than the threshold value 25% greater than setting, printing effect after the gradual change is as shown in Fig. 3, be that printing ink is deceived to the complete of the right in vain from the complete of regional left side, judge to satisfy construct the condition of non-gradual change site by the gradual change site after, then begin to construct non-progressive site.
Subsequent is the generating mode (step S13) of selecting non-progressive site.
Generate if non-progressive site generating mode is set is direct linked network, then according to step S14, direct linked network, method is as follows:
Method according to direct net suspension mode generates non-progressive site, and namely functional module is according to generate non-progressive site such as minor function:
Construct non-progressive lattice point net hanging function Ψ by function bunch F and progressive lattice point net hanging function phi Φ, F(P) generate the site, wherein, progressive lattice point net hanging function phi, refer to for certain discrete space Ω=(i, j) | 0≤i<Width, 0≤j<Height}, the gray level image space that defines on it is I G={ Ω → [0,1] }, the bianry image space is I 2={ Ω → { if 0,1}} is gray level image P, P ' ∈ I G, and for any i, there is P in j Ij≤ P ' Ij, then be defined as P≤P ', progressive linked network mapping function Φ: I G→ I 2, satisfy Φ (P)≤Φ (P ');
Wherein, described function bunch F={F 0, F 1..., F N-1, n is the integer greater than 1, F 0, F 1..., F N-1Be the domain of definition for [0,1], codomain are the continuous function of [0,1], satisfy F 0(x) 〉=F 1(x) 〉=... 〉=F N-1And ∑ (x), K=0 N-1(1) kF k(x)=x, wherein 0≤x≤1;
Described gray level image P=∑ Ijα (P Ij), α (P Ij) be that coordinate is the brightness of the pixel of (i, j) among the gray level image P.
A described function bunch F is defined as follows:
1) F={F 0, F 1, F 2, wherein
F 0 ( x ) = 2 x , if 0 ≤ x ≤ 1 2 1 , if 1 2 ≤ x ≤ 1
F 1(x)=x
F 2 ( x ) = 0 , if 0 ≤ x ≤ 1 2 2 x - 1 , if 1 2 ≤ x ≤ 1
2) F={F 0, F 1, F 2, wherein
F 0 ( x ) = x , if 0 ≤ x ≤ 1 4 3 x - 1 2 , if 1 4 ≤ x ≤ 1 2 1 , if 1 2 ≤ x ≤ 1
F 1 ( x ) = 0 , if 0 ≤ x ≤ 1 4 2 x - 1 2 , if 1 4 ≤ x ≤ 3 4 1 , if 3 4 ≤ x ≤ 1
F 2 ( x ) = 0 , if 0 ≤ x ≤ 1 2 3 x - 3 2 , if 1 2 ≤ x ≤ 3 4 x , if 3 4 ≤ x ≤ 1
3) F={F 0, F 1, wherein
F 0 ( x ) = 3 2 x , if 0 ≤ x ≤ 1 2 1 2 + 1 2 x , if 1 2 ≤ x ≤ 1
F 1 ( x ) = 1 2 x , if 0 ≤ x ≤ 1 2 1 2 - 1 2 x , if 1 2 ≤ x ≤ 1
4) F={F 0, F 1, wherein
F 0(x)=2x-x 2
F 1(x)=x-x 2
Namely generated new non-progressive site, as shown in Figure 5.And original progressive site is as shown in Figure 4, and contrast can find, progressive site is to generate in the process of non-progressive site, and function bunch F carries out disturbance to it so that each site forms concentric annular structure, its ring-type bandwidth according to printing ink than different.
Embodiment two:
Other are identical with embodiment one, and difference is: the threshold value of setting in the step 2 is 60%; In the step 3, if it is the site optimal way that non-progressive site generating mode is set, then according to step S15, at first generate progressive site, as shown in Fig. 4, then generate new site (step S16) according to function identical in above-described embodiment one bunch F, and carry out the XOR stack in the progressive site that Fig. 4 generates, to generate new non-progressive site (step S14).
In the present embodiment, function bunch F supports recursive call, namely generate once new site on basis, progressive site, foundation once new site generates the secondary site again, so until the site printing ink that function bunch F generates stop than surpassing limit value, then oppositely the XOR stack generates non-progressive site, i.e. secondary site and a site XOR, and a final site and progressive site XOR generate non-progressive site.
In the present embodiment, site printing ink is 20% to 80% than the limit value that arranges, and then generates once new site on basis, progressive site, again generates the secondary site according to a site and judges site printing ink than surpassing above-mentioned interval, then the new site of generating function bunch F no longer.Site bianry image and the stack of progressive site bianry image XOR finally generate non-progressive site as shown in Figure 5.
The method for dot shape without specific limited, but for non-circular, such as linked network sites such as rhombus, triangles, understand easily, according to the method for present embodiment, need to guarantee that zone, size, the gradual change direction of two images are consistent with the linked network angle during the stack of binary picture XOR.
In above-described embodiment, site printing ink is namely set the setting on the border of the non-progressive site of structure than limit value according to empirical value, and its concrete numerical value is different with paper because of printing ink, and operated by rotary motion is between 5% to 95%.
Can find out by above-described embodiment, the present invention is by proposing a kind of function bunch F computational methods of simplification, realized that improvement on progressive linked network algorithm is to generate non-progressive linked network, also can be optimized progressive site by the method, by generating the nested dot shape of annular multilayer, as shown in Fig. 2, this non-progressive site, take full advantage of the dark collimation error of invading easily light color on the human visual, have following significant effect:
1) printing effect is beautiful, and fade effect is fine and smooth level and smooth;
2) new site tubular shape has reduced the continuous area of printing ink, and the use amount to printing ink in concrete printing reduces, and has shown among Fig. 2 that it saves principle and the effect of printing ink;
3) site ring-type interval region can be adjusted flexibly according to characteristics such as printing ink and paper in new site, adapts to the requirement of multiple paper and printing ink.
Method of the present invention is not limited to the embodiment described in the embodiment, those skilled in the art's technical scheme according to the present invention draws other execution mode, such as, by setting computation rule, the mode of structure printing ink point ring-type is to reduce the printing ink use amount, and the method for improving picture brightness, belong to equally technological innovation scope of the present invention.

Claims (9)

  1. One kind the structure non-progressive site method, may further comprise the steps:
    Step 1 is at first determined progressive lattice point net hanging zone, then obtains in the progressive lattice point net hanging zone gradual change ratio along progressive direction;
    Step 2, judge gradual change along progressive direction than whether greater than the threshold value of setting, if so, then changes step 3 over to and begin to construct non-progressive site, otherwise processing finishes;
    Step 3 is constructed non-progressive site, by defined function bunch F, in the scope of progressive site, constructs nested ring-type site.
  2. 2. a kind of method of constructing non-progressive site as claimed in claim 1 is characterized in that, in the step 3, constructs non-progressive site by direct net suspension mode, and concrete grammar is:
    Construct non-progressive lattice point net hanging function Ψ by function bunch F and progressive lattice point net hanging function phi Φ, F(P) generate non-progressive site, described non-progressive lattice point net hanging function Ψ Φ, F(P)={ Ψ Φ, F(P) Ij, described Ψ Φ, F(P) IjBe direct linked network function, Ψ Φ, F(P) Ij=∑ K=0 N-1(1) kΦ (F k(P)) Ij, wherein, F k(P) Ij=F k(P Ij);
    Described function bunch F={F 0, F 1..., F N-1, n is the integer greater than 1, F 0, F 1..., F N-1Be the domain of definition for [0,1], codomain are the continuous function of [0,1], satisfy F 0(x) 〉=F 1(x) 〉=... 〉=F N-1And ∑ (x), K=0 N-1(1) kF k(x)=x, wherein 0≤x≤1; Described progressive lattice point net hanging function phi is defined as follows: for certain discrete space Ω=(i, j) | 0≤i<Width, 0≤j<Height}, the gray level image space that defines on it is I G={ Ω → [0,1] }, the bianry image space is I 2={ Ω → { if 0,1}} is gray level image P, P ' ∈ I G, and for any i, there is P in j Ij≤ P ' Ij, then be defined as P≤P ', progressive lattice point net hanging function phi: I G→ I 2, satisfy Φ (P)≤Φ (P '), described gray level image P=∑ Ijα (P Ij), α (P Ij) be that coordinate is the brightness of the pixel of (i, j) among the gray level image P.
  3. 3. a kind of method of constructing non-progressive site as claimed in claim 1 is characterized in that, in the step 3, constructs non-progressive site by the site optimal way, and concrete grammar is:
    At first directly generate progressive site according to progressive lattice point net hanging function phi, then generate new site according to function bunch F, and carry out the XOR stack in progressive site, to generate new non-progressive site;
    Described function bunch F={F 0, F 1..., F N-1, n is the integer greater than 1, F 0, F 1..., F N-1Be the domain of definition for [0,1], codomain are the continuous function of [0,1], satisfy F 0(x) 〉=F 1(x) 〉=... 〉=F N-1And ∑ (x), K=0 N-1(1) kF k(x)=x, wherein 0≤x≤1; Described progressive lattice point net hanging function phi is defined as follows: for certain discrete space Ω=(i, j) | 0≤i<Width, 0≤j<Height}, the gray level image space that defines on it is I G={ Ω → [0,1] }, the bianry image space is I 2={ Ω → { if 0,1}} is gray level image P, P ' ∈ I G, and for any i, there is P in j Ij≤ P ' Ij, then be defined as P≤P ', progressive lattice point net hanging function phi: I G→ I 2, satisfy Φ (P)≤Φ (P '), described gray level image P=∑ Ijα (P Ij), α (P Ij) be that coordinate is the brightness of the pixel of (i, j) among the gray level image P.
  4. 4. a kind of method of constructing non-progressive site as claimed in claim 2 or claim 3, it is characterized in that: the threshold value described in the step 2 is [α (P I ' j ')-α (P Ij)]/α (P I ' j '), it is worth more than or equal to 25%, less than or equal to 1, wherein, P I ' j 'Be high-high brightness pixel among the gray level image P, P IjBe least bright pixels point among the gray level image P.
  5. 5. such as a kind of method of constructing non-progressive site as described in claim 2 or 3, it is characterized in that: a described function bunch F is defined as follows:
    1) F={F 0, F 1, F 2, wherein
    F 0 ( x ) = 2 x , if 0 ≤ x ≤ 1 2 1 , if 1 2 ≤ x ≤ 1
    F 1(x)=x
    F 2 ( x ) = 0 , if 0 ≤ x ≤ 1 2 2 x - 1 , if 1 2 ≤ x ≤ 1
    2) F={F 0, F 1, F 2, wherein
    F 0 ( x ) = x , if 0 ≤ x ≤ 1 4 3 x - 1 2 , if 1 4 ≤ x ≤ 1 2 1 , if 1 2 ≤ x ≤ 1
    F 1 ( x ) = 0 , if 0 ≤ x ≤ 1 4 2 x - 1 2 , if 1 4 ≤ x ≤ 3 4 1 , if 3 4 ≤ x ≤ 1
    F 2 ( x ) = 0 , if 0 ≤ x ≤ 1 2 3 x - 3 2 , if 1 2 ≤ x ≤ 3 4 x , if 3 4 ≤ x ≤ 1
    3) F={F 0, F 1, wherein
    F 0 ( x ) = 3 2 x , if 0 ≤ x ≤ 1 2 1 2 + 1 2 x , if 1 2 ≤ x ≤ 1
    F 1 ( x ) = 1 2 x , if 0 ≤ x ≤ 1 2 1 2 - 1 2 x , if 1 2 ≤ x ≤ 1
    4) F={F 0, F 1, wherein
    F 0(x)=2x-x 2
    F 1(x)=x-x 2
  6. 6. a kind of method of constructing non-progressive site as claimed in claim 3 is characterized in that: when carrying out the XOR stack, the zone of two images, size, gradual change direction and linked network angle are consistent.
  7. 7. a kind of method of constructing non-progressive site as claimed in claim 3, it is characterized in that: described function bunch F supports recursive call, namely generate once new site on basis, progressive site, foundation once new site generates the secondary site again, so until the site printing ink that function bunch F generates stop than surpassing limit value, then oppositely the XOR stack generates non-progressive site, i.e. secondary site and a site XOR, and a final site and progressive site XOR generate non-progressive site.
  8. One kind the structure non-progressive site system, comprise with lower module:
    Progressive site constructing module be used for to be determined progressive lattice point net hanging zone, then obtains in the progressive lattice point net hanging zone gradual change ratio along progressive direction;
    The threshold decision module, be used for to judge gradual change along progressive direction than whether greater than the threshold value of setting;
    Non-progressive site constructing module is used for constructing non-progressive site in gradual change than greater than the threshold value set the time, by defined function bunch F, in the scope of progressive site, constructs nested ring-type site.
  9. 9. a kind of system that constructs non-progressive site as claimed in claim 8 is characterized in that, also is provided with following submodule in the constructing module of described non-progressive site:
    Construct the submodule of non-progressive site by direct net suspension mode, concrete grammar is: construct non-progressive lattice point net hanging function Ψ by function bunch F and progressive lattice point net hanging function phi Φ, F(P) generate non-progressive site, described non-progressive lattice point net hanging function Ψ Φ, F(P)={ Ψ Φ, F(P) Ij, described Ψ Φ, F(P) IjBe direct linked network function, Ψ Φ, F(P) IjK=0 N-1(1) kΦ (F k(P)) IjWherein, F k(P) Ij=F k(P Ij);
    Construct the submodule of non-progressive site by the site optimal way, concrete grammar is: at first directly generate progressive site according to progressive lattice point net hanging function phi, then generate new site according to function bunch F, and carry out the XOR stack in progressive site, to generate new non-progressive site;
    Described function bunch F={F 0, F 1..., F N-1, n is the integer greater than 1, F 0, F 1..., F N-1Be the domain of definition for [0,1], codomain are the continuous function of [0,1], satisfy F 0(x) 〉=F 1(x) 〉=... 〉=F N-1And ∑ (x), K=0 N-1(1) kF k(x)=x, wherein 0≤x≤1; Described progressive lattice point net hanging function phi is defined as follows: for certain discrete space Ω=(i, j) | 0≤i<Width, 0≤j<Height}, the gray level image space that defines on it is I G={ Ω → [0,1] }, the bianry image space is I 2={ Ω → { if 0,1}} is gray level image P, P ' ∈ I G, and for any i, there is P in j Ij≤ P ' Ij, then be defined as P≤P ', progressive lattice point net hanging function phi: I G→ I 2, satisfy Φ (P)≤Φ (P '), described gray level image P=∑ Ijα (P Ij), α (P Ij) be that coordinate is the brightness of the pixel of (i, j) among the gray level image P.
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