CN108009980A - A kind of more sparse dictionary gray-scale map colorization methods of feature based classification details enhancing - Google Patents
A kind of more sparse dictionary gray-scale map colorization methods of feature based classification details enhancing Download PDFInfo
- Publication number
- CN108009980A CN108009980A CN201710606589.3A CN201710606589A CN108009980A CN 108009980 A CN108009980 A CN 108009980A CN 201710606589 A CN201710606589 A CN 201710606589A CN 108009980 A CN108009980 A CN 108009980A
- Authority
- CN
- China
- Prior art keywords
- colorization
- image
- gray
- classification
- feature
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000000034 method Methods 0.000 title claims abstract description 31
- 230000002708 enhancing effect Effects 0.000 title claims abstract description 21
- 239000011159 matrix material Substances 0.000 claims description 10
- 238000012549 training Methods 0.000 claims description 10
- 238000005457 optimization Methods 0.000 claims description 6
- 235000013399 edible fruits Nutrition 0.000 claims description 4
- 230000000694 effects Effects 0.000 abstract description 13
- 230000004927 fusion Effects 0.000 abstract description 2
- 230000000007 visual effect Effects 0.000 abstract description 2
- 230000005540 biological transmission Effects 0.000 abstract 1
- 238000010586 diagram Methods 0.000 description 3
- 238000005070 sampling Methods 0.000 description 3
- PCHJSUWPFVWCPO-UHFFFAOYSA-N gold Chemical compound [Au] PCHJSUWPFVWCPO-UHFFFAOYSA-N 0.000 description 2
- 239000010931 gold Substances 0.000 description 2
- 229910052737 gold Inorganic materials 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000004364 calculation method Methods 0.000 description 1
- 230000007812 deficiency Effects 0.000 description 1
- 238000002156 mixing Methods 0.000 description 1
- 238000002360 preparation method Methods 0.000 description 1
- 238000000926 separation method Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T3/00—Geometric image transformations in the plane of the image
- G06T3/04—Context-preserving transformations, e.g. by using an importance map
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T5/00—Image enhancement or restoration
- G06T5/73—Deblurring; Sharpening
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/10—Image acquisition modality
- G06T2207/10024—Color image
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/20—Special algorithmic details
- G06T2207/20016—Hierarchical, coarse-to-fine, multiscale or multiresolution image processing; Pyramid transform
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/20—Special algorithmic details
- G06T2207/20081—Training; Learning
Landscapes
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- Theoretical Computer Science (AREA)
- Image Analysis (AREA)
- Image Processing (AREA)
Abstract
The invention discloses a kind of more sparse dictionary gray-scale map colorization methods of feature based classification details enhancing, tagsort and more sparse dictionaries are combined first, colorization processing model is established, realizes the colorization to gray level image；Again, for classification inaccuracy the problem of, propose corresponding local restriction algorithm, improve classification accuracy, further lift colorization effect；Finally for rarefaction representation intrinsic loss in detail the problem of, based on laplacian pyramid, propose detail enhancement algorithms, effectively solving the problems, such as loss in detail at the same time, improving the speed of image colorization.The present invention achieves the strong gray level image colorization effect of the visual custom for meeting people, natural sense, and applies also for other field, the color transmission between the colorization of such as grayscale fusion image and infrared image, coloured image.
Description
Technical field
The invention belongs to gray level image colorization processing technology field, is related to a kind of the more of feature based classification details enhancing
Sparse dictionary gray-scale map colorization method.
Background technology
At this stage, no manual intervention's algorithm of the colorization processing based on rarefaction representation is broadly divided into based on single dictionary
Colorization processing handles two kinds with the colorization based on more dictionaries, wherein, traditional colorization algorithm based on single dictionary is only
Preferable effect can be obtained on the single image of tone, the image enriched for color content, it may appear that substantial amounts of to colour by mistake
Point.To solve the problems, such as this, Uruma K etc. propose improved sparse optimization algorithm, achieve relatively good as a result, but colorization
Still there are more mistake colored spots for effect；Liang Hai etc. proposes the colorization algorithm based on classifying dictionary and rarefaction representation, should
Algorithm is basic herein by training classifying dictionary with being formed based on the dictionary pattern matching that reconstruction error minimizes and colorization two parts
On, Liang Hai etc. so that propose based on joint dictionary and rarefaction representation image colorization algorithm, both algorithms realize more
The colorization of content objective gray level image, and innovatory algorithm effect is preferable, and still, both algorithms are dilute without solving to pass through
The problem of dictionary carries out details missing, the edge blurry that colorization is brought is dredged, also, for coloury image, is still deposited
In more mistake colored spots.
Therefore, it is necessary to a kind of new more sparse dictionary gray-scale map colorization methods to solve the above problems.
The content of the invention
In view of the deficiencies of the prior art, the present invention provides a kind of more sparse dictionaries ash of feature based classification details enhancing
Spend figure colorization method.
To achieve the above object, the present invention provides following technical solution：
A kind of more sparse dictionary gray-scale map colorization methods of feature based classification details enhancing, comprise the following steps：
1), classified according to similar reference image block to target gray image block, obtain point of target gray image block
Class result；
2) processing, is optimized to the classification results of step 1), using the colorization algorithm of single dictionary to gray level image
Carry out colorization processing；
3) details enhancing processing, is carried out to the colorization result of step 2) with laplacian pyramid.
Further, target gray image block classify according to similar reference image block in step 1), it is following to include
Step：
First, the selection coloured image similar to target gray image, which is used as, refers to image, and carries out piecemeal to reference picture
Processing, calculates " brightness-feature " information of each reference image block；
2nd, corresponding " brightness-feature-color " the sparse dictionary collection of each reference picture is gone out with KSVD Algorithm for Training,
And utilize libSVM classifier trainings " brightness-feature " model；
3rd, piecemeal processing is carried out to target gray image, calculates " brightness-feature " information of target gray image block, and
Classified using " brightness-feature " model to target gray image block, obtain the corresponding classification of each target gray image block
As a result.
Further, processing is optimized to the classification results of step 1) in step 2), comprised the following steps：
A, according to the classification results of target gray image block, foundation and the one-to-one two-dimensional matrix of gray level image block, and
The value of two-dimensional matrix is used as using classification results；
B, according to the consistent principle of feature of local area image, with the rectangle frame traversal two-dimensional matrix of N × N
Whole region, and the most value of classification results value as rectangular area central value, realizes the optimization of classification results using in rectangle frame.
It is proposed the algorithm based on local restriction, improve classification accuracy, further lift colorization effect.
Further, colorization processing bag carries out gray level image using the colorization algorithm of single dictionary in step 2)
Include following steps：
C, according to obtained classification results, corresponding sparse dictionary is obtained, and use single sparse dictionary colorization method
Colorization processing is carried out to each gray-like image picture block, obtains the colorization result of whole gray level image.
Further, carrying out details enhancing processing in step 3) to colorization result with laplacian pyramid includes
Following steps：
A1, obtain Laplacian-pyramid image to target gray image progress Laplacian pyramid；
If b1, target gray image are bottom images, directly by R, G, B triple channel component point of colorization result
Do not want to add with Laplacian-pyramid image bottom image, obtain final colorization result；If target gray image is
The top image of pyramid diagram picture, by R, G, B triple channel component of colorization result respectively with Laplacian-pyramid image
Top image addition, and next tomographic image is obtained with gaussian pyramid, repeat the above steps, until obtaining bottom figure
Picture, obtains final colorization result.
Details enhancing is carried out to colorization result using laplacian pyramid effectively to solve to consolidate based on rarefaction representation algorithm
Some loss in detail problems, and improve image colorization speed.
Inventive principle：More sparse dictionary gray-scale map colorization methods of feature based classification details enhancing of the present invention first will
Tagsort and more sparse dictionaries are combined, and are established colorization processing model, are realized the colorization to gray level image；Again, pin
The problem of inaccurate to classification, propose corresponding local restriction algorithm, improve classification accuracy, further lift colorization effect
Fruit；Finally for rarefaction representation intrinsic loss in detail the problem of, based on laplacian pyramid, propose that details enhancing is calculated
Method, is effectively solving the problems, such as loss in detail at the same time, is improving the speed of image colorization, it is final to obtain gray level image colorization
As a result.
Beneficial effect：More sparse dictionary gray-scale map colorization methods of the feature based classification details enhancing of the present invention can be real
The now colorization of more content images, effect meet the visual observation custom of people, and natural sense is strong.It is proposed the calculation based on local restriction
Method, improves classification accuracy, further lifts colorization effect.Effectively solve to lose based on the intrinsic details of rarefaction representation algorithm
Mistake problem, and improve image colorization speed.
Brief description of the drawings
Fig. 1 is the method for the present invention schematic diagram；
Fig. 2 is the two-dimensional matrix structure figure of the method for the present invention step 2；
Fig. 3 is the method for the present invention and beam sea algorithm effect comparison diagram；
Fig. 4 is application effect figure of the method for the present invention in blending image colorization field；
Fig. 5 is application effect figure of the method for the present invention in infrared image colorization field；
Fig. 6 is the application effect figure that the method for the present invention color between coloured image transmits field.
Embodiment
Below in conjunction with the attached drawing in the embodiment of the present invention, the technical solution in the embodiment of the present invention is carried out clear, complete
Site preparation describes, it is clear that described embodiment is only part of the embodiment of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, those of ordinary skill in the art are obtained every other without making creative work
Embodiment, belongs to the scope of protection of the invention.
Please refer to Fig.1 with shown in Fig. 2, more sparse dictionary gray-scale maps of feature based proposed by the present invention classification details enhancing
The step of colorization method, is as follows：
Step 1：The colorization of the more sparse dictionaries of feature based classification
Tagsort and more sparse dictionaries are combined by the present invention, are established colorization processing model, are realized to gray level image
Colorization, detailed process is described as follows：
1st, the selection coloured image similar to target gray image, which is used as, refers to image, and reference picture is carried out at piecemeal
Reason, calculates " brightness --- feature " information of each reference image block, and with libSVM classifier trainings " brightness --- spy
Sign " model；Then, with sparse dictionary collection of the KSVD Algorithm for Training using reference image block as classification, the side of training sparse dictionary
Formula is identical with the training method of the color reference figure of single dictionary, i.e. training is sparse with " brightness --- feature --- color "
Wordbook, as shown in formula (1), wherein, under be designated as gray and represent dictionary luminance part, subscript f represents dictionary characteristic, subscript
Dictionary chrominance section is represented, such as formula (2)：
D=[dictionary1, dictionary2dictionaryn]T=[Dgray,Df,Dc]T (1)
2nd, assume that target gray image is divided into m blocks altogether, such as formula (3), the present invention is according to the " bright of each gray level image block
Degree --- feature " information, with reference to described " brightness --- the feature " model, each image block pair is asked for libSVM graders
The classification answered, it is assumed that the classification results of target gray image block such as formula (4)：
Blockgray=[block1gray,block2gray,···,blockmgray] (3)
Category=[category1, category1, categoryn] (4)
3rd, the target gray image block for belonging to the i-th class is set as Blockgray[index (i)], index (i), which is represented, belongs to i-th
Row belonging to the target gray image block of class, remaining row are set to 0, and corresponding dictionary is D (i), then its sparse coefficient S'(i) can be by
Formula (5) is tried to achieve：
Blockgray[index (i)]=Dgray(i)×S'(i) (5)
Therefore, belonging to the colorization of the target gray image block of the i-th class can be expressed as：
Blockc[index (i)]=Dc(i)×S'(i) (6)
The rest may be inferred, and the colorization of whole gray level image piecemeal can be expressed as：
Step 2：Classification results optimization based on local restriction
The target gray image block with libSVM when being classified, for similar in content complexity and texture
Image, occurs the point of indivedual misclassifications once in a while, and then colorization map picture can be caused to there are colored spots by mistake, therefore, base of the present invention
In local restriction, classification results are optimized with processing, detailed process is described as follows：
1st, the corresponding classification results of each gray level image block that the present invention is divided into according to target gray image, build Two-Dimensional Moment
Battle array, and using classification results as two-dimensional matrix in be worth accordingly, as shown in Figure 2.
2nd, according in certain area, the consistent principle of feature of image, in the field of image, it, which is classified, ties
Fruit should be consistent.Digitized representation classification results in Fig. 2, selection area Ω, if the label value at region Ω centers is F, area size
For N × N, region Ω classification results values matrix is M, such as formula (8)：
In above formula, t takes interior all classification results values successively, g (t) represent in the corresponding numbers of classification results value t, F
Value can be corrected by formula (9)：
F=max (g (t)) t ∈ M (9)
Whole two-dimensional matrix is traveled through with the rectangle frame (region Ω) of N × N, according in formula (8) and formula (9) correction rectangular area
Center value, you can to realize the optimization of classification results.
Step 3：Details enhancing based on laplacian pyramid
Classification results optimization based on local restriction can solve to colour by mistake caused by classification error, can not but solve to take
The problem of loss of length and the details brought by sparse representation theory.Therefore, the present invention is carried based on laplacian pyramid
Detail enhancement algorithms are gone out, detailed process is described as follows：.
If original image is I, the gaussian pyramid bottom is G0, and convolution is carried out to it using Gaussian kernel, then to convolution after
Image carry out down-sampling obtain last layer image G1, and so on, gaussian pyramid can be represented by (10), Laplce's gold word
Tower image can be represented by formula (11)：
Li=Gi-upsample(Gi+1) (11)
The present invention carries out Laplacian pyramid to target gray image first and obtains corresponding Laplce's gold word
Tower image Li_grayIf colorization result figure is I, the separation of R, G, B triple channel is carried out to I, obtains IR, IG, IBTriple channel image, so
Triple channel image is added with corresponding Laplacian-pyramid image afterwards to obtain enhanced triple channel image Ii_R, Ii_G,
Ii_BIf colorization result figure is top, need to carry out convolution up-sampling to triple channel image, such as formula (12), so as to obtain
Final colorization map picture；If colorization result figure and target gray figure are same layer, i.e., colorization result figure is the bottom
Image, then carry out convolution up-sampling, such as formula (13), you can obtain final colorization map picture without triple channel image：
I0_j=L0_gray+IjJ=R, G, B (13)
In order to illustrate advantage of the present invention in terms of gray level image colorization, the present invention is with the method for the present invention to gray-scale map
As carrying out colorization processing, and compared with the algorithm of beam sea, illustrate the validity of the method for the present invention, as shown in Figure 3.Except this it
Outside, the present invention respectively the colorization to grayscale fusion image and infrared image, color between coloured image transmit three fields into
Row color processing, respectively as shown in Figure 4,5, 6, illustrates inventive algorithm in multi-field applicability.
Claims (5)
- A kind of 1. more sparse dictionary gray-scale map colorization methods of feature based classification details enhancing, it is characterised in that：Including with Lower step：1), classified according to similar reference image block to target gray image block, obtain the classification knot of target gray image block Fruit；2) processing, is optimized to the classification results of step 1), gray level image is carried out using the colorization algorithm of single dictionary Colorization processing；3) details enhancing processing, is carried out to the colorization result of step 2) with laplacian pyramid.
- 2. more sparse dictionary gray-scale map colorization methods of feature based classification details enhancing according to claim 1, its It is characterized in that：Classification is carried out in step 1) to target gray image block according to similar reference image block to comprise the following steps：First, the selection coloured image similar to target gray image, which is used as, refers to image, and carries out piecemeal processing to reference picture, Calculate " brightness-feature " information of each reference image block；2nd, corresponding " brightness-feature-color " the sparse dictionary collection of each reference picture, and profit are gone out with KSVD Algorithm for Training With libSVM classifier trainings " brightness-feature " model；3rd, piecemeal processing is carried out to target gray image, calculates " brightness-feature " information of target gray image block, and utilized " brightness-feature " model classifies target gray image block, obtains the corresponding classification knot of each target gray image block Fruit.
- 3. more sparse dictionary gray-scale map colorization methods of feature based classification details enhancing according to claim 1, its It is characterized in that：Processing is optimized to the classification results of step 1) in step 2), is comprised the following steps：A, according to the classification results of target gray image block, foundation and the one-to-one two-dimensional matrix of gray level image block, and to divide Value of the class result as two-dimensional matrix；B, according to the consistent principle of feature of local area image, with the whole of the rectangle frame traversal two-dimensional matrix of N × N Region, and the most value of classification results value as rectangular area central value, realizes the optimization of classification results using in rectangle frame.
- 4. more sparse dictionary gray-scale map colorization methods of feature based classification details enhancing according to claim 1, its It is characterized in that：Colorization processing is carried out to gray level image using the colorization algorithm of single dictionary in step 2) includes following step Suddenly：C, according to obtained classification results, corresponding sparse dictionary is obtained, and using single sparse dictionary colorization method to every A kind of gray level image block carries out colorization processing, obtains the colorization result of whole gray level image.
- 5. more sparse dictionary gray-scale map colorization methods of feature based classification details enhancing according to claim 1, its It is characterized in that：Details enhancing processing is carried out to colorization result in step 3) with laplacian pyramid to comprise the following steps：A1, obtain Laplacian-pyramid image to target gray image progress Laplacian pyramid；If b1, target gray image are bottom images, directly by R, G, B triple channel component of colorization result respectively with Laplacian-pyramid image bottom image is wanted to add, and obtains final colorization result；If target gray image is golden word The top image of tower image, R, G, B triple channel component of colorization result are most pushed up with Laplacian-pyramid image respectively Tomographic image is added, and obtains next tomographic image with gaussian pyramid, is repeated the above steps, until obtaining bottom image, is obtained Take final colorization result.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710606589.3A CN108009980B (en) | 2017-07-24 | 2017-07-24 | Multi-sparse dictionary gray level map colorization method based on feature classification detail enhancement |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710606589.3A CN108009980B (en) | 2017-07-24 | 2017-07-24 | Multi-sparse dictionary gray level map colorization method based on feature classification detail enhancement |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN108009980A true CN108009980A (en) | 2018-05-08 |
| CN108009980B CN108009980B (en) | 2024-03-26 |
Family
ID=62047657
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710606589.3A Active CN108009980B (en) | 2017-07-24 | 2017-07-24 | Multi-sparse dictionary gray level map colorization method based on feature classification detail enhancement |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN108009980B (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114648531A (en) * | 2022-05-20 | 2022-06-21 | 领伟创新智能系统(浙江)有限公司 | Solar panel surface dust identification method based on color channel brightness distribution |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102779351A (en) * | 2012-06-08 | 2012-11-14 | 温州大学 | Interactive grayscale image colorizing method based on local linear model optimization |
| US20140072209A1 (en) * | 2012-09-13 | 2014-03-13 | Los Alamos National Security, Llc | Image fusion using sparse overcomplete feature dictionaries |
| CN106971379A (en) * | 2017-03-02 | 2017-07-21 | 天津大学 | A kind of underwater picture Enhancement Method merged based on stratified calculation |
-
2017
- 2017-07-24 CN CN201710606589.3A patent/CN108009980B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102779351A (en) * | 2012-06-08 | 2012-11-14 | 温州大学 | Interactive grayscale image colorizing method based on local linear model optimization |
| US20140072209A1 (en) * | 2012-09-13 | 2014-03-13 | Los Alamos National Security, Llc | Image fusion using sparse overcomplete feature dictionaries |
| CN106971379A (en) * | 2017-03-02 | 2017-07-21 | 天津大学 | A kind of underwater picture Enhancement Method merged based on stratified calculation |
Non-Patent Citations (4)
| Title |
|---|
| KAZUNORI URUMA 等: "Image colorization algorithm using series approximated sparse function" * |
| SATOSHI IIZUKA 等: "Let there be color!: joint end-to-end learning of global and local image priors for automatic image colorization with simultaneous classification" * |
| 梁海: "基于多字典的多内容灰度图像彩色化算法研究" * |
| 罗鸿斌: "基于拉普拉高斯金字塔的数字图像融合研究" * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114648531A (en) * | 2022-05-20 | 2022-06-21 | 领伟创新智能系统(浙江)有限公司 | Solar panel surface dust identification method based on color channel brightness distribution |
Also Published As
| Publication number | Publication date |
|---|---|
| CN108009980B (en) | 2024-03-26 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN107220980B (en) | A kind of MRI image brain tumor automatic division method based on full convolutional network | |
| CN105069746B (en) | Video real-time face replacement method and its system based on local affine invariant and color transfer technology | |
| CN109360206A (en) | Crop field spike of rice dividing method based on deep learning | |
| CN108876737A (en) | A kind of image de-noising method of joint residual error study and structural similarity | |
| CN107507134A (en) | Super-resolution method based on convolutional neural networks | |
| CN104376529B (en) | A kind of gray level image colorization system and method based on GLCM | |
| CN109858466A (en) | A kind of face critical point detection method and device based on convolutional neural networks | |
| CN103208102B (en) | A kind of remote sensing image fusion method based on rarefaction representation | |
| CN108399362A (en) | A kind of rapid pedestrian detection method and device | |
| CN102902956B (en) | A kind of ground visible cloud image identifying processing method | |
| CN108229425A (en) | A kind of identifying water boy method based on high-resolution remote sensing image | |
| CN107392130A (en) | Classification of Multispectral Images method based on threshold adaptive and convolutional neural networks | |
| CN107392925A (en) | Remote sensing image terrain classification method based on super-pixel coding and convolutional neural networks | |
| CN109829855A (en) | A kind of super resolution ratio reconstruction method based on fusion multi-level features figure | |
| CN107408211A (en) | Method for distinguishing is known again for object | |
| CN107437092A (en) | The sorting algorithm of retina OCT image based on Three dimensional convolution neutral net | |
| CN107123123A (en) | Image segmentation quality evaluating method based on convolutional neural networks | |
| CN107369160A (en) | A kind of OCT image median nexus film new vessels partitioning algorithm | |
| CN102063623A (en) | Method for extracting image region of interest by combining bottom-up and top-down ways | |
| CN109657612B (en) | Quality sorting system based on facial image features and application method thereof | |
| CN107122701A (en) | A kind of traffic route sign based on saliency and deep learning | |
| CN109191428A (en) | Full-reference image quality evaluating method based on masking textural characteristics | |
| CN107424161A (en) | A kind of indoor scene image layout method of estimation by thick extremely essence | |
| CN107527054A (en) | Prospect extraction method based on various visual angles fusion | |
| CN107154058A (en) | A kind of method for guiding user to reduce magic square |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |