CN107918926A - A kind of digital image magnification method based on quadrangle and triangle surface - Google Patents

A kind of digital image magnification method based on quadrangle and triangle surface Download PDF

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CN107918926A
CN107918926A CN201711173266.6A CN201711173266A CN107918926A CN 107918926 A CN107918926 A CN 107918926A CN 201711173266 A CN201711173266 A CN 201711173266A CN 107918926 A CN107918926 A CN 107918926A
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徐李添
叶才增
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    • 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
    • G06T3/40—Scaling of whole images or parts thereof, e.g. expanding or contracting
    • G06T3/4007—Scaling of whole images or parts thereof, e.g. expanding or contracting based on interpolation, e.g. bilinear interpolation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
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Abstract

The invention discloses a kind of digital image magnification method based on quadrangle and triangle surface, this method comprises the following steps：16 pixels on each 4 × 4 region in enlarged drawing picture element matrix are treated, are classified according to gray value difference；The splitting scheme of the regional center position quadrilateral mesh is determined by classification results, quadrangular mesh partition is divided for two triangular mesh or not；On the quadrilateral mesh of two triangles is divided into, constructs a cubic polynomial and a quadratic polynomial patch is fitted two different objects of former scene respectively, two patch are discontinuous in junction, can more preferably be fitted former scene surface；Bicubic polynomials patch is constructed on the quadrilateral mesh not being divided；All patch are stitched together, obtain the fitting surface of former scene；Increase sampling density on fitting surface, image magnification is completed by resampling.By the above-mentioned means, division methods of the present invention are simple, accuracy rate is high, can not only preferably keep image detail and edge, and efficiency of algorithm is higher.

Description

A kind of digital image magnification method based on quadrangle and triangle surface
Technical field
The present invention relates to technical field of image processing, and in particular to a kind of number being fitted based on quadrangle and triangle surface Word image magnification method.
Background technology
Image magnification is related to image magnification technology or generates the technology of high-definition picture (HR), is image procossing, calculates The general character problem in science and key technology in the fields such as machine graphics, computer vision and digital content creation, at medical image The fields such as reason, satellite sounding, geological prospecting, virtual reality and Entertainment have a wide range of applications.With Internet video, movement The development of phone and HDTV, image magnification receive more and more attention.
Digital picture is the number that the former scene perception data obtained by sensor are changed into by spatial sampling and grey level quantization Word.Spatial sampling is more, portrays finer to the details of former scene surface.To image magnification problem, if can be according to figure As data back reconstructs the surface that former scene surface visible part forms, resampling then is carried out to surface, is adopted by increase Sample density can be obtained by details and enrich and clearly enlarged drawing.So image magnification problem can be attributed to by image reversal weight The problem of building former scene surface.
Digital picture represents that adjacent four pixels can form a quadrilateral mesh in the form of picture element matrix.Assuming that figure As P (being made of n × n pixel) is obtained from former scene curved surface F (x, y) up-sampling, it may be assumed that each sampled point is in list Each pixel p of sampling, then image P in plane producti,j, i, j=1,2 ..., n, is：
Usual way is the Proximal surface of the former scene of construction.First with pixel Pi,jCentered on each 3rd × 3 area A quadratic interpolation patch is constructed on domain
fi,j(x, y)=b1x2+b2y2+b3xy+b4x+b5y+b6,
Again by the patch f on four adjacent pixelsi,j(x, y), fi,j+1(x, y), fi+1,j(x, y) and fi+1,j+1(x, y) adds Weight average forms overall fitting surface f (x, y).
In above-mentioned algorithm, if four adjacent pixels are up-sampled from the same object of former scene, Can be there are the edge of image in quadrilateral mesh region, then this fitting surface based on quadrilateral mesh construction can the smooth side Edge, causes edge blurry herein or distortion.
The content of the invention
The purpose of the present invention is exactly to solve the above-mentioned problems, there is provided one kind is fitted based on quadrangle and triangle surface Scene curved surface, so that the method that original image is amplified.
To achieve these goals, the present invention adopts the following technical scheme that：
Image represents that every four adjacent pixels may make up a quadrilateral mesh in the form of picture element matrix.One kind is based on four The digital image magnification method of side shape and triangle surface, treats each 4 × 4 region in enlarged drawing picture element matrix first 16 pixels are classified, determined according to classification results the quadrilateral mesh at the regional center position be to maintain it is constant still It is divided into two triangular mesh；On the quadrilateral mesh of two triangles is divided into, a cubic polynomial and one is constructed A quadratic polynomial patch is fitted two of former scene different objects respectively, two patch in junction be it is discontinuous, Former scene surface can be more preferably fitted；Bicubic polynomials patch is constructed on the quadrilateral mesh not being divided；Will be all Patch is stitched together, obtains the fitting surface of former scene；Increase sampling density on fitting surface, realized by resampling The amplification of image.
The present invention's concretely comprises the following steps：
1) classify to 16 pixels on each 4 × 4 region in image pixel matrix；
2) splitting scheme of the quadrilateral mesh of the regional center position is determined according to classification results, quadrilateral mesh is drawn It is divided into triangular mesh or not divides；
3) construction of quadrangle and triangular curved piece：Constructed respectively on the quadrilateral mesh of two triangles is divided into One cubic polynomial and a quadratic polynomial patch；Bicubic polynomials are constructed on the quadrilateral mesh not being divided Patch；
4) it is all patch are stitched together, obtain the fitting surface of former scene；
5) increase sampling density on fitting surface, image magnification is completed by resampling.
Beneficial effects of the present invention：
(1) for the region containing edge pixel, triangular grids are carried out by constraint of edge, division methods are simple, Accuracy rate is higher.
(2) it can largely eliminate and produce fuzzy at image border, obtain gratifying amplification effect.
(3) realize image magnification by constructing fitting of a polynomial curved surface, similitude, rarefaction representation and machine are based on than existing The image magnification method speed of device study etc. is fast, and efficiency of algorithm is high.
Brief description of the drawings
Fig. 1 is the flow diagram of the present invention；
Fig. 2 is the grid schematic diagram of image pixel matrix
Fig. 3 is 4 kinds of division state diagrams of quadrilateral area
Fig. 4 is the coefficient table diagram of status1
Embodiment
One width digital picture is the sampling to certain scene surface, and sampling is more, portrays just to the details of former scene surface It is finer.It is right if the surface of former scene surface visible part composition can be reconstructed according to image reversal to image magnification problem Scene carries out resampling, it is possible to obtains details and enriches and clearly enlarged drawing.Image represents in the form of picture element matrix, every four A adjacent pixel may make up a quadrilateral mesh, as shown in Figure 2.
The invention will be further described with embodiment below in conjunction with the accompanying drawings.
As shown in Figure 1, comprise the following steps：
1) to 16 pixels in each 4 × 4 region in image pixel matrix, two classes are divided into according to gray value difference, Two different sample objects in corresponding former scene respectively.
Since the pixel gray value sampled to same target in former scene is roughly the same, and different objects are sampled Obtained each pixel gray value difference is larger.Therefore, whether may determine that according to classification results on quadrilateral area same Object up-sampling, if it is not, then being likely that there are edge.16 pixels are first according to the sequence of gray value size, row It is divided into two classes after sequence, E is calculated respectively to possible 15 kinds of classification results1And E2。
Wherein, m (1≤m≤15) is the number of first kind pixel, and p' is the gray average of pixel in the first kind, and p " is The gray average of pixel in second class.Meet ENERGY Eq=E1+E2The classification to 16 pixels, i.e. m can be realized for minimum m Set up following formula：
argmin(E1+E2) (2)
2) splitting scheme of the quadrilateral mesh of 4 × 4 regional center position is determined by classification results, by network of quadrilaterals Lattice are divided into two triangular mesh or not divide：
If four vertex pixels up-sample to obtain from former scene same target, then do not have in the quadrilateral area Edge, at this moment, four vertex grey scale pixel values identical (or close) can also be assigned to same class, and reason can be constructed on quadrangle The fitting surface thought；If four vertex pixels up-sample to obtain from different objects, then four vertex grey scale pixel values Difference is larger will not to be divided into one kind, which has larger there may be edge, the directly construction fitting surface meeting on quadrangle Smooth edge, it is therefore desirable to divided.Image border uses quadrilateral mesh constructing curve for horizontal and vertical situation Piece has substantially no effect on the quality of enlarged drawing, therefore, division when this method only considers to have three vertex belong to same class.Such as figure Shown in 2, for quadrangle p5p6p10p9If p5、p9And p10For one kind, p6To be another kind of, then along p5p10Direction is likely that there are The edge of image.Due to the continuity of sample area, the pixel grey scale field of same sample objects is continuous, therefore also needs to examine Consider p4And p14, p2、p3And p7Affiliated classification.It is as the same by symmetry, other situations.
2-1) according to the classification results on four vertex, quadrilateral area is divided into two triangles, then there are two kinds of divisions As a result totally four kinds of states, as shown in Figure 3；
According to classification results, quadrilateral mesh is divided into two triangular mesh along 45 ° of directions：If three vertex are same The triangle of class is in the upper left corner of grid, and two pixels adjacent along 45 ° of directions of upper left right-angled apices fall within such； Meanwhile another vertex and its belong to another kind of as other three points on the quadrilateral mesh where the upper left corner on grid When, it is denoted as status1；According to symmetry, it is situation of the similar triangle in the lower right corner of grid that can obtain three vertex, is denoted as status2。
According to classification results, quadrilateral mesh is divided into two triangular mesh along 135 ° of directions：If three vertex are Similar triangle is in the upper right corner of grid, and two pixels adjacent along 135 ° of directions of upper right right-angled apices fall within this Class；Meanwhile another vertex and its belong to another as other three points on the quadrilateral mesh where the upper right corner on grid During class, status3 is denoted as；According to symmetry, it is situation of the similar triangle in the lower left corner of grid that can obtain three vertex, note For status4.
For four vertex pixel ps of quadrangle at 4 × 4 regional center position as shown in Figure 25p6p10p9：
(connecting P5P10) is divided along 45 ° of directions：
1. if P5, P9, P10, P4 and P14 are one kind, P6, P2, P3 and P7 are denoted as status1 another kind of；
2. if P5, P6, P10, P1 and P11 are one kind, P9, P8, P12 and P13 are denoted as status2 another kind of；
(connecting P6P9) is divided along 135 ° of directions：
1. if P6, P10, P9, P7 and P13 are one kind, P5, P0, P1 and P4 are denoted as status3 another kind of；
2. if P6, P5, P9, P2 and P8 are one kind, P10, P11, P14 and P15 are denoted as status4 another kind of；
Quadrilateral mesh is not divided 2-2)：
Above-mentioned four kinds of class conditions are unsatisfactory for, which not divides.
3) construction of quadrangle top-surface camber piece：Quadrangle for being divided into two triangles, in three vertex pixel categories In constructing a cubic polynomial patch on of a sort triangle, on vertex, pixel is not belonging to structure on of a sort triangle A quadratic polynomial patch is made, two patch are discontinuous in junction, can more preferably be fitted former scene surface； On the quadrangle not being divided, bicubic polynomials patch is constructed.
3-1) the building method of quadratic polynomial interpolation curved surface piece.
With each pixel p of imagei,jCentered on 3 × 3 regions on, construct quadratic polynomial interpolation curved surface piece fi,j (x,y)。
fi,j(x, y)=b1x2+b2y2+b3xy+b4x+b5y+b6 (3)
It is the definite method of each term coefficient in formula (3) below.
For formula (3), by sampling formulaIt can obtain
Then there are 4 following relational equations：
b4=e1,b5=e2,b4+b5=e3,b4-b5=e4
Wherein Pi+k,j+l, k, l=-1,0,1 are with pixel pi,jCentered on 9 pixels, and have：
e1=(Pi+1,j-Pi-1,j)/2, e2=(Pi,j+1-Pi,j-1)/2
e3=(Pi+1,j+1-Pi-1,j-1)/2, e4=(Pi+1,j-1-Pi-1,j+1)/2
Two unknown quantity b in four equations are determined using weighted least-squares method1And b2:
G(b4,b5)=w1(b4-e1)2+w2(b5-e2)2+w3(b4+b5-e3)2+w4(b4-b5-e4)2, minimization obtains b4And b5, I.e.：
WhereinAnd
λ is adjustment factor, and α is determined by the classification situation of 9 pixels on 3 × 3 regions.In this method：With middle imago The factor alpha of the of a sort pixel of vegetarian refreshments is 1, is otherwise 0.2.
Known by formula (4)：
Known by formula (3)：
According to the 8 of surrounding pixels, b is equally determined by the least square method of belt restraining1, b2And b3：
Minimize to obtain b1, b2And b3。
Wherein
Finished in this way, quadratic polynomial coefficient solves.
3-2) on the quadrangle of two triangles is divided into, construct a cubic polynomial respectively and one secondary multinomial Formula patch.
3-2-1) belong to of a sort delta-shaped region for vertex, fitting surface piece is constructed on the triangle that numbering is t Bt(x,y).As shown in figure 4, method is as follows：
fi,j(x, y), fi,j+1(x, y), fi+1,j+1(x, y) is 3-1) in respectively with pi,j,pi,j+1And pi+1,j+1Centered on The quadratic polynomial interpolation curved surface of construction.Bt(x, y) is the weighted average of these three patch：
Bt(x, y)=Lifi,j(x,y)+Ljfi+1,j+1(x,y)+Lkfi,j+1(x,y)+ALiLjLk
Wherein, Li,Lj,LkIt is respectively in four kinds of states：
A is by all and p on 4 × 4 regionsi,j,pi,j+1And pi+1,j+1Belong to of a sort pixel, obtained with least square method Arrive.
3-2-2) the fitting surface that vertex is not belonging on of a sort triangle directly inserting using that remaining apex It is worth patch fi,j(x,y)。
3-3) for the quadrilateral area not being divided, construction bicubic polynomials fitting surface piece Bi,j(x,y).Four sides The interpolation curved surface piece of four apexes in shape region is fi,j(x, y), fi+1,j(x, y), fi,j+1(x, y), fi+1,j+1, by they plus Weight average generates bicubic fitting surface piece, i.e.,
Bi,j(x, y)=wi,jfi,j(x,y)+wi+1,jfi+1,j(x,y)+wi,j+1fi,j+1(x,y)+wi+1,j+1fi+1,j+1
Wherein
4) it is all patch are stitched together, obtain the fitting surface of former scene；
The Proximal surface of former scene is Bi,j(x,y)、Bt(x, y) and fi,jThe split of (x, y) three kinds of patch.By patch Construction process understands that adjacent curved surface piece is identical in intersecting position function value, meets C0Continuously.
5) increase sampling density on fitting surface, image magnification is completed by resampling.
Resampling is carried out to the former scene fitting surface of construction, increases sampling density, it is possible to obtains details and enriches and clearly Clear enlarged drawing.
To sum up, the present invention by constructing fitting of a polynomial curved surface realizes image magnification, it is proposed that one kind based on quadrangle and The digital image magnification method of triangle surface.The method of the present invention closes the region containing edge pixel using edge as constraint The mesh generation of reason.By constructing the fitting of a polynomial patch of different accuracy respectively on quadrangle and triangular mesh, very Good maintains image detail and edge, and the efficiency of algorithm is higher.
Although above-mentioned be described the embodiment of the present invention with reference to attached drawing, model not is protected to the present invention The limitation enclosed, those skilled in the art should understand that, on the basis of technical scheme, those skilled in the art are not Need to make the creative labor the various modifications that can be made or deformation still within protection scope of the present invention.

Claims (6)

  1. A kind of 1. digital image magnification method based on quadrangle and triangle surface, it is characterised in that
    Step 1, to 16 pixels in each 4 × 4 region in image pixel matrix, two classes are divided into according to gray value difference, Two different sample objects in corresponding former scene respectively；
    Step 2, the splitting scheme of the quadrilateral mesh at the regional center position is determined according to classification results, by quadrilateral mesh It is divided into two triangular mesh or not divides：
    2-1) according to classification results, quadrilateral mesh is divided into two triangular mesh along 45 ° of directions：
    If three vertex are similar triangles in the upper left corner of grid, and upper left right-angled apices are along adjacent two in 45 ° of directions Pixel falls within such；Meanwhile another vertex and its it is used as other on the quadrilateral mesh where the upper left corner on grid When three points belong to another kind of, status1 is denoted as；
    According to symmetry, it is situation of the similar triangle in the lower right corner of grid that can obtain three vertex, is denoted as status2；
    2-2) according to classification results, quadrilateral mesh is divided into two triangular mesh along 135 ° of directions：
    If three vertex are similar triangles in the upper right corner of grid, and upper right right-angled apices are along adjacent two in 135 ° of directions Pixel falls within such；Meanwhile another vertex and its it is used as other on the quadrilateral mesh where the upper right corner on grid When three points belong to another kind of, status3 is denoted as；
    According to symmetry, it is situation of the similar triangle in the lower left corner of grid that can obtain three vertex, is denoted as status4；
    The quadrilateral area for 2-3) being unsatisfactory for above-mentioned class condition not divides；
    Step 3, the construction of quadrangle and triangular curved piece：On the quadrilateral mesh of two triangles is divided into, construction one A cubic polynomial and a quadratic polynomial patch are fitted two different objects of former scene respectively；In four not be divided Bicubic polynomials patch is constructed on the shape grid of side：
    Of a sort delta-shaped region, construction quadratic polynomial patch f are not belonged to for vertex 3-1)i,j(x,y)；
    3-2) belong to of a sort delta-shaped region, construction cubic polynomial patch B for vertext(x,y)；
    3-3) the quadrilateral area construction bicubic polynomials fitting surface piece B for not being dividedi,j(x,y)；
    Step 4, it is all patch are stitched together, obtain the fitting surface of former scene；
    Step 5, increase sampling density on fitting surface, image magnification is completed by resampling.
  2. 2. a kind of digital image magnification method based on quadrangle and triangle surface as claimed in claim 1, its feature exist In the step 1) includes：16 pixels are ranked up according to gray value size, then to possible 15 kinds of classification results Its energy is calculated respectively, and the classification situation to meet energy minimum is used as optimal pixel classification results.
  3. 3. a kind of digital image magnification method based on quadrangle and triangle surface as claimed in claim 2, its feature exist In, it is described that its energy is calculated respectively to possible 15 kinds of classification results, to meet the classification situation of energy minimum as optimal Pixel classification results, including：
    <mrow> <msub> <mi>E</mi> <mn>1</mn> </msub> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>-</mo> <msup> <mi>p</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow>
    <mrow> <msub> <mi>E</mi> <mn>2</mn> </msub> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> <mn>16</mn> </munderover> <msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>-</mo> <msup> <mi>p</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow>
    Wherein, E1And E2It is the energy value of two classifications respectively, m (1≤m≤15) is the number of first kind pixel, and p' is first The gray average of pixel in class, p " are the gray averages of pixel in the second class, gross energy Eq=E1+E2It can be realized pair for minimum m The classification of 16 pixels, i.e. m set up following formula：
    argmin(E1+E2)。
  4. 4. a kind of digital image magnification method based on quadrangle and triangle surface as claimed in claim 1, its feature exist In the 3-1) construction quadratic polynomial patch fi,j(x, y) includes：
    fi,j(x, y)=b1x2+b2y2+b3xy+b4x+b5y+b6
    Weight function w during each term coefficient is determined in formulaiIt is defined as：
    And
    Wherein λ is adjustment factor, and α is determined by the classification situation of 9 pixels on 3 × 3 regions.
  5. 5. a kind of digital image magnification method based on quadrangle and triangle surface as claimed in claim 1, its feature exist In the 3-2) construction cubic polynomial patch Bt(x, y) includes：
    Bt(x, y)=Lifi,j(x,y)+Ljfi,j+1(x,y)+Lkfi+1,j+1(x,y)+ALiLjLk
    Wherein, Li,Lj,LkIt is respectively in four kinds of states：
    Li=1-x
    Lj=y status1,
    Lk=x-y
    Li=1-y
    Lj=y-x status2,
    Lk=x
    Li=1-x-y
    Lj=y status3,
    Lk=x
    Li=1-x
    Lj=x+y-1status4；
    Lk=1-y
    The value of A is by all and p on 4 × 4 regionsi,j,pi,j+1And pi+1,j+1Belong to of a sort pixel, use least square method Obtain.
  6. 6. a kind of digital image magnification method based on quadrangle and triangle surface as claimed in claim 1, its feature exist In the 3-3) construction bicubic polynomials curved surface Bi,j(x, y) includes：
    Bi,j(x, y)=wi,jfi,j(x,y)+wi+1,jfi+1,j(x,y)+wi,j+1fi,j+1(x,y)+wi+1,j+1fi+1,j+1
    Wherein
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