CN107918926B - A kind of digital image magnification method based on quadrangle and triangle surface - Google Patents

Abstract

The digital image magnification method based on quadrangle and triangle surface that the invention discloses a kind of, this approach includes the following steps：16 pixels on 4 × 4 region of each of enlarged drawing picture element matrix are treated, are classified according to gray value difference；Quadrangular mesh partition is two triangular mesh or not divided by the splitting scheme that the regional center position quadrilateral mesh is determined by classification results；On the quadrilateral mesh for being divided into two triangles, 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 not divided quadrilateral mesh；All patch are stitched together, the fitting surface of former scene is obtained；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 high definition television, image magnification receive more and more attention.

Digital picture is the number changed by spatial sampling and grey level quantization by the former scene perception data that sensor obtains 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 increasing Sample density can be obtained by details and enrich and clearly enlarged drawing.Image magnification problem can be attributed to by image reversal weight in this way The problem of building former scene surface.

Digital picture indicates that adjacent four pixels constitute 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 Sampling in plane product, then each pixel p of image P_i,j, i, j=1,2 ..., n is：

Usual way is the Proximal surface of the former scene of construction.First with pixel P_i,jCentered on each of 3rd × 3 area A quadratic interpolation patch is constructed on domain

f_i,j(x, y)=b₁x²+b₂y²+b₃xy+b₄x+b₅y+b₆,

Again by the patch f on four adjacent pixels_i,j(x, y), f_i,j+1(x, y), f_i+1,j(x, y) and f_i+1,j+1(x, y) adds Weight average forms whole fitting surface f (x, y).

In above-mentioned algorithm, if four adjacent pixels are up-sampled from the same object of former scene, There can be the edge of image in quadrilateral mesh region, then this fitting surface based on quadrilateral mesh construction can the smooth side Edge leads to edge blurry herein or distortion.

Invention content

The purpose of the present invention is exactly to solve the above-mentioned problems, to provide one kind based on quadrangle and triangle surface to be fitted Scene curved surface, to the method for amplifying original image.

To achieve the goals above, the present invention adopts the following technical scheme that：

Image indicates that every four adjacent pixels may make up a quadrilateral mesh in the form of picture element matrix.One kind being based on four The digital image magnification method of side shape and triangle surface treats 4 × 4 region of each of enlarged drawing picture element matrix first 16 pixels are classified, according to classification results determine 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 for being divided into two triangles, a cubic polynomial and one is constructed A quadratic polynomial patch is fitted two different objects of former scene respectively, two patch in junction be it is discontinuous, Former scene surface can be more preferably fitted；Bicubic polynomials patch is constructed on not divided quadrilateral mesh；To own Patch is stitched together, obtains the fitting surface of former scene；Increase sampling density on fitting surface, is realized by resampling The amplification of image.

The present invention the specific steps are：

1) classify to 16 pixels on 4 × 4 region of each of image pixel matrix；

2) splitting scheme that the quadrilateral mesh of the regional center position is determined according to classification results draws quadrilateral mesh It is divided into triangular mesh or not divides；

3) construction of quadrangle and triangular curved piece：It is constructed respectively on the quadrilateral mesh for being divided into two triangles One cubic polynomial and a quadratic polynomial patch；Bicubic polynomials are constructed on not divided quadrilateral mesh Patch；

4) 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) it is that constraint carries out triangular grids with edge for the region containing edge pixel, division methods are simple, Accuracy rate is higher.

(2) it can largely eliminate and generate fuzzy at image border, obtain satisfactory amplification effect.

(3) it realizes image magnification by constructing fitting of a polynomial curved surface, similitude, rarefaction representation and machine is based on than existing The image magnification method speed of device study etc. is fast, and efficiency of algorithm is high.

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

Specific implementation mode

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, so that it may be enriched and clearly enlarged drawing with obtaining details.Image indicates 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, including the following steps：

1) to 16 pixels in 4 × 4 region of each of 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, it whether may determine that on quadrilateral area same according to classification results Object up-sampling, if it is not, then being likely that there are edge.It sorts first, in accordance with gray value size to 16 pixels, row It is divided into two classes after sequence, E is calculated separately 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 E_q=E₁+E₂The classification to 16 pixels, i.e. m can be realized for minimum m Following formula is set to set up：

argmin(E₁+E₂) (2)

2) splitting scheme that 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, 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, four vertex grey scale pixel values Difference is larger will not to be divided into one kind, the region have it is larger there may be edges, fitting surface meeting is directly constructed on quadrangle Smooth edge, it is therefore desirable to be divided.Image border is that horizontal and vertical situation uses quadrilateral mesh constructing curve Piece has substantially no effect on the quality of enlarged drawing, therefore, division when this method only considers to belong to same class there are three vertex.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 sampling area, the pixel grey scale field of same sample objects is continuous, therefore also needs to examine Consider p₄And p₁₄, p₂、p₃And p₇Affiliated classification.By symmetry, other situations are as the same.

2-1) according to the classification results on four vertex, quadrilateral area is divided into two triangles, then there are two types of divide 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 also belong to such； Meanwhile another vertex and its belonging 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 similar triangle the lower right corner of grid the case where 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 also belong to this Class；Meanwhile another vertex and its belonging to another as other three points on the quadrilateral mesh where the upper right corner on grid When class, it is denoted as status3；According to symmetry, it is similar triangle the lower left corner of grid the case where that can obtain three vertex, note For status4.

For four vertex pixel ps of quadrangle at 4 × 4 regional center as shown in Figure 2 position₅p₆p₁₀p₉：

(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：For being divided into the quadrangle of 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 not divided quadrangle, bicubic polynomials patch is constructed.

3-1) the building method of quadratic polynomial interpolation curved surface piece.

With each pixel p of image_i,jCentered on 3 × 3 regions on, construct quadratic polynomial interpolation curved surface piece f_i,j (x,y)。

f_i,j(x, y)=b₁x²+b₂y²+b₃xy+b₄x+b₅y+b₆ (3)

It is the determination 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 P_i+k,j+l, k, l=-1,0,1 are with pixel p_i,jCentered on 9 pixels, and have：

e₁=(P_i+1,j-P_i-1,j)/2, e₂=(P_i,j+1-P_i,j-1)/2

e₃=(P_i+1,j+1-P_i-1,_j-1)/2, e₄=(P_i+1,j-1-P_i-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

In this way, the solution of quadratic polynomial coefficient finishes.

3-2) on the quadrangle for being divided into two triangles, constructs a cubic polynomial respectively and one secondary multinomial Formula patch.

Of a sort delta-shaped region 3-2-1) is belonged to for vertex, fitting surface piece is constructed on the triangle that number is t B_t(x,y).As shown in figure 4, method is as follows：

f_i,j(x, y), f_i,j+1(x, y), f_i+1,j+1(x, y) is 3-1) in respectively with p_i,j,p_i,j+1And p_i+1,j+1Centered on The quadratic polynomial interpolation curved surface of construction.B_t(x, y) is the weighted average of these three patch：

B_t(x, y)=L_if_i,j(x,y)+L_jf_i+1,j+1(x,y)+L_kf_i,j+1(x,y)+AL_iL_jL_k

Wherein, L_i,L_j,L_kIt is respectively in four kinds of states：

A is by all and p on 4 × 4 regions_i,j,p_i,j+1And p_i+1,j+1Belong to of a sort pixel, is obtained with least square method It arrives.

3-2-2) vertex is not belonging to directly the inserting using that remaining apex of the fitting surface on of a sort triangle It is worth patch f_i,j(x,y)。

3-3) for not divided quadrilateral area, construction bicubic polynomials fitting surface piece B_i,j(x,y).Four sides The interpolation curved surface piece of four apexes in shape region is f_i,j(x, y), f_i+1,j(x, y), f_i,j+1(x, y), f_i+1,j+1, by they plus Weight average generates bicubic fitting surface piece, i.e.,

B_i,j(x, y)=w_i,jf_i,j(x,y)+w_i+1,jf_i+1,j(x,y)+w_i,j+1f_i,j+1(x,y)+w_i+1,j+1f_i+1,j+1

Wherein

4) all patch are stitched together, obtain the fitting surface of former scene；

The Proximal surface of former scene is B_i,j(x,y)、B_t(x, y) and f_i,jThe split of (x, y) three kinds of patch.By patch Construction process meets C it is found that adjacent curved surface piece is identical in the position function value of intersection⁰Continuously.

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, so that it may is abundant and clear to obtain details Clear enlarged drawing.

To sum up, the present invention, which passes through, constructs fitting of a polynomial curved surface and 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 is constraint with edge, is closed to the region containing edge pixel 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.

Above-mentioned, although the foregoing specific embodiments of the present invention is described with reference to the accompanying drawings, not protects model to the present invention The limitation enclosed, those skilled in the art should understand that, based on the technical solutions of the present invention, those skilled in the art are not Need to make the creative labor the various modifications or changes that can be made still within protection scope of the present invention.

Claims (6)

1. a kind of digital image magnification method based on quadrangle and triangle surface, which is characterized in that

Step 1, to 16 pixels in 4 × 4 region of each of 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 that 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 also belongs to such；Meanwhile another vertex and its as other on the quadrilateral mesh where the upper left corner on grid When three points belong to another kind of, it is denoted as status1；

According to symmetry, it is similar triangle the lower right corner of grid the case where 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 also belongs to such；Meanwhile another vertex and its as other on the quadrilateral mesh where the upper right corner on grid When three points belong to another kind of, it is denoted as status3；

According to symmetry, it is similar triangle the lower left corner of grid the case where 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 for being divided into two triangles, construction one A cubic polynomial and a quadratic polynomial patch are fitted two different objects of former scene respectively；Not divided four 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)；

Of a sort delta-shaped region, construction cubic polynomial patch B 3-2) are belonged to for vertex_t(x,y)；

3-3) for not divided quadrilateral area construction bicubic polynomials fitting surface piece B_i,j(x,y)；

Wherein i, j are the position marks of pixel, and i, j=1,2 ... n；

Step 4, 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. a kind of digital image magnification method based on quadrangle and triangle surface as described in claim 1, 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 separately, to meet the classification situation of energy minimum as optimal pixel classification results.

3. a kind of digital image magnification method based on quadrangle and triangle surface as claimed in claim 2, feature exist In, it is described that its energy is calculated separately to possible 15 kinds of classification results, to meet the classification situation of energy minimum as optimal Pixel classification results, including：

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, make gross energy E_q=E₁+E₂Reach m when minimum value 16 pixels can be divided into two classes, preceding m pixel P₁,P₂,...P_mFor the first kind, i.e. m makes following formula set up：

arg min(E₁+E₂)。

4. a kind of digital image magnification method based on quadrangle and triangle surface as described in claim 1, feature exist In the 3-1) construction quadratic polynomial patch f_i,j(x, y) includes：

f_i,j(x, y)=b₁x²+b₂y²+b₃xy+b₄x+b₅y+b₆

Weight function w when each term coefficient is determined in formula_iIt is defined as：

And

Wherein λ is adjustment factor, and 4 α values are respectively by horizontal on 3 × 3 regions, vertical, the pixel class in 45 ° and 135 ° directions is true Fixed, α is 1 if 3 pixels on certain direction belong to same class, is otherwise 0.2.

5. a kind of digital image magnification method based on quadrangle and triangle surface as described in claim 1, feature exist In the 3-2) construction cubic polynomial patch B_t(x, y) includes：

B_t(x, y)=L_if_i,j(x,y)+L_jf_i,j+1(x,y)+L_kf_i+1,j+1(x,y)+AL_iL_jL_k,

Wherein, L_i,L_j,L_kIt is respectively in four kinds of states：

The value of A is set as P by all pixels for belonging to same class C with triangle three vertex pixels on 4 × 4 regions_s, s= 0,1 ... 15, it is obtained with least square method, i.e. minimization object function：

6. a kind of digital image magnification method based on quadrangle and triangle surface as described in claim 1, feature exist In the 3-3) construction bicubic polynomials curved surface B_i,j(x, y) includes：

B_i,j(x, y)=w_i,jf_i,j(x,y)+w_i+1,jf_i+1,j(x,y)+w_i,j+1f_i,j+1(x,y)+w_i+1,j+1f_i+1,j+1

Wherein