CN101197996A - Digital image interpolation and amplifying method combining edge vectorization and cube convolution - Google Patents
Digital image interpolation and amplifying method combining edge vectorization and cube convolution Download PDFInfo
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- CN101197996A CN101197996A CNA2007100327757A CN200710032775A CN101197996A CN 101197996 A CN101197996 A CN 101197996A CN A2007100327757 A CNA2007100327757 A CN A2007100327757A CN 200710032775 A CN200710032775 A CN 200710032775A CN 101197996 A CN101197996 A CN 101197996A
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Abstract
The invention belongs to the digital image zoom technical field. A digital image interpolation zoom method integrating edge vectorization and cube convolution detects the pixel in the prior digital image with pagin operator, fits detected boundary line pixel sets through n times of spline curves, defines the n-time spline fitting curvilinear equation and zooms according to pixel point coordinates of the boundary pixel, defines and amplifies the coordinates of the corresponding pixel points, carries out pixel point interpolation according to the corresponding zoom curvilinear equation between each two adjacent corresponding pixel points and obtains a zoom insertion pixel point, inserts pixel values of the boundary pixel into corresponding zoom related pixel points, takes k zoom related pixel points which are arranged adjacently, carries out pixel value interpolation for the zoom insertion pixel points according to the pixel value of each zoom related pixel and n-time curvilinear equation of the pixel value, and carries out pixel value interpolation for the pixel points in the zoom pixel sets through a neighborhood copy method and superimposes on pixel sets of the cube convolution method.
Description
Technical field
The invention belongs to digital image amplifying technique field, especially relate to and a kind ofly edge neighborhood vector is carried out the method for picture element interpolation after to digital image multiplication based on cube convolution.
Background technology
Existing non-film ball is admired in playback equipment and other extraordinary video display apparatus, and the resolution of general logarithm word image all has very high requirement.And in existing manufacturing technology and photographic equipment, can not realize the image of ultrahigh resolution.Therefore, realize the image processing and amplifying, and the image after guaranteeing to change there is preferable quality to be very important by a kind of effective image interpolation method.
The image interpolation algorithm that generally adopts has nearest neighbor point method, bilinear interpolation and cube convolution method at present.Described nearest neighbor point method has another name called the zeroth order interpolation algorithm, and the sampled point pixel value of this algorithm is to determine according to the value of 4 adjacent around it pixels, is its pixel value from the pixel value of its nearest pixel.The advantage of this algorithm is to calculate simply, computational speed is very fast, shortcoming is not consider the correlation of other neighbors, so the pixel value of the image after the interpolation has tangible discontinuity, image can produce square or sawtooth effect, apparent in view mosaic effect occurs, the distortion of image is bigger.
Described bilinear interpolation, be called the single order interpolation algorithm again, it is a kind of improvement to the nearest neighbor point method, and the sampled point pixel value of this algorithm is to make linear interpolation according to the pixel value of 4 adjacent around its mapping point in input picture known pixels points on both direction to obtain.Bilinear interpolation is mainly carried out set operation to image in two steps: at first, image is carried out space coordinate transformation; Secondly, image is carried out grey scale interpolation.Described bilinear interpolation has overcome the discontinuity of pixel value of the pixel of nearest neighbor point method, considered to treat the correlation of sampled point 4 neighbor pixels on every side, but increased amount of calculation, simultaneously, it only considers the correlation of the pixel value of adjacent 4 pixels, and do not consider the rate of change of pixel value between each adjoint point, still there is the problem of the inconsiderate and image degradation that produces of computation model and precision reduction.Image boundary after the interpolation is fuzzyyer.Described cube convolution method, this algorithm are the improvement to bilinear interpolation, and it has also considered the rate of change of pixel value between each adjoint point except the correlation of the pixel of considering adjacent 4 pixels.The pixel value for the treatment of sampled point of cube convolution method is made cubic interpolation according to the pixel value of 16 consecutive points around its input point.This method generally uses cubic polynomial S (u) that the sinc function is carried out match.
Two kinds of algorithms of cube convolution algorithm and front are compared, and the characteristics of following aspect are arranged: it has considered to treat the interior correlation of bigger adjacent domains of sampled point, and the information of collection point is more complete, therefore, treats that the pixel value of sampled point will more approach initial value.Because considered that the pixel value rate of change has solved the problem that nearest neighbor point method and bilinear interpolation exist to a certain extent to the influence of sampled point between the pixel value of direct adjoint point and adjoint point, image effect is obviously good than preceding two kinds of methods.But also there are some image quality issues in the cube convolution method, such as image has small distortion after edge blurry and the interpolation.
Summary of the invention
The digital image interpolation amplification method that the object of the present invention is to provide a kind of edge vectorization to combine with cube convolution on the basis of cube convolution, carries out the edge vectorization interpolation to the pixel of former digital picture, realizes the amplification to digital picture.
For realizing purpose of the present invention, the digital image interpolation amplification method that described edge vectorization combines with cube convolution comprises the steps:
According to each pixel value that amplifies respective pixel in conjunction with R
z, G
z, B
zN curvilinear equation, calculate the equation of determining to carry out the pixel value interpolation by solving an equation, between per two adjacent amplification respective pixel according to sequence number, insert the interpolation that pixel carries out pixel value according to the equation that carries out the pixel value interpolation to amplifying, in view of the above the whole pixels in the set of intensified image vegetarian refreshments are carried out the interpolation of pixel value, form and amplify the pixel set;
Step 9, to the set of each pixel catastrophe point with coordinate points (x
Org, y
Org) be initial point, m
xBe the multiplication factor on the x direction of principal axis, m
yFor the multiplication factor on the y direction of principal axis is amplified, for being in pixel in the corresponding amplification pixel set after this set amplification, adopt neighborhood copy image interpolator arithmetic that pixel is carried out the pixel value interpolation, finish amplification interpolation thus, form and amplify the set of sudden change pixel the pixel of whole pixel catastrophe point correspondences;
Step 10, with coordinate points (x
Org, y
Org) be initial point, pixel in the former digital picture is amplified the multiple that image carries out step 3 according to the cube convolution image multiplication method, form the set of cube convolution interpolating pixel, and amplification that will be above-mentioned sudden change set of pixels is combined in the cube convolution interpolating pixel and gathers and superpose.
Description of drawings
The drawing of accompanying drawing is described as follows
Serve as reasons single pixel catastrophe point of Fig. 1 constitutes the pixel catastrophe point set of ring-type and the coordinate diagram of n time corresponding spline fit curve.
Serve as reasons single pixel catastrophe point of Fig. 2 constitutes the pixel catastrophe point set of linear and the coordinate diagram of n time corresponding spline fit curve.
Fig. 3 is the coordinate diagram of a pixel catastrophe point.
Fig. 4 is the pixel catastrophe point set that a plurality of pixel catastrophe point width constitute ring-types, and at the coordinate diagram of n the spline fit curve of pixel of its boundary line pixel.
Fig. 5 is the pixel catastrophe point set that a plurality of pixel catastrophe point width constitute linears, and at the coordinate diagram of n the spline fit curve of pixel of its boundary line pixel.
Fig. 6 carries out the coordinate diagram of interpolation again for after the pixel catastrophe point among Fig. 4, n spline fit curve are amplified according to amplified curve.
Fig. 7 carries out the coordinate diagram of interpolation again for after the plain catastrophe point among Fig. 5, n spline fit curve are amplified according to amplified curve.
Fig. 8 is the pixel after the pixel catastrophe point among Fig. 2, n spline fit curve are amplified, the coordinate diagram of amplified curve.
Fig. 9 is for carrying out the coordinate diagram of interpolation according to the pixel among Fig. 8, amplified curve.
Serve as reasons single pixel catastrophe point of Figure 10 constitutes the pixel catastrophe point set of linear and the coordinate diagram of n time corresponding spline fit curve.
Figure 11 carries out the coordinate diagram of pixel value interpolation again for after the plain catastrophe point among Figure 10, n spline fit curve are amplified.
Below in conjunction with accompanying drawing, embodiments of the invention are described further.
If the pixel coordinate on the pixel of boundary line is that (x, y), then the equation of n spline curve is p
Y=a
0+ a
1X+a
2x
2+ a
3x
3+ ... + a
nx
n, formula (1), n ∈ [2,5] wherein,
If t is the pixel number of boundary line pixel set, then in the set of boundary line pixel, fit to one section n spline curve by adjacent n point, the end point of n spline curve of i section is same some t with the first point of (i+1) section
i(x
Ti, y
Ti), by that analogy,, then form n spline curve of (t-1)/(n-1) section if be integer (t-1)/(n-1).If (t-1)/(n-1) remainder is arranged, wherein remainder is as 1 section.If the i section is respectively with the equation of n spline curve of the i+1 section that is adjacent
y
i=f
i(x)=a
0i+ a
1iX+a
2ix
2+ a
3ix
3+ ... + a
Nix
n, formula (2),
y
I+1=f
I+1(x)=a
0 (i+1)+ a
1 (i+1)X+a
2 (i+1)x
2+ a
3 (i+1)x
3+ ... + a
N (i+1)x
n, formula (3),
And
f
i' (x
Ti)=f
I+1' (x
Ti), formula (4)
f
i" (x
Ti)=f
I+1" (x
Ti), formula (5)
With the i section and (i+1) the pixel coordinate p of n boundary line pixel of section (x y) distinguishes substitution formula (2), formula (3), formula (4) and formula (5), can be in the hope of a
0i, a
1i, a
2i, a
3iA
N (i+1), a
0 (i+1), a
1 (i+1), a
2 (i+1), a
3 (i+1)A
N (i+1), obtain n the spline fit curve equation of this section.As shown in Figure 2, the pixel number of this boundary line pixel set is t=11, gets n=4 pixel and carries out match, amounts to 4 sections, for ease of expression, represents with two sections solid lines and two sections dotted lines of space.If dotted line i is 4 spline curve of i section, solid line i+1 is 4 spline curve of i+1 section, in the coordinate figure substitution formula (2) on each line segment, (3), (4), (5), and just can be in the hope of n spline fit curve equation of i section.By that analogy, can try to achieve n the spline fit curve equation of other section respectively.The summation of n the spline fit curve of all sections constitutes n spline fit curve of this boundary line pixel set.
When n=3,, then adopt fitting a straight line between the pixel coordinate of the pixel coordinate of this boundary line pixel and adjacent boundary line pixel if the pixel coordinate of a unnecessary boundary line pixel is arranged.
When n=4,, then adopt fitting a straight line between the pixel coordinate of the pixel coordinate of this boundary line pixel and adjacent boundary line pixel if the pixel coordinate of one or two unnecessary boundary line pixel is arranged.
When n=5,, then adopt fitting a straight line between the pixel coordinate of the pixel coordinate of this boundary line pixel and adjacent boundary line pixel if the pixel coordinate of one, two or three unnecessary boundary line pixel is arranged.
If n spline curve of i section amplify the coordinate of arbitrfary point on the corresponding curve in back be P (X, Y), the corresponding curvilinear equation Y=A that amplifies of i section then
0i+ A
1iX+A
2iX
2+ A
3iX
3+ ... + A
NiX
n, formula (6),
Coordinate on coordinate on the curve and n the spline fit curve satisfies following functional relation
X=xm
x+ x
Org(1-m
x), formula (7),
Y=ym
y+ y
Org(1-m
y), formula (8),
Can try to achieve A by formula (2), (7), (8)
0i, A
1i, A
2i, A
3i... A
NiValue, obtain i section amplified curve equation.As shown in Figure 8, the phantom line segments among Fig. 8 is corresponding to the amplified curve of the phantom line segments among Fig. 2, and the real segment among Fig. 8 is corresponding to the amplified curve of the real segment among Fig. 2.Each section amplified curve summation constitutes total amplified curve.
If corresponding sequence number 1 ... n curvilinear equation of the pixel value of the pixel between the k is as follows
With p
1(r
1, g
1, b
1), p
2(r
2, g
2, b
2) ... p
k(r
k, g
k, b
K) in pixel value and its corresponding sequence number k respectively R, G, B and the z in substitution formula (9) can try to achieve each a respectively
R0, a
R1, a
R2A
Rn, a
G0, a
G1, a
G2A
Gn, a
B0, a
B1, a
B2A
BnValue, the pixel value that obtains adjacent k amplification respective pixel carries out the equation of pixel value interpolation according to sequence number.
With { 1+1/m, 1+2/m,, 1+ (m-1)/m}, { 2+1/m, 2+2/m, 2+ (m-1)/m} ..., (k-1)+and 1/m, (k-1)+2/m ... (k-1)+(m-1)/m} respectively substitution tried to achieve adjacent k the pixel value that amplifies respective pixel carry out independent variable z in the equation of pixel value interpolation according to sequence number, then correspondence obtains p respectively
1(r
1, g
1, b
1) and p
2(r
2, g
2, b
2), p
2(r
2, g
m, b
2) and p
3(r
3, g
3, b
3) ..., p
(k-1)(r
(k-1), g
(k-1), b
(k-1)) and p
k(r
k, g
k, b
k) between per two adjacent amplification respective pixel, need the amplification of inserting to insert the pixel value of pixel.The rest may be inferred, can amplify the pixel set in the hope of the whole pixels in the set of intensified image vegetarian refreshments being carried out the interpolation of pixel value, forming.As n=3, k=4, p
1(129,40,40), p
2(177,66,66), p
3(03,29,29), p
4(152,18,18), the numeral in the bracket are represented three primary colors R, the G of this point correspondence, the pixel value of B respectively, with these numerals respectively correspondence bring R in the formula (9) into
z, G
z, B
zIn, the index number of p then among the substitution z, can be tried to achieve a
R0, a
R1, a
R2, a
R3, a
G0, a
G1, a
G2, a
G3, a
B0, a
B1, a
B2, a
B3Concrete numerical value.If m=2 is then at p
1With p
2Between insert the pixel value of z=1+1/2, p
2With p
3Between insert the pixel value of z=2+1/2, p
3With p
4Between insert the pixel value of z=3+1/2.If m=3 is then at p
1With p
2Between insert the pixel value of z=1+1/3, z=1+2/3, p
2With p
3Between insert the pixel value of z=2+1/3, z=2+2/3, p
3With p
4Between insert the pixel value of z=3+1/3, z=3+2/3, by that analogy.
Step 9, set adopts formula (7), formula (8) to amplify to each pixel catastrophe point, for being in pixel in the corresponding amplification pixel set after this set amplification, adopt neighborhood copy image interpolator arithmetic that pixel is carried out the pixel value interpolation, finish amplification interpolation thus, form and amplify the set of sudden change pixel the pixel of whole pixel catastrophe point correspondences.As shown in Figure 6, hollow fork round dot 8 is for being in the zone that two curves 5 surround.
Step 10, with coordinate points (x
Org, y
Org) be initial point, pixel in the former digital picture is amplified the multiple that image carries out step 3 according to the cube convolution image multiplication method, form the set of cube convolution interpolating pixel, and amplification that will be above-mentioned sudden change set of pixels is combined in the cube convolution interpolating pixel and gathers and superpose.
The present invention is directed to the digital picture processing and amplifying and disclose the image amplification interpolation method that a kind of edge vectorization interpolation combines with cube convolution, the pixel catastrophe point is divided into boundary line pixel and interior pixels, and uses different interpolation algorithms respectively boundary line pixel and interior pixels to be amplified interpolation arithmetic.For the boundary line pixel, adopt the edge vectorization interpolation method, at first utilize handkerchief gold operator to search out the Pixel of Digital Image catastrophe point, then adjacent boundary line pixel is carried out match with n spline curve, again matched curve is amplified, carry out interpolation according to amplified curve, obtain the set of intensified image vegetarian refreshments.Carry out the interpolation of pixel value again according to n spline curve.Amplify interpolation for interior pixels, then adopt neighborhood copy image interpolator arithmetic to operate, reach the interpolation effect that improves image resolution ratio.The digital image interpolation amplification method that edge vectorization of the present invention combines with cube convolution, follow pixel value rate of change and pixel value the rule that influences to sampled point, handle by digital picture being carried out sub-regional interpolation, guarantee the total quality of image after the interpolation, obtained the better image amplification effect.
Claims (6)
1. digital image interpolation amplification method that edge vectorization combines with cube convolution is characterized in that:
Step 1, utilize handkerchief gold operator that the pixel in the former digital picture is detected;
Step 2, by n spline curve respectively to detected boundary line pixel set carry out match, (x y), determines spline fit curve equation y=a n time according to the pixel coordinate p of boundary line pixel
0+ a
1X+a
2x
2+ a
3x
3+ ... + a
nx
n
Step 3, with coordinate points (x
Org, y
Org) be initial point, m
xBe the multiplication factor on the x direction of principal axis, m
yBe the multiplication factor on the y direction of principal axis, n spline fit curve amplified, obtain amplified curve equation Y=A
0+ A
1X+A
2X
2+ A
3X
3+ ... + A
nX
n
Step 4, with the pixel coordinate p of boundary line pixel (x y), amplifies according to the setting in the step 3, obtain pixel on n spline curve coordinate p (x, y) after amplification corresponding amplification respective pixel point coordinates P (X, Y);
Step 5, between two adjacent amplification respective pixel point coordinates, carry out the pixel interpolation according to its corresponding amplified curve equation, produce to amplify insert the pixel coordinate;
Step 6, the step 4, five of passing through, can insert pixel in the hope of the amplification between all adjacent amplification corresponding pixel points, the rest may be inferred, can insert pixel in the hope of other amplification corresponding pixel points and amplification, the set of pixel formation intensified image vegetarian refreshments is inserted in described amplification corresponding pixel points and amplification;
Step 7, according to step 1, if pixel set in boundary line has only a pixel, then (X Y) locates and inserts m on every side at P
x* m
yIndividual pixel;
Step 8, the pixel value of boundary line pixel is inserted on the corresponding amplification corresponding pixel points, gets k that adjacent sequential arranges again and amplify corresponding pixel points, establish the pixel value R of k amplification corresponding pixel points
z, G
z, B
zN curvilinear equation as follows
According to each pixel value that amplifies respective pixel in conjunction with R
z, G
z, B
zN curvilinear equation, calculate the equation of determining to carry out the pixel value interpolation by solving an equation, between per two adjacent amplification respective pixel according to sequence number, insert the interpolation that pixel carries out pixel value according to the equation that carries out the pixel value interpolation to amplifying, in view of the above the whole pixels in the set of intensified image vegetarian refreshments are carried out the interpolation of pixel value, form and amplify the pixel set;
Step 9, to the set of each pixel catastrophe point with coordinate points (x
Org, y
Org) be initial point, m
xBe the multiplication factor on the x direction of principal axis, m
yFor the multiplication factor on the y direction of principal axis is amplified, surround middle pixel for being in corresponding amplification pixel set after this set amplification, adopt neighborhood copy image interpolator arithmetic that pixel is carried out the pixel value interpolation, finish amplification interpolation thus, form and amplify the set of sudden change pixel the pixel of whole pixel catastrophe point correspondences;
Step 10, with coordinate points (x
Org, y
Org) be initial point, pixel in the former digital picture is amplified the multiple that image carries out step 3 according to the cube convolution image multiplication method, form the set of cube convolution interpolating pixel, and amplification that will be above-mentioned sudden change set of pixels is combined in the cube convolution interpolating pixel and gathers and superpose.
2. the digital image interpolation amplification method that edge vectorization according to claim 1 combines with cube convolution, it is characterized in that: described n ∈ [2,5], in boundary line pixel set by adjacent n pixel coordinate be one group and with the pixel of this group end be that adjacent n pixel coordinate of starting point organized for another and fitted to two sections n spline curve respectively, by that analogy, determine spline fit curve equation y=a n time
0+ a
1X+a
2x
2+ a
3x
3+ ... + a
nx
n
3. the digital image interpolation amplification method that edge vectorization according to claim 2 combines with cube convolution is characterized in that described two sections n spline curve, and the equation that is made as i section and n spline curve of the i+1 section that is adjacent is respectively
y
i=f
i(x)=a
0i+ a
1iX+a
2ix
2+ a
3ix
3+ ... + a
Nix
n, formula (2),
y
I+1=f
I+1(x)=a
0 (i+1)+ a
1 (i+1)X+a
2 (i+1)x
2+ a
3 (i+1)x
3+ ... + a
N (i+1) x
n, formula (3),
And f
i' (x
Ti)=f
I+1' (x
Ti), formula (4),
f
i" (x
Ti)=f
I+1" (x
Ti), formula (5),
With the i section and (i+1) the pixel coordinate p of n boundary line pixel of section (x y) distinguishes substitution formula (2), formula (3), formula (4) and formula (5), can be in the hope of a
0i, a
1i, a
2i, a
3iA
N (i+1), a
0 (i+1), a
1 (i+1), a
2 (i+1), a
3 (i+1)A
N (i+1), obtain n the spline fit curve equation of this section, determine n spline fit curve equation by that analogy.
4. the digital image interpolation amplification method that edge vectorization according to claim 1 and 2 combines with cube convolution, it is characterized in that: when n=3, if the pixel coordinate of a unnecessary boundary line pixel is arranged, then adopt fitting a straight line between the pixel coordinate of the pixel coordinate of this boundary line pixel and adjacent boundary line pixel.
5. the digital image interpolation amplification method that edge vectorization according to claim 1 and 2 combines with cube convolution, it is characterized in that: when n=4, if the pixel coordinate of one or two unnecessary boundary line pixel is arranged, then adopt fitting a straight line between the pixel coordinate of the pixel coordinate of this boundary line pixel and adjacent boundary line pixel.
6. the digital image interpolation amplification method that edge vectorization according to claim 1 and 2 combines with cube convolution, it is characterized in that: when n=5, if the pixel coordinate of one, two or three unnecessary boundary line pixel is arranged, then adopt fitting a straight line between the pixel coordinate of the pixel coordinate of this boundary line pixel and adjacent boundary line pixel.
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