CN101807291A - Biquadratic B-spline local interpolation-based image scaling method - Google Patents

Abstract

The invention discloses a biquadratic B-spline local interpolation-based image scaling algorithm. The core of the algorithm is to perform interpolation description on 16 pixels in a local 4*4 area of a source image by adopting a biquadratic B-spline function, and realizes the scaling of an image by performing resampling on the function. The algorithm avoids the problem of phase distortion caused by the conventional quadratic interpolation method, and can achieve an effect similar to a bicubic algorithm on vision effect. The algorithm is a localized algorithm, each processing unit and the utilized pixel resource are mutually independent, and the processing processes thereof have very good parallelism, so the algorithm can be accelerated in a CPU. Therefore, the efficiency of the algorithm is improved on the basis of ensuring the effect of the bicubic algorithm, and the real-time requirement on image processing is met.

Description

Image-scaling method based on Biquadratic B-spline local interpolation

Technical field

The present invention relates to Computer Image Processing and image zoom field, particularly relate to a kind of image-scaling method based on Biquadratic B-spline local interpolation.

Background technology

Image zoom is exactly the resolution that changes image, comprise from low resolution and dwindling to high-resolution image amplification and the image from the high resolving power to the low resolution, its key problem is how to distribute according to the pixel color of source images and the various features of image, the make new advances pixel color value of target image under the resolution of reconstruct.Therefore, image zoom also can be understood as the resampling in the image reconstruction.

The image zoom algorithm is numerous, and the modal interpolation algorithm that is based on kernel function comprise zeroth order interpolation, linear interpolation and various improved cubic interpolation function, and the quadratic interpolation function is mentioned by the people seldom.According to the viewpoint of Schafer and Rabiner (referring to Thomas M.Lehmann, Claudia

Klaus Spitzer.Survey:Interpolation Methods in Medical ImageProcessing[J] .IEEE Transactions on Medical Imaging, 1999,18 (11): 1049-1075), if the sampled point that adopts in interpolation process is an odd number, the number of times that is interpolating function is an even number, as based on the quadratic interpolation function of three sampled points, based on four interpolating functions of five sampled points etc., all can cause linear distortion and be not suitable for being used for carrying out image interpolation; And based on the odd number of even number of samples point time interpolating function such as cubic interpolation, five interpolation, can not bring the result of linear distortion, thereby also be fit to be applied to the image interpolation field.This theoretical analysis thinks that quadratic interpolation mainly contains following problem: the one, and the quadratic interpolation function of three sampled points of interpolation is not a linear shift invariant system, is used for image zoom and can brings image fault, causes bad visual effect; The 2nd, quadratic function has only adopted three sampled points in the process of interpolation, can cause two sampling optimizations in a current side, sampling optimization asked a little in the asymmetric situation of opposite side.By contrast, asking in the linear interpolation algorithm a little each side has a sampled point, and ask in the cubic interpolation algorithm two sampled points is arranged each side a little, all is symmetrically distributed.

Early stage widely used zeroth order interpolation and bilinear interpolation algorithm have the advantages of simplicity and high efficiency characteristics, but can produce tangible sawtooth or edge fog phenomenon; Cubic interpolation has improved the ill-defined shortcoming of low order interpolation to a certain extent, but calculated amount is bigger, has reduced counting yield.

Summary of the invention

The invention provides a kind of image-scaling method, when obtaining to be similar to the bicubic interpolation algorithm effect, improved counting yield greatly based on Biquadratic B-spline local interpolation.

A kind of image-scaling method based on Biquadratic B-spline local interpolation comprises the steps:

(1) with resolution be the source images of M * N by the RGB color space conversion to the YUV color space, the monochrome information of the Y representative image in the yuv space, U, V represent chrominance information.Since human eye to the susceptibility of monochrome information much larger than susceptibility to chrominance information, then when handling coloured image, only need the Y component is adopted the algorithm of more complicated, and adopt fairly simple algorithm between the U, V component, can improve the processing speed and the efficient of entire image like this;

(2) source images that will be transformed into behind the YUV color space amplifies, obtain the target image that resolution is nM * nN, n represents that source images needs amplification multiple, combination of pixels matrix with n * n travels through this target image as a processing unit, each processing unit is carried out following three operations, until the Y component brightness value that obtains scaled images:

A. this processing unit is mapped to forward in the source images, generates a mapping point;

The matrix area of b. getting 4 * 4 pixels around this mapping point in source images is as a sampled point space, make mapping point become the 2nd row the 2nd column element of sampled point space quadravalence matrix for this reason, with a Biquadratic B-spline function Y component brightness value of 16 pixels in this sampled point space is carried out interpolation, obtain the control vertex matrix matrix P of this Biquadratic B-spline function;

C. the sampled point space is amplified the resampling space that n doubly obtains 4n * 4n, will apply to the resampling space by the control vertex matrix P that operation b obtains and obtain 4n * 4n matrix, and n+1 in this 4n * 4n matrix walked to 2n is capable, n+1 be listed as to the common n of 2n row ²Individual element assignment is given the respective pixel when pretreatment unit, as the Y component brightness value of these pixels;

(3) U, the V component of the target image that obtains afterwards finishing dealing with through step (2) carry out the bilinear interpolation computing, obtain U, the V component brightness value of scaled images;

(4) according to Y, U and the V component of scaled images, scaled images is transformed into the RGB color space.

As follows to the conversion method of YUV color space in the described step (1) by the RGB color space conversion:

$\left\{\begin{array}{c}Y=0.299\×R+0.587\×G+0.114\×B\\ U=0.492\×(B-Y)\\ V=0.877\×(R-Y)\end{array}\right.$

The red, green, blue color value of R, G, B difference remarked pixel in the formula, Y is the luminance channel value of pixel, U and V are two color channel values of pixel, the expression aberration.

Interpolation process among the operation b of described step (2) is as follows:

For the pixel of 16 interpolations in this sampled point space, with (x _c, y _d) the expression sampled point (c, position coordinates d), 1≤c≤4,1≤d≤4 wherein, D be the brightness value matrix in this sampled point space, it is a quadravalence matrix, the brightness value of each element correspondence relevant position pixel:

$D=\left[\begin{array}{cccc}{D}_{11}& D_{12}& D_{13}& D_{14}\\ D_{21}& D_{22}& D_{23}& D_{24}\\ D_{31}& D_{32}& D_{33}& D_{34}\\ D_{41}& D_{42}& D_{43}& D_{44}\end{array}\right]$

To these 16 element interpolation, (u v) makes promptly to be to locate a Biquadratic B-spline function S

P is the control vertex matrix of Biquadratic B-spline function, and u, v are two parameter axles of Biquadratic B-spline function, and valid interval is 2≤u≤4,2≤v≤4, and Nu, Nv are respectively two spline base functions on the parameter axle, with the position coordinates (x of pixel _c, y _d) parametrization to the valid interval of u, v parameter axle, form evenly cutting apart on this valid interval, promptly get x ₁=2, x ₂=8/3, x ₃=10/3, x ₄=4; y ₁=2, y ₂=8/3, y ₃=10/3, y ₄=4, calculation control summit matrix

Wherein

$N_u=\left[\begin{array}{cccc}{N}_{\mathrm{1,4}}\left(x_1\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(x_1\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(x_1\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(x_1\right)\\ N_{\mathrm{1,4}}\left(x_2\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(x_2\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(x_3\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(x_2\right)\\ N_{\mathrm{1,4}}\left(x_3\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(x_3\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(x_3\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(x_3\right)\\ N_{\mathrm{1,4}}\left(x_4\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(x_4\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(x_4\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(x_4\right)\end{array}\right]$

$=\left[\begin{array}{cccc}1/2& 1/2& 0& 0\\ 1/18& 13/18& 2/9& 0\\ 0& 2/9& 13/18& 0\\ 0& 0& 1/2& 1/2\end{array}\right]$

$N_v=\left[\begin{array}{cccc}{N}_{\mathrm{1,4}}\left(y_1\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(y_1\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(y_1\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(y_1\right)\\ N_{\mathrm{1,4}}\left(y_2\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(y_2\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(y_2\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(y_2\right)\\ N_{\mathrm{1,4}}\left(y_3\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(y_3\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(y_3\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(y_3\right)\\ N_{\mathrm{1,4}}\left(y_4\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(y_4\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(y_4\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(y_4\right)\end{array}\right]$

$=\left[\begin{array}{cccc}1/2& 1/2& 0& 0\\ 1/18& 13/18& 2/9& 0\\ 0& 2/9& 13/18& 0\\ 0& 0& 1/2& 1/2\end{array}\right]$

Obtain thus a Biquadratic B-spline function S (u, v)=N _uP (N _v) ^T, to realize interpolation to each sampled point.

Among described step (2) the operation c, for the resampling space, with (x _e, y _f) the new pixel of expression (e, f) position coordinates, 1≤e≤4n wherein, 1≤f≤4n to u, v parameter axle, forms evenly cutting apart on the valid interval with this position coordinate parametersization, gets

Accounting equation:

$S^{,}(u,v)={\mathrm{\&Sigma;}}_{i=1}^4{\mathrm{\&Sigma;}}_{j=1}^4{P}_{\mathrm{ij}}{N}_{i,4}^{,}\left(u\right)N_{i,4}^{,}\left(v\right)=N_u^{,}P{\left(N_v^{,}\right)}^T$

Wherein P is the control vertex matrix of being asked, and N ' u, N ' v are the spline base functions that this branch is cut off:

$N_u^{,}=\left[\begin{array}{cccc}{N}_{\mathrm{1,4}}\left(x_1\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(x_1\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(x_1\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(x_1\right)\\ N_{\mathrm{1,4}}\left(x_2\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(x_2\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(x_2\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(x_2\right)\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ N_{\mathrm{1,4}}\left(x_{4n}\right)& N_{\mathrm{2,4}}\left(x_{4n}\right)& N_{\mathrm{3,4}}\left(x_{4n}\right)& N_{\mathrm{4,4}}\left(x_{4n}\right)\end{array}\right]$

$N_v^{,}=\left[\begin{array}{cccc}{N}_{\mathrm{1,4}}\left(y_1\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(y_1\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(y_1\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(y_1\right)\\ N_{\mathrm{1,4}}\left(y_2\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(y_2\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(y_2\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(y_2\right)\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ N_{\mathrm{1,4}}\left(y_{4n}\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(y_{4n}\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(y_{4n}\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(y_{4n}\right)\end{array}\right]$

Obtain a 4n * 4n matrix S thus ' _{4n * 4n}, and with this matrix n+1 walk to that 2n is capable, n+1 is listed as to 2n row n altogether ²Individual element assignment is given the respective pixel when pretreatment unit in the target image, as the Y component brightness value of these pixels.

The bilinear interpolation calculating process is in the described step (3):

With f (x, y) certain pixel (x, U y), V component value in the expression source images (5), 1≤x≤M, 1≤y≤N is with T (s, t) pixel (s, U t), V component value, 1≤s≤nM in the expression target image (6), 1≤t≤nN, n are enlargement factor, note s1=int (s/n), s2=s/n-s1, t1=int (t/n), t2=t/n-t1, int is a bracket function, and then the corresponding relation formula of target image (6) U, V component value and source images (5) U, V component value is:

T(s，t)＝(1-s2)·(1-t2)·f(s1，t1)+(1-s2)·t2·f(s1，t1+1)+s2·(1-t2)·f(s1+1，t1)+s2·t2·f(s1+1，t1+1)。

As follows to the conversion method of RGB color space in the described step (4) by the YUV color space conversion:

$\left\{\begin{array}{c}R=Y+1.14\&times;Y\\ G=Y-0.394\&times;U-0.581\&times;V\\ B=Y+2.032\&times;U\end{array}\right.$

The present invention proposes a kind of image-scaling method based on Biquadratic B-spline local interpolation, adopted four sampled points to be different from traditional quadratic interpolation function, has good locality, be easy to Parallel Implementation, can quicken at GPU, thereby can obtain to be similar to the bicubic interpolation algorithm effects, improve efficient simultaneously.

Description of drawings

Algorithm synoptic diagram when Fig. 1 amplifies twice for adopting image-scaling method of the present invention to image;

Fig. 2 is the process flow diagram of image-scaling method of the present invention.

Embodiment

Referring to Fig. 1,2, the present invention is based on the image-scaling method of Biquadratic B-spline local interpolation, be example to amplify twice, may further comprise the steps:

(1) with pixel resolution be 5 * 5 source images 5 by the RGB color space conversion to the YUV color space, conversion method is as follows:

$\left\{\begin{array}{c}Y=0.299*R+0.587*G+0.114*B\\ U=0.492*(B-Y)\\ V=0.877(R-Y)\end{array}\right.$

The red, green, blue color value of R, G, B difference remarked pixel in the formula, Y is the luminance channel value of pixel, U and V are two color channel values of pixel, the expression aberration;

(2) source images 5 being mapped to resolution is 10 * 10 target image 6, and the combination of pixels matrix with 2 * 2 is divided into 25 processing units as a processing unit 1 with this target image 6, and each processing unit 1 is carried out following three operations:

A. this processing unit 1 is mapped to forward in the source images 5, generates a mapping point 2;

B. in source images 5, get around this mapping point 24 * 4 matrix area as a sampled point space 3, make 2 one-tenth of mapping points, the second row secondary series element of sampled point space 3 quadravalence matrixes for this reason, (u v) carries out interpolation to 16 sampled points in this sampled point space 3 with a Biquadratic B-spline function S.Interpolation process is as follows:

For the pixel of 16 interpolations in this sampled point space (3), with (x _c, y _d) the expression sampled point (c, position coordinates d), 1≤c≤4,1≤d≤4 wherein, D be the brightness value matrix in this sampled point space (3), it is a quadravalence matrix, the brightness value of each element correspondence relevant position pixel:

$D=\left[\begin{array}{cccc}{D}_{11}& D_{12}& D_{13}& D_{14}\\ D_{21}& D_{22}& D_{23}& D_{24}\\ D_{31}& D_{32}& D_{33}& D_{34}\\ D_{41}& D_{42}& D_{43}& D_{44}\end{array}\right]$

To these 16 element interpolation, (u v) makes promptly to be to locate a Biquadratic B-spline function S P is the control vertex matrix of Biquadratic B-spline function, and u, v are two parameter axles of Biquadratic B-spline function, and valid interval is 2≤u≤4,2≤v≤4, and Nu, Nv are respectively two spline base functions on the parameter axle, with the position coordinates (x of pixel _c, y _d) parametrization to the valid interval of u, v parameter axle, form evenly cutting apart on this valid interval, promptly get x ₁=2, x ₂=8/3, x ₃=10/3, x ₄=4; y ₁=2, y ₂=8/3, y ₃=10/3, y ₄=4, calculation control summit matrix

Wherein

$N_u=\left[\begin{array}{cccc}{N}_{\mathrm{1,4}}\left(x_1\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(x_1\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(x_1\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(x_1\right)\\ N_{\mathrm{1,4}}\left(x_2\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(x_2\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(x_3\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(x_2\right)\\ N_{\mathrm{1,4}}\left(x_3\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(x_3\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(x_3\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(x_3\right)\\ N_{\mathrm{1,4}}\left(x_4\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(x_4\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(x_4\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(x_4\right)\end{array}\right]$

$=\left[\begin{array}{cccc}1/2& 1/2& 0& 0\\ 1/18& 13/18& 2/9& 0\\ 0& 2/9& 13/18& 0\\ 0& 0& 1/2& 1/2\end{array}\right]$

$N_v=\left[\begin{array}{cccc}{N}_{\mathrm{1,4}}\left(y_1\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(y_1\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(y_1\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(y_1\right)\\ N_{\mathrm{1,4}}\left(y_2\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(y_2\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(y_2\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(y_2\right)\\ N_{\mathrm{1,4}}\left(y_3\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(y_3\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(y_3\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(y_3\right)\\ N_{\mathrm{1,4}}\left(y_4\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(y_4\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(y_4\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(y_4\right)\end{array}\right]$

$=\left[\begin{array}{cccc}1/2& 1/2& 0& 0\\ 1/18& 13/18& 2/9& 0\\ 0& 2/9& 13/18& 0\\ 0& 0& 1/2& 1/2\end{array}\right]$

Obtain thus a Biquadratic B-spline function S (u, v)=N _uP (N _v) ^T, to realize interpolation to each sampled point.

C. will finish sampled point space after the interpolation and amplify 2 times and obtain 8 * 8 resampling space 4, will apply to resampling space 4 by the control vertex matrix P that operation b obtains, the space 4 that resamples hereto is with (x _e, y _f) (wherein 1≤e≤8,1≤f≤8 to u, v parameter axle, form evenly cutting apart on the valid interval with this position coordinate parametersization to the new pixel of expression, get for e, f) position coordinates

Accounting equation:

$S^{,}(u,v)={\mathrm{\&Sigma;}}_{i=1}^4{\mathrm{\&Sigma;}}_{j=1}^4{P}_{\mathrm{ij}}{N}_{i,4}^{,}\left(u\right)N_{i,4}^{,}\left(v\right)=N_u^{,}P{\left(N_v^{,}\right)}^T$

The control vertex matrix asked of matrix P wherein, N ' u, N ' v are the spline base functions that this branch is cut off:

$N_u^{,}=\left[\begin{array}{cccc}{N}_{\mathrm{1,4}}\left(x_1\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(x_1\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(x_1\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(x_1\right)\\ N_{\mathrm{1,4}}\left(x_2\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(x_2\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(x_2\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(x_2\right)\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ N_{\mathrm{1,4}}\left(x_{4n}\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(x_{4n}\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(x_{4n}\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(x_{4n}\right)\end{array}\right]$

$N_v^{,}=\left[\begin{array}{cccc}{N}_{\mathrm{1,4}}\left(y_1\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(y_1\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(y_1\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(y_1\right)\\ N_{\mathrm{1,4}}\left(y_2\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(y_2\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(y_2\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(y_2\right)\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ N_{\mathrm{1,4}}\left(y_{4n}\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,4}}\left(y_{4n}\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,4}}\left(y_{4n}\right)& {\mathrm{<figure-callout\; id="4"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{4,4}}\left(y_{4n}\right)\end{array}\right]$

As shown in Figure 1,4 * 4 sampled point space 3 is amplified to 8 * 8 resampling space S ' _{8 * 8}After, can find S ' through observing _{8 * 8}In what use only is the part in the upper left corner 4 * 4, so in calculating in order to reduce calculated amount, can only calculate this part, promptly for 8 * 4 matrix N ' _uAnd N ' _v, the part that only need get its first half 4 * 4 gets final product, and then has:

$N_u^{,}=N_v^{,}=\left[\begin{array}{cccc}{N}_{\mathrm{0,3}}\left(x_0\right)& N_{\mathrm{1,3}}\left(x_0\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,3}}\left(x_0\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,3}}\left(x_0\right)\\ N_{\mathrm{0,3}}\left(x_1\right)& N_{\mathrm{1,3}}\left(x_1\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,3}}\left(x_1\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,3}}\left(x_1\right)\\ N_{\mathrm{0,3}}\left(x_2\right)& N_{\mathrm{1,3}}\left(x_2\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,3}}\left(x_2\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,3}}\left(x_2\right)\\ N_{\mathrm{0,3}}\left(x_3\right)& N_{\mathrm{1,3}}\left(x_3\right)& {\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{2,3}}\left(x_3\right)& {\mathrm{<figure-callout\; id="3"\; label="N"\; filenames="HSA00000097964200011.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\mathrm{3,3}}\left(x_3\right)\end{array}\right]$

$=\left[\begin{array}{cccc}0.5& 0.5& 0& 0\\ 0.2551& 0.7041& 0.0408& 0\\ 0.0918& 0.7449& 0.1633& 0\\ 0.0102& 0.6224& 0.3673& 0\end{array}\right]$

Obtain one 8 * 8 matrix S thus ' _{8 * 8}, and with this matrix the 3rd walk to the 4th row, the 3rd row to the 4th row totally 4 element assignment give respective pixel in the target image when pretreatment unit 1, as the Y component brightness value of these pixels.

(3) U, the V component of the target image that obtains afterwards finishing dealing with through step (2) carry out the bilinear interpolation computing, obtain new images, and the bilinear interpolation calculating process is:

With f (x, y) certain pixel (x, U y), V component value in the expression source images (5), 1≤x≤M, 1≤y≤N is with T (s, t) pixel (s, U t), V component value, 1≤s≤nM in the expression target image (6), 1≤t≤nN, n are enlargement factor, note s1=int (s/n), s2=s/n-s1, t1=int (t/n), t2=t/n-t1, int is a bracket function, and then the corresponding relation formula of target image (6) U, V component value and source images (5) U, V component value is:

T(s，t)＝(1-s2)·(1-t2)·f(s1，t1)+(1-s2)·t2·f(s1，t1+1)+s2·(1-t2)·f(s1+1，t1)+s2·t2·f(s1+1，t1+1)；

(4) with new images by the YUV color space conversion to the RGB color space, obtain final processing result image, conversion method is as follows:

$\left\{\begin{array}{c}Y=0.299\&times;R+0.587\&times;G+0.114\&times;B\\ U=0.492\&times;(B-Y)\\ V=0.877\&times;(R-Y)\end{array}\right.$

The red, green, blue color value of R, G, B difference remarked pixel in the formula, Y is the luminance channel value of pixel, U and V are two color channel values of pixel, the expression aberration.

Claims (6)

1. image-scaling method based on Biquadratic B-spline local interpolation, this method may further comprise the steps:

(1) with resolution be the source images (5) of M * N by the RGB color space conversion to the YUV color space;

(2) source images (5) that will be transformed into behind the YUV color space amplifies, obtain the target image that resolution is nM * nN (6), n represents that source images needs amplification multiple, combination of pixels matrix with n * n travels through this target image (6) as a processing unit (1), each processing unit (1) is carried out following three operations, until the Y component brightness value that obtains scaled images:

A. this processing unit (1) is mapped to forward in the source images (5), generates a mapping point (2);

B. in source images (5), get this mapping point (2) on every side the matrix area of 4 * 4 pixels as a sampled point space (3), make mapping point (2) become the 2nd row the 2nd column element of sampled point space (3) quadravalence matrix for this reason, with a Biquadratic B-spline function Y component brightness value of 16 pixels in this sampled point space (3) is carried out interpolation, obtain the control vertex matrix P of this Biquadratic B-spline function;

C. sampled point space (3) are amplified the resampling space (4) that n doubly obtains 4n * 4n, to apply to resampling space (4) by the control vertex matrix P that operation b obtains and obtain 4n * 4n matrix, and with n+1 in this 4n * 4n matrix walk to that 2n is capable, n+1 be listed as to the 2n row altogether n2 element assignment give the respective pixel of working as pretreatment unit (1), as the Y component brightness value of these pixels;

(3) U, the V component of the target image (6) that obtains afterwards finishing dealing with through step (2) carry out the bilinear interpolation computing, obtain U, the V component of scaled images;

(4) according to Y, U and the V component of scaled images, scaled images is transformed into the RGB color space.

2. image-scaling method according to claim 1 is characterized in that: and usefulness Biquadratic B-spline function S in the step (2) (u, v)=N _uP (N _v) ^TY component brightness value to 16 pixels in sampled point space (3) carries out interpolation, in the described Biquadratic B-spline function:

P is the control vertex matrix of Biquadratic B-spline function;

U, v are two parameter axles of Biquadratic B-spline function;

Nu, Nv are respectively the spline base function on two parameter axles of Biquadratic B-spline function.

3. image-scaling method according to claim 2 is characterized in that: the control vertex matrix P=N of described Biquadratic B-spline function _u ^-1D (N _v ^T) ^-1, wherein D is the brightness value matrix in sampled point space (3).

4. image-scaling method according to claim 3 is characterized in that: described

$N_u=\left[\begin{array}{cccc}1/2& 1/2& 0& 0\\ 1/18& 13/18& 2/9& 0\\ 0& 2/9& 13/18& 0\\ 0& 0& 1/2& 1/2\end{array}\right];$

$N_v=\left[\begin{array}{cccc}1/2& 1/2& 0& 0\\ 1/18& 13/18& 2/9& 0\\ 0& 2/9& 13/18& 0\\ 0& 0& 1/2& 1/2\end{array}\right].$

5. image-scaling method according to claim 4 is characterized in that: the 4n described in the step (2) * 4n matrix is:

S ' (u, v)=N _u' P (N _v') ^T, wherein

$N_u^{,}=\left[\begin{array}{cccc}{N}_{\mathrm{1,4}}\left(x_1\right)& N_{\mathrm{2,4}}\left(x_1\right)& N_{\mathrm{3,4}}\left(x_1\right)& N_{\mathrm{4,4}}\left(x_1\right)\\ N_{\mathrm{1,4}}\left(x_2\right)& N_{\mathrm{2,4}}\left(x_2\right)& N_{\mathrm{3,4}}\left(x_2\right)& N_{\mathrm{4,4}}\left(x_2\right)\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ N_{\mathrm{1,4}}\left(x_{4n}\right)& N_{\mathrm{2,4}}\left(x_{4n}\right)& N_{\mathrm{3,4}}\left(x_{4n}\right)& N_{\mathrm{4,4}}\left(x_{4n}\right)\end{array}\right];$

$N_v^{,}=\left[\begin{array}{cccc}{N}_{\mathrm{1,4}}\left(y_1\right)& N_{\mathrm{2,4}}\left(y_1\right)& N_{\mathrm{3,4}}\left(y_1\right)& N_{\mathrm{4,4}}\left(y_1\right)\\ N_{\mathrm{1,4}}\left(y_2\right)& N_{\mathrm{2,4}}\left(y_2\right)& N_{\mathrm{3,4}}\left(y_2\right)& N_{\mathrm{4,4}}\left(y_2\right)\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ N_{\mathrm{1,4}}\left(y_{4n}\right)& N_{\mathrm{2,4}}\left(y_{4n}\right)& N_{\mathrm{3,4}}\left(y_{4n}\right)& N_{\mathrm{4,4}}\left(y_{4n}\right)\end{array}\right].$

6. image-scaling method according to claim 5 is characterized in that: U, V component brightness value T (s, t)=(1-s2) (1-t2) f (s1 of scaled images in the step (3), t1)+(1-s2) t2f (s1, t1+1)+and s2 (1-t2) f (s1+1, t1)+s2t2f (s1+1, t1+1);

Wherein s, t are the pixel coordinate in the scaled images;

s1＝int(s/n)；

s2＝s/n-s1；

t1＝int(t/n)；

t2＝t/n-t1；

(wherein x, y are the coordinate of this pixel in source images (5) to f for x, y) U, the V component value of certain pixel in the expression source images (5);

N is an enlargement factor.

Images