CN1858800A - Full phase discrete cosine changing interpolating kernel function and change for image resolution - Google Patents

Abstract

This invention relates to a total phase scatter cosine transformation interpolation core function and the change used in image resolution, in which, the improvent to the change of image resolution includes: total phase DCT core function replaces the 6-point cubic interpolation core function, namely, the value of an interpolation filter is computed with the expression of the total phase DCT core function and a regulation of coordinate, the pixel point values of a new image by computing the interpolation filter and the original image pixel value to get a new image after altering the resolution, in which, the scatter cosine transformation is Am=DCT(Xn) and the counter is Xn=IDCT(Am). Advantage: the value of the interpolation filter is computed by total phase DCT interpolation core function and the quality of the 6-point total phase DCT core function is higher than that of 6-point cubic core function.

Description

Full phase discrete cosine conversion interpolating kernel function and be used for the change of image resolution ratio

[technical field]: the present invention relates to the improvement of interpolating kernel function in the Computer Image Processing and be used for the technical field of Flame Image Process.

[background technology]: in Computer Image Processing, when needs change image resolution ratio, generally need: 1, input original image through following process; 2,, calculate the position of interpolation point according to the requirement of resolution changing; 3, calculate the value of interpolation filter according to the expression formula of interpolating kernel function; 4, by the value of interpolation filter and the pixel point value of original image calculated for pixel values new images; 5, obtain changing the later new images of resolution.This shows that the fine or not key of Computer Image Processing depends on interpolating kernel function.

The interpolating kernel function to changing image resolution ratio that exists at present has: bilinear interpolation kernel function, nearest-neighbor interpolating kernel function, the Sinc function that blocks, the Sinc function of windowing, secondary approach, cube interpolating kernel function, B-spline function and Gauss's interpolating kernel function.Above-mentioned several interpolating kernel function respectively has quality, and bilinear interpolation kernel function and nearest field interpolating kernel function are to use kernel function the most widely, but interpolation quality is not too excellent.The Sinc function that blocks, the Sinc function calculation amount of windowing is very big.Kernel functions such as secondary approaches interpolation quality in some interpolation task is very not high.6 * 6 cube interpolating kernel function with continuous second derivative is to calculate 6 the fastest nuclears in realization, and its Fourier local characteristics is also very good, is easy to realize having less interpolated error.B spline interpolation has above advantage too, however the boundary effect that 6 * 6 cube interpolation has avoided B batten technology to be produced by method itself.In the interpolation task of reality, there is not a kind of absolute interpolating method that surpasses other, particularly the occasion of having relatively high expectations for interpolation qualities such as geometric transformation that resembles medical image and Digital Television needs better interpolating method, so the interpolating kernel function leeway and the needs that also make further progress.

[summary of the invention]: the objective of the invention is to improve the interpolation quality of interpolating kernel function, a kind of full phase discrete cosine conversion interpolating kernel function is provided and is used for the change of image resolution ratio to view data.

The concrete construction process of the building method of full phase discrete cosine conversion provided by the invention (dct transform) interpolating kernel function is as follows:

(1) to known finite digital signal x (t), 0≤(t)＜NT, T are sampling interval, and N is a sampling number, X _n=x (nT), n=0,1, Λ, N-1 makes that discrete cosine transform is A _m=DCT (X _n), inverse discrete cosine transformation is X _n=IDCT (A _m), then have:

$A\left(l\right)=\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}\mathrm{\α}(l,n)x\left(n\right)---l=\mathrm{0,1},\mathrm{\Λ},N-1,$

$x\left(m\right)=\underset{l=0}{\overset{N-1}{\mathrm{\Σ}}}\mathrm{\β}(m,l)A\left(l\right)---m=\mathrm{0,1},\mathrm{\Λ},N-1,$

α represents the discrete cosine transform matrix; β represents the inverse discrete cosine transformation matrix;

(2) make t=m in the following formula, 0≤t≤N-1, t ∈ R, then signal can be by following formula reconstruct:

$\hat{x}\left(t\right)=\underset{l=0}{\overset{N-1}{\mathrm{\Σ}}}\mathrm{\β}(t,l)A\left(l\right)$

$=\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}H(t,n)x\left(n\right)$

Wherein, $H(t,n)=\underset{l=0}{\overset{N-1}{\mathrm{\Σ}}}\mathrm{\β}(t,l)\mathrm{\α}(l,n),$

If x (n) is the starting point of first data segment, interpolation point is τ apart from the distance of x (n), 0≤τ＜1,

What the reconstruction value that defines full phase interpolation was a N-1 data segment in the reconstruction value of interpolation point is average:

$\hat{x}\left(\mathrm{\τ}\right)=\frac{1}{N-1}\underset{i=0}{\overset{N-2}{\mathrm{\Σ}}}{\hat{x}}_i\left(\mathrm{\τ}\right)=\frac{1}{N-1}\underset{i=0}{\overset{N-2}{\mathrm{\Σ}}}\left[\underset{j=0}{\overset{N-1}{\mathrm{\Σ}}}H(i+\mathrm{\τ},j)x(n-i+j)\right]$

Make k=i-j,

Then:

$\hat{x}\left(\mathrm{\τ}\right)=\frac{1}{(N-1)}\underset{k=0}{\overset{N-2}{\mathrm{\Σ}}}x(n-k)\underset{i=k}{\overset{N-2}{\mathrm{\Σ}}}H(i+\mathrm{\τ},i-k)+\frac{1}{(N-1)}\underset{k=-N+1}{\overset{-1}{\mathrm{\Σ}}}x(n-k)\underset{i=0}{\overset{N-1+k}{\mathrm{\Σ}}}H(i+\mathrm{\τ},i-k)$

$\hat{x}\left(\mathrm{\τ}\right)=\frac{1}{N-1}\underset{k=-N+1}{\overset{N-2}{\mathrm{\Σ}}}x(n-k)h\left(k\right)$

Wherein, $h\left(k\right)=\left\{\begin{array}{cc}\frac{1}{N-1}\underset{i=k}{\overset{N-2}{\mathrm{\Σ}}}H(i+\mathrm{\τ},i-k)& k=\mathrm{0,1},\mathrm{\Λ},N-2\\ \frac{1}{N-1}\underset{i=0}{\overset{N-1+k}{\mathrm{\Σ}}}H(i+\mathrm{\τ},i-k)& k=-N+1,-N+2,\mathrm{\Λ},-1\end{array}\right.$ Be the discrete cosine transform interpolating kernel function.

The above-mentioned discrete cosine transform interpolating kernel function of a kind of employing is used for the change of image resolution ratio, and the change process of its image resolution ratio is as follows:

(1), input original image;

(2), according to the requirement of resolution changing, calculate the position of interpolation point;

(3), calculate the value of interpolation filter according to the expression formula of above-mentioned discrete cosine transform interpolating kernel function;

(4), by the value of interpolation filter and the pixel point value of original image calculated for pixel values new images;

(5), obtain changing the later new images of resolution.

Advantage of the present invention and good effect: interpolating kernel function provided by the invention is to be made of cosine function, experiment shows that the interpolation quality of 6 full-phase DCT kernel functions is higher than the interpolation quality of 6 cubes of kernel functions, and this point is contrasted as can be seen by the picture quality of Fig. 4, Fig. 5.The present invention is particularly useful for the occasion that interpolation qualities such as the geometric transformation of medical image and Digital Television are had relatively high expectations.

[description of drawings]:

Fig. 1 is the signal reconstruction principle schematic in the DCT territory;

Fig. 2 is to be the regulation synoptic diagram of example explanation interpolation formula coordinate with N=4;

Fig. 3 is an original image to be transformed;

Fig. 4 is first with behind 500 * 500 original image sub-sampling to 250 * 250, image is become again 500 * 500 result schematic diagram through 6 cubes of kernel function interpolations (existing method);

Fig. 5 is first with behind 500 * 500 original image sub-sampling to 250 * 250, image is become again 500 * 500 result schematic diagram through 6 full-phase DCT kernel function interpolations (the inventive method);

Fig. 6 is the original image that is used for conversion, and Fig. 6-1 is the image of 256 gray levels of 300 * 300; Fig. 6-2 is images of 256 gray levels of 256 * 256; Fig. 6-3 is images of 256 gray levels of 512 * 512; Fig. 6-4 is images of 256 gray levels of 500 * 500, and transformation results sees Table 1.

[embodiment]:

Embodiment 1

Employing discrete cosine transform provided by the invention (dct transform) interpolating kernel function, the detailed process that is used to change image resolution ratio are as follows:

(1), input original image;

(2), according to the requirement of resolution changing, calculate the position of interpolation point;

(3), calculate the value of interpolation filter according to the expression formula of above-mentioned discrete cosine transform interpolating kernel function;

(4), by the value of interpolation filter and the pixel point value of original image calculated for pixel values new images;

(5), obtain changing the later new images of resolution.

The detailed process of the building method of full phase discrete cosine conversion provided by the invention (dct transform) interpolating kernel function is as follows:

To known finite digital signal x (t), 0≤t＜NT is a sampling interval with T, and sampling number is N, X _n=x (nT), n=0,1, Λ, N-1; Make that discrete cosine transform is A _m=DCT (X _n), inverse discrete cosine transformation is X _n=IDCT (A _m), α represents the dct transform matrix; β represents the idct transform matrix, as shown in Figure 1:

$A\left(l\right)=\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}\mathrm{\α}(l,n)x\left(n\right)---l=\mathrm{0,1},\mathrm{\Λ},N-1$

Obtain original signal through the contravariant transducing again:

$x\left(m\right)=\underset{l=0}{\overset{N-1}{\mathrm{\Σ}}}\mathrm{\β}(m,l)A\left(l\right)---m=\mathrm{0,1},\mathrm{\Λ},N-1$

As in following formula, making t=m, 0≤t≤N-1, t ∈ R, then signal can be by following formula reconstruct:

$\hat{x}\left(t\right)=\underset{l=0}{\overset{N-1}{\mathrm{\Σ}}}\mathrm{\β}(t,l)A\left(l\right)$

$=\underset{l=0}{\overset{N-1}{\mathrm{\Σ}}}\mathrm{\β}(t,l)\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}\mathrm{\α}(l,n)x\left(n\right)$

$=\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}\left[\underset{l=0}{\overset{N-1}{\mathrm{\Σ}}}\mathrm{\β}(t,l)\mathrm{\α}(l,n)\right]x\left(n\right)$

$=\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}H(t,n)x\left(n\right)$

Wherein, $H(t,n)=\underset{l=0}{\overset{N-1}{\mathrm{\Σ}}}\mathrm{\β}(t,l)\mathrm{\α}(l,n)$

If x (n) is the starting point of first data segment, interpolation point is τ apart from the distance of x (n), and 0≤τ＜1 has N-1 data segment to comprise this interpolation point by the definition in full phase data space, and this N-1 data segment is respectively in the reconstruction value of interpolation point

${\hat{x}}_0\left(\mathrm{\τ}\right)=\underset{j=0}{\overset{N-1}{\mathrm{\Σ}}}H(\mathrm{\τ},j)x_0\left(j\right)=\underset{j=0}{\overset{N-1}{\mathrm{\Σ}}}H(\mathrm{\τ},j)x(n+j)$

${\hat{x}}_1\left(\mathrm{\τ}\right)=\underset{j=0}{\overset{N-1}{\mathrm{\Σ}}}H(1+\mathrm{\τ},j)x_1\left(j\right)=\underset{j=0}{\overset{N-1}{\mathrm{\Σ}}}H(1+\mathrm{\τ},j)x(n-1+j)$

${\hat{x}}_{N-2}\left(\mathrm{\τ}\right)=\underset{j=0}{\overset{N-1}{\mathrm{\Σ}}}H((N-2)+\mathrm{\τ},j)x_{N-2}\left(j\right)=\underset{j=0}{\overset{N-1}{\mathrm{\Σ}}}H((N-2)+\mathrm{\τ},j)x(n-N+2+j)$

What the reconstruction value that defines full phase interpolation was this N-1 data segment in the reconstruction value of interpolation point is average:

$\hat{x}\left(\mathrm{\τ}\right)=\frac{1}{N-1}\underset{i=0}{\overset{N-2}{\mathrm{\Σ}}}{\hat{x}}_i\left(\mathrm{\τ}\right)=\frac{1}{N-1}\underset{i=0}{\overset{N-2}{\mathrm{\Σ}}}\left[\underset{j=0}{\overset{N-1}{\mathrm{\Σ}}}H(i+\mathrm{\τ},j)x(n-i+j)\right]$

Make k=i-j, then:

$\hat{x}\left(\mathrm{\τ}\right)=\frac{1}{(N-1)}\underset{k=0}{\overset{N-2}{\mathrm{\Σ}}}x(n-k)\underset{i=k}{\overset{N-2}{\mathrm{\Σ}}}H(i+\mathrm{\τ},i-k)+\frac{1}{(N-1)}\underset{k=-N+1}{\overset{-1}{\mathrm{\Σ}}}x(n-k)\underset{i=0}{\overset{N-1+k}{\mathrm{\Σ}}}H(i+\mathrm{\τ},i-k)$

Then: $\hat{x}\left(\mathrm{\τ}\right)=\frac{1}{N-1}\underset{k=-N+1}{\overset{N-2}{\mathrm{\Σ}}}x(n-k)h\left(k\right)$

Wherein, $h\left(k\right)=\left\{\begin{array}{cc}\frac{1}{N-1}\underset{i=k}{\overset{N-2}{\mathrm{\Σ}}}H(i+\mathrm{\τ},i-k)& k=\mathrm{0,1},\mathrm{\Λ},N-2\\ \frac{1}{N-1}\underset{i=0}{\overset{N-1+k}{\mathrm{\Σ}}}H(i+\mathrm{\τ},i-k)& k=-N+1,-N+2,\mathrm{\Λ},-1\end{array}\right.$ Be the discrete cosine transform interpolating kernel function.The image that changes through the inventive method as shown in Figure 5.

Embodiment 2

As shown in Figure 2, be the regulation of the separable interpolation formula coordinate in example explanation DCT territory with N=4, " * " among the figure represents the position of interpolated point, 0≤τ＜1.

When N=4, $h\left(k\right)=\left\{\begin{array}{cc}\frac{1}{3}\underset{i=k}{\overset{2}{\mathrm{\Σ}}}H(i+\mathrm{\τ},i-k)& k=\mathrm{0,1,2}\\ \frac{1}{3}\underset{i=0}{\overset{3+k}{\mathrm{\Σ}}}H(i+\mathrm{\τ},i-k)& k=-1,-2,-3\end{array}\right.$

If true origin is positioned at interpolation point, variable x represents the distance of sampled point to interpolation point, is that the weighting function of sampled point is based on the interpolating kernel function of 6 dot informations (N=4) then:

$h_6\left(x\right)=\begin{array}{}\left\{\begin{array}{cc}\frac{1}{3}H(-x,0)& -3<x\&le;-2\\ \frac{1}{2}[H(-x,0)+H(1-x,1)]& -2<x\&le;-1\\ \frac{1}{3}[H(-x,0)+H(1-x,1)+H(2-x,2)]& -1<x\&le;0\\ \frac{1}{3}[H(1-x,1)+H(2-x,2)+H(3-x,3)]& 0<x\&le;1\\ \frac{1}{3}[H(2-x,2)+H(3-x,3)]& 1<x\&le;2\\ \frac{1}{3}H(3-x,3)& 2<x\&le;3\end{array}\right.\end{array}$

Its edge is more level and smooth than Fig. 4 as seen from Figure 5, and the ringing effect at edge does not have Fig. 4 obvious, illustrates that its picture quality is than Fig. 4 height.

From as shown in table 1 by the interpolation result that Fig. 6 implemented:

Image PSNR (dB) relatively after table 1 interpolation

	6 cubes	6 full-phase DCTs
			Fig. 6-1	37.018	37.135
Fig. 6-2	25.938	26.140
			Fig. 6-3	33.703	33.525
Fig. 6-4	18.409	18.741

Table 1 is: with Fig. 6-1 by 300 * 300 sub-samplings to 150 * 150 after, image is become again 300 * 300 result through 6 full-phase DCT kernel function interpolations; With Fig. 6-2 by 256 * 256 sub-samplings to 128 * 128 after, image is become again 256 * 256 result through 6 full-phase DCT kernel function interpolations; With Fig. 6-3 by 512 * 512 sub-samplings to 256 * 256 after, image is become again 512 * 512 result through 6 full-phase DCT kernel function interpolations; With Fig. 6-4 by 500 * 500 sub-samplings to 250 * 250 after, image is become again 500 * 500 result through 6 full-phase DCT kernel function interpolations.

6 full-phase DCT kernel function interpolations are better than 6 cubes of interpolation effects as can be seen from Table 1.

Claims (2)

1, the building method of full phase discrete cosine conversion interpolating kernel function is characterized in that the construction process of this interpolating kernel function is as follows:

(1) to known finite digital signal x (t), 0≤t＜NT, T are sampling interval, and N is a sampling number, X _n=x (nT), n=0,1, Λ, N-1 makes that discrete cosine transform is A _m=DCT (X _n), inverse discrete cosine transformation is X _n=IDCT (A _m), then have:

$A\left(l\right)=\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\mathrm{\&alpha;}(l,n)x\left(n\right),l=\mathrm{0,1},\mathrm{\&Lambda;},N-1,$

$x\left(m\right)=\underset{l=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\mathrm{\&beta;}(m,l)A\left(l\right),m=\mathrm{0,1},\mathrm{\&Lambda;},N-1,$

α represents the discrete cosine transform matrix; β represents the inverse discrete cosine transformation matrix;

(2) make t=m in the following formula, 0≤t≤N-1, t ∈ R, then signal can be by following formula reconstruct:

$\hat{x}\left(t\right)=\underset{l=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\mathrm{\&beta;}(t,l)A\left(l\right)$

$=\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}H(t,n)x\left(n\right)$

Wherein, $H(t,n)=\underset{l=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\mathrm{\&beta;}(t,l)\mathrm{\&alpha;}(l,n),$

If x (n) is the starting point of first data segment, interpolation point is τ apart from the distance of x (n), 0≤τ＜1, and what the reconstruction value that defines full phase interpolation was a N-1 data segment in the reconstruction value of interpolation point is average:

$\hat{x}\left(\mathrm{\&tau;}\right)=\frac{1}{N-1}\underset{i=0}{\overset{N-2}{\mathrm{\&Sigma;}}}{\hat{x}}_i\left(\mathrm{\&tau;}\right)=\frac{1}{N-1}\underset{i=0}{\overset{N-2}{\mathrm{\&Sigma;}}}\left[\underset{j=0}{\overset{N-1}{\mathrm{\&Sigma;}}}H(i+\mathrm{\&tau;},j)x(n-i+j)\right]$

Make k=i-j, then:

$\hat{x}\left(\mathrm{\&tau;}\right)=\frac{1}{(N-1)}\underset{k=0}{\overset{N-2}{\mathrm{\&Sigma;}}}x(n-k)\underset{i=k}{\overset{N-2}{\mathrm{\&Sigma;}}}H(i+\mathrm{\&tau;},i-k)+\frac{1}{(N-1)}\underset{k=-N+1}{\overset{-1}{\mathrm{\&Sigma;}}}x(n-k)\underset{i=0}{\overset{N-1+k}{\mathrm{\&Sigma;}}}H(i+\mathrm{\&tau;},i-k)$

Then: $\hat{x}\left(\mathrm{\&tau;}\right)=\frac{1}{N-1}\underset{k=-N+1}{\overset{N-2}{\mathrm{\&Sigma;}}}x(n-k)h\left(k\right)$

Wherein, $h\left(k\right)=\left\{\begin{array}{cc}\frac{1}{N-1}\underset{i=k}{\overset{N-2}{\mathrm{\&Sigma;}}}H(i+\mathrm{\&tau;},i-k)& k=\mathrm{0,1},\mathrm{\&Lambda;},N-2\\ \frac{1}{N-1}\underset{i=0}{\overset{N-1+k}{\mathrm{\&Sigma;}}}H(i+\mathrm{\&tau;},i-k)& k=-N+1,-N+2,\mathrm{\&Lambda;},-1\end{array}\right.$ Be the discrete cosine transform interpolating kernel function.

2, a kind of change of adopting the described discrete cosine transform interpolating kernel function of claim 1 to be used for image resolution ratio is characterized in that following process is passed through in the change of image resolution ratio:

(1), input original image;

(2), according to the requirement of resolution changing, calculate the position of interpolation point;

(3), the expression formula of discrete cosine transform interpolating kernel function according to claim 1 is calculated the value of interpolation filter;

(4), by the value of interpolation filter and the pixel point value of original image calculated for pixel values new images;

(5), obtain changing the later new images of resolution.

Images