CN100563295C - A kind of image magnification method based on estimation error in the linear interpolation arithmetic - Google Patents
A kind of image magnification method based on estimation error in the linear interpolation arithmetic Download PDFInfo
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Abstract
The invention belongs to Digital Image Processing and video display technology field, be specifically related to image magnification method based on linear interpolation arithmetic.The present invention proposes a kind of image magnification method based on linear interpolation arithmetic, can keep the image high-frequency information preferably, specifically may further comprise the steps: a, the position of calculating interpolation point P; B, obtain the pixel value of adjacent 4 pixels of interpolation point P present position; The estimation error of c, the calculated for pixel values linear interpolation by adjacent 4 pixels is with the compensation of described estimation error as the linear interpolation result; D, calculating linear interpolation result and estimation error sum, its result is the pixel value of interpolation point P.The present invention has overcome former linear interpolation arithmetic and has caused that high frequency is degenerated, image blurring defective.Image amplification effect after handling by the present invention has reached the image effect after the bicubic interpolation algorithm process substantially, and operand is little, is easy to hardware and realizes.
Description
Technical Field
The invention belongs to the technical field of digital image processing and video display, and particularly relates to an image amplification method based on linear interpolation operation.
Background
Image magnification is one of the most important techniques in digital image processing, and commonly used magnification methods include nearest neighbor interpolation, bilinear interpolation, bicubic interpolation and the like. The nearest interpolation is simple and fast, but the amplified image has serious mosaic phenomenon; bilinear interpolation can degrade the high-frequency part of the image, and cause the blurring of the image; the bicubic interpolation algorithm well retains high-frequency information of an image, edges are sharper, details are clearer, and the computation amount and hardware implementation difficulty are large.
Disclosure of Invention
The invention aims to solve the technical problem of providing an image amplification method based on linear interpolation operation, which can better reserve high-frequency information of an image, and enable edges to be sharper and details to be clearer.
The technical scheme adopted by the invention for solving the technical problems is that the image amplification method based on error estimation in linear interpolation operation is characterized by comprising the following steps:
a. calculating the position of the interpolation point P;
b. when interpolation in the horizontal direction is carried out, pixel values of 4 adjacent pixel points of the horizontal position of an interpolation point P are obtained; when interpolation in the vertical direction is carried out, pixel values of 4 adjacent pixel points in the vertical position of an interpolation point P are obtained;
c. calculating error estimation of linear interpolation according to pixel values of 4 adjacent pixel points, and taking the error estimation as compensation of a linear interpolation result;
d. and calculating the sum of the linear interpolation result and the error estimation, wherein the result is the pixel value of the interpolation point P.
Specifically, the error estimation is that when interpolation in the horizontal direction is performed, the error estimation is as follows:
wherein the pixel values of 4 points adjacent to the interpolation point P in the horizontal direction are respectively f (P)i-1)、f(Pi)、f(Pi+1)、f(Pi+2) (ii) a x is an interpolation point P and an adjacent pixel point PiX ∈ (0, 1); then, the pixel value f (P) of the interpolation point P when performing interpolation in the horizontal direction is:
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the error estimation when interpolation in the vertical direction is performed is as follows:
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wherein the pixel values of 4 points adjacent to the interpolation point P in the vertical direction are respectively f (P)j-1)、f(Pj)、f(Pj+1)、f(Pj+2) (ii) a y is an interpolation point P and an adjacent pixel point PiY e (0, 1); then, the pixel value f (P) of the interpolation point P when the interpolation is performed in the vertical direction is:
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the method has the advantages that the interpolation point of the original bilinear interpolation method is determined by the values of 4 pixel points around the original image, and the determination of the pixel value of the interpolation point refers to the values of 16 pixel points around the point after the improvement of error estimation is introduced. The invention overcomes the defects of high-frequency degradation and image blurring caused by the original linear interpolation operation. The image amplification effect processed by the method basically achieves the image effect processed by the bicubic interpolation algorithm, and the method is small in operand and easy to realize by hardware.
Drawings
FIG. 1 is a schematic diagram of the present invention;
fig. 2 is a schematic diagram of the derivation of the error estimate.
Detailed Description
The principle of the calculation of the error estimate E relative to cubic interpolation in linear interpolation is as follows:
linear interpolation is shown in FIG. 1, PiAnd Pi+1For the adjacent 2 pixels of the interpolation point P in the horizontal direction, the formula f' (P) of linear interpolation is f (P)i)+[f(Pi+1)-f(Pi)]X, x ∈ (0, 1); linear interpolation is not smooth and can cause degradation of high frequency portions of the image. To keep the high-frequency information of the image, a curve formed by the interpolation point P and the pixel point needs to be as smooth as possible, so that an error estimation E is introduced, and the calculation method of the pixel value of the interpolation point P is perfected:
f(P)＝f(Pi)+[f(Pi+1)-f(Pi)]·x+E，x∈(0，1)；
the error estimate E is derived as follows:
the newton first order interpolation polynomial is:
wherein,
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error estimation for newton first order interpolation polynomial;
as shown in fig. 2, the-1, 0, 1, 2 respectively indicate the position of the interpolation point x adjacent to the 4 points in the horizontal direction, if: x is the number of0Substituting-1, h-3 into formula (1) to obtain:
if: x is the number of0Substituting 0, h-1 into formula (1) to obtain:
in the error estimation of the present invention, it is assumed that f "(x) has a small shift in x e (-1, 2), i.e.: f' (xi)1)≈f″(ξ2) And is uniformly expressed by f' (sigma), and is obtained by subtracting the two expressions of the expression (2) and the expression (3):
let x be 1/2 to give:
when x is 1/2, the value of point a is: f (0) + [ f (1) -f (0) ] (1/2); the values of point B are:
from the above, the length of the line segment AB is used as an approximate estimation value of f' (σ), and the length in equation (3) is expressedAs the error of the linear interpolation, and the variable E as the estimated value of the error. Will be provided with
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Bringing in
When x is 1/2, it is concluded that the error estimate E is AB/8.
Then, a quadratic function is used and an error estimation value E is introduced to approximate and estimate an error curve ferror(x) As shown in fig. 2, we obtain: f. of1(x)＝-4·E·x2+(4·E-a)·x；f2(x) The error curve is curve f1(x) And the straight line f2(x) The difference between: thus: f. oferror(x)＝4·E·x·(1-x)；
Bringing E ═ AB/8 into the above formula to give
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E is ferror(x) The 4 points adjacent to the interpolation point in the horizontal direction are respectively Pi-1、Pi、Pi+1、Pi+2Then there is error estimation in the horizontal direction interpolationThe evaluation E is:
similarly, let 4 points adjacent to each other in the horizontal direction of the interpolation point be Pj-1、Pj、Pj+1、Pj+2From the above derivation, the error estimation value E during interpolation in the vertical direction is:
examples
In the process of realizing image amplification, the invention firstly amplifies the image in the horizontal direction to obtain a transition image, and then amplifies the transition image in the vertical direction to obtain the final amplified image. Of course, the magnification in the vertical direction may be performed first and then the magnification in the horizontal direction may be performed. The essence of the amplification is to interpolate the two-dimensional signal in one dimension.
Let the original image size be M × N, the enlarged image size be X × Y, and the first row (column) count starting with zero row (column) and the last row (column) be M-1 row (N-1 column).
Firstly, interpolation operation in the horizontal direction is carried out, and the specific steps are as follows:
1. for the r-th row (r is 0, 1, 2 … … M-1) of the original image, the horizontal position s of the interpolation point P is calculated in turn: s ═ 0.5+ N/(2 x Y) + C x N/Y; where C is 0, 1, 2 … … Y-1 is the number of columns after the image is enlarged.
Therefore, four known points which are adjacent to each other before and after the position of the interpolation point P can be found: pi-1＝floor(s)-1、Pi＝floor(s)、Pi+1＝floor(s)+1、Pi+2Floor(s) + 2; where the function floor(s) is rounded down for s.
2. Calculating P to PiDistance x of (2): x ═ s-floor(s);
3. according to the interpolation formula provided by the invention, the pixel value of the interpolation point P is calculated:
4. and sequentially completing the interpolation operation of the lines from 0 to M-1 in the horizontal direction, and thus completing the amplification of the whole image in the horizontal direction to obtain a transition image T with the size of M multiplied by Y.
Then, the interpolation in the vertical direction is carried out, and the specific steps are as follows:
5. for the C-th column of the transition image T, C is 0, 1, 2 … … Y-1, and the vertical position T of the interpolation point P is sequentially calculated in the vertical direction as: t is-0.5 + M/(2X) + R M/X, wherein R is 0, 1, 2 … … X-1, which is the line number after the image is enlarged;
obtaining four adjacent known points above and below the position of the point P to be inserted: pj-1＝floor(t)-1、Pj＝floor(t)、Pj+1＝floor(t)+1、Pj+2＝floor(t)+2；
6. Calculating P to PjDistance y of (d): y-floor (t);
7. according to the interpolation formula provided by the invention, the pixel value of the point P to be interpolated is calculated:
8. and sequentially finishing the interpolation operation in the vertical direction from the O to the Y-1 columns, and finishing the amplification of the whole transition image T in the vertical direction to obtain a final amplified image with the size of X multiplied by Y.
The experiment verifies that: the image processed by the invention is obviously improved compared with the image processed by bilinear interpolation, the overall amplification effect is equivalent to bicubic interpolation, but the computation amount is far lower than that of bicubic interpolation.
Claims (1)
1. An image amplification method based on error estimation in linear interpolation operation is characterized by specifically comprising the following steps:
a. calculating the position of the interpolation point P;
b. when interpolation in the horizontal direction is carried out, pixel values of 4 adjacent pixel points of the horizontal position of an interpolation point P are obtained; when interpolation in the vertical direction is carried out, pixel values of 4 adjacent pixel points in the vertical position of an interpolation point P are obtained;
c. calculating error estimation of linear interpolation according to pixel values of 4 adjacent pixel points, and taking the error estimation as compensation of a linear interpolation result;
d. calculating the sum of the linear interpolation result and the error estimation, wherein the result is the pixel value of the interpolation point P;
the error estimation in the step c is specifically that when interpolation in the horizontal direction is performed, the error estimation is as follows:
wherein the pixel values of 4 adjacent pixel points in the horizontal direction of the interpolation point P are respectively
f(Pi-1)、f(Pi)、f(Pi+1)、f(Pi+2) (ii) a x is an interpolation point P and an adjacent pixel point PiX ∈ (0, 1); in step d, levelWhen the direction is interpolated, the pixel value f (P) of the interpolation point P is:
the error estimation in the interpolation in the vertical direction is as follows:
wherein the pixel values of 4 pixel points adjacent to the interpolation point P in the vertical direction are respectively f (P)j-1)、f(Pj)、f(Pj+1)、f(Pj+2) (ii) a y is an interpolation point and an adjacent pixel point PjY e (0, 1); in step d, the pixel value f (P) of the interpolation point P when performing interpolation in the vertical direction is:
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| CN101437137B (en) * | 2008-12-19 | 2010-08-25 | 四川虹微技术有限公司 | Field interpolation method |
| CN101815157B (en) * | 2009-02-24 | 2013-01-23 | 虹软(杭州)科技有限公司 | Image and video amplification method and relevant image processing device |
| CN102263924B (en) * | 2010-05-29 | 2014-05-28 | 比亚迪股份有限公司 | Image processing method based on bicubic interpolation and image display method |
| CN102760281A (en) * | 2011-04-26 | 2012-10-31 | 撖龙 | Image resizing method |
| CN103366342B (en) * | 2013-07-02 | 2015-12-23 | 天津大学 | Be applied to the subsection linearity inser value method that video image amplifies |
| CN104184981B (en) * | 2014-08-27 | 2017-12-15 | 深圳市华星光电技术有限公司 | A kind of low-res display methods and equipment based on reduction pixel sampling processing |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN1094209A (en) * | 1993-01-14 | 1994-10-26 | 三星电子株式会社 | The interpolation method of digital image data and circuit thereof |
| CN1614635A (en) * | 2004-12-13 | 2005-05-11 | 北京中星微电子有限公司 | Method for image amplifying interpolation |
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| CN1094209A (en) * | 1993-01-14 | 1994-10-26 | 三星电子株式会社 | The interpolation method of digital image data and circuit thereof |
| CN1614635A (en) * | 2004-12-13 | 2005-05-11 | 北京中星微电子有限公司 | Method for image amplifying interpolation |
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