Amplification and reduction of images (3)--double cube interpolation algorithm __ Image recognition

-----------------------------reprinted from Jia20003 blog " double cubic interpolation of image scaling" -----------------------------------

One: Mathematical Principles

If you know a function f (x) and its derivative at x=0,x=1, then the function can be interpolated between [0,1], when the function

When expressed as a three-time polynomial, we call the cubic interpolation. A three-time polynomial and its derivative:

F (x) =ax^3 +bx^2 + cx + D

F ' (x) =3ax^2 + 2bx +c

The polynomial at x=0, the X=1 value and its derivative values are:

F (0) = D;

F (1) = a + B + C + D;

F ' (0) =c

F ' (1) =3a + 2b + C

The above four equations can be equivalent to the following transformations:

A= 2f (0) –2f (1) + F ' (0) + F ' (1)

b= -3f (0) + 3f (1) –2f ' (0) –f ' (1)

c= F ' (0)

D= f ' (1)

Suppose you have four point values P0, p1, p2, p3 respectively in X=-1, X=0, X=1, x=2, assign values to f (0), F (1), F ' (0), respectively,

F ' (1) is:

F (0) = P1

F (1) = P2

F ' (0) = (p2–p0)/2

F ' (1) = (P3-P1)/2

This our cubic interpolation formula becomes:

F (p0,p1,p2,p3, X) = ( -1/2p0 + 3/2p1-3/2p2+ 1/2p3) X^3 + (p0-5/2p1 + 2p2-1/2d) x^2 + ( -1/2p0 +

1/2P2) x + p1

The two-cubic interpolation is the expression of cubic interpolation in two-dimensional space, and the interpolation formula can be expressed as:

G (x, y) = f (f (p00, P01, P02, p03, y), F (p10,p11, P12, P13, y), F (P20, P21, P22, P23, y), F (P30, p31, P32, P33, y), X)

The value of a g (x, y) target interpolation point can be obtained by solving the 16 parameters.

Two: dual-cubic interpolation advantages and disadvantages

Double-cubic interpolation in the image amplification process can retain more image details, enlarge the image with anti-aliasing after the function,

At the same time, the effect of image and source image is more real, the disadvantage is that the computational volume is relatively large, is a common three kinds of image amplification algorithm

One of the largest computational weights, it is said that Photoshop image amplification is the basic two-cubic interpolation optimization algorithm

Third: The operation effect of the program is as follows:

Four: Critical code resolution

Do not want to explain too much, the most important thing is to calculate the number of floating-point coordinates of the decimal part, that is, X, y range of values between [0,1]

V: Java-based program complete source code

[Java]   View plain  copy package cn.edu.jxau.luoweifu;      public class  bicubicinterpolationscale {          private static  double a00, a01, a02, a03;       private static  double a10, a11, a12, a13;       private static  double a20, a21, a22, a23;       private static  double a30, a31, a32, a33;       private static int  srcWidth;       private static int srcHeight;              /**       *  Double cubic interpolation        *  @param  inPixelsData  pixel matrix array         * @param  srcW  Original image width        *  @param  srcH  original image high         *  @param  destW  target image width        *  @param  destH  target Image High        *  @return   processed push three matrix array         */       public static int[] imgscale (int[)  INPIXELSDATA, INT SRCW, INT SRCH, INT DESTW, INT DESTH)  {            double[][][] input3DData =  Processonetothreedeminsion (INPIXELSDATA, SRCH, SRCW);            int[][][] outputthreedeminsionda