图像放缩之双线性内插值

一：数学原理

在临近点插值的数学基础上，双线性插值，不是简单copy源像素的值，而是获取四个最邻

近目标像素的像素值乘以权重系数，简单的数学公式可以表示为:

D(x, y) = S(j, k) * a + S(j+1, k) *b + S(j+1,k+1) * c + S(j, K+1) * d 公式一

问题转化如何提取源像素的中四个临近点，根据临近点插值中从目标像素寻找最临近的源像

素点的方法:

Sx= Dx * (Sh/Dh) // row

Sy= Dy * (Sw/Dw) // column

公式的详细说明参见这里http://blog.csdn.net/jia20003/article/details/6907152

计算出来的值是浮点数坐标，分别取整数部分坐标为(j, k), 小数部分坐标为(t, u)



根据小数部分的(t,u)坐标，首先进行水平方向的权重计算得出

Q11 = S(j,k) * (1-t) + S(j, k+1) * t;

Q22 = S(j+1, k) * (1-t) + S(j+1,K+1) *t

利用Q11, Q22的值，进行垂直方向权重计算得出计算采样点值

D(x, y) = Q11*(1-u) + Q22 * u; 把Q11, Q22带入,最终有等式:

D(x, y) = S(j, k) *(1-t)*(1-u) + S(j, k+1)*t*(1-u) + S(j+1,k)*(1-t)*u + S(j+1,k+1)*t*u

从而得出四个对应的权重系数分别为:

a = (1-t)*(1-u)

b = (1-t)*u

c = t*u

d = t*(1-u)

带入公式一，即可得出目标像素的值。

二：双线性内插值算法优缺点

双线性内插值算法在图像的放缩处理中，具有抗锯齿功能, 是最简单和常见的图像放缩算法，但是双线性内插值算法没有考虑边缘和图像的梯度变化，相比之下双立方插值算法更好解决这些问题。

三：关键程序代码解析

根据目标像素坐标，计算采样点浮点数坐标的代码如下：

float rowRatio = ((float)srcH)/((float)destH);

float colRatio = ((float)srcW)/((float)destW);

double srcRow = ((float)row)*rowRatio;

double srcCol = ((float)col)*colRatio;

计算采样点的整数坐标和小数部分坐标代码如下：

double j = Math.floor(srcRow);

double t = srcRow – j

double k = Math.floor(srcCol);

double u = srcCol - k;

根据小数坐标(t,u)来计算四个相邻像素点权重系数代码如下：

double coffiecent1 = (1.0d-t)*(1.0d-u);

double coffiecent2 = (t)*(1.0d-u);

double coffiecent3 = t*u;

double coffiecent4 = (1.0d-t)*u;

处理边缘像素代码如下：

return x>max ? max : x<min? min : x;

四：程序运行效果如下






左边为源图像，右边为基于双线性内插值放大两倍以后的图像

五：双线性内插值JAVA算法代码

public class BilineInterpolationScale implements ImageScale {
public BilineInterpolationScale() {

}
/**
*
*/
@Override
public int[] imgScale(int[] inPixelsData, int srcW, int srcH, int destW, int destH) {
double[][][] input3DData = processOneToThreeDeminsion(inPixelsData, srcH, srcW);
int[][][] outputThreeDeminsionData = new int[destH][destW][4];
float rowRatio = ((float)srcH)/((float)destH);
float colRatio = ((float)srcW)/((float)destW);
for(int row=0; row<destH; row++) {
// convert to three dimension data
double srcRow = ((float)row)*rowRatio;
double j = Math.floor(srcRow);
double t = srcRow - j;
for(int col=0; col<destW; col++) {
double srcCol = ((float)col)*colRatio;
double k = Math.floor(srcCol);
double u = srcCol - k;
double coffiecent1 = (1.0d-t)*(1.0d-u);
double coffiecent2 = (t)*(1.0d-u);
double coffiecent3 = t*u;
double coffiecent4 = (1.0d-t)*u;

outputThreeDeminsionData[row][col][0] = (int)(coffiecent1 * input3DData[getClip((int)j,srcH-1,0)][getClip((int)k,srcW-1, 0)][0] +
coffiecent2 * input3DData[getClip((int)(j+1),srcH-1,0)][getClip((int)k,srcW-1,0)][0] +
coffiecent3 * input3DData[getClip((int)(j+1),srcH-1,0)][getClip((int)(k+1),srcW-1,0)][0] +
coffiecent4 * input3DData[getClip((int)j,srcH-1,0)][getClip((int)(k+1),srcW-1,0)][0]); // alpha

outputThreeDeminsionData[row][col][1] = (int)(coffiecent1 * input3DData[getClip((int)j,srcH-1,0)][getClip((int)k,srcW-1, 0)][1] +
coffiecent2 * input3DData[getClip((int)(j+1),srcH-1,0)][getClip((int)k,srcW-1,0)][1] +
coffiecent3 * input3DData[getClip((int)(j+1),srcH-1,0)][getClip((int)(k+1),srcW-1,0)][1] +
coffiecent4 * input3DData[getClip((int)j,srcH-1,0)][getClip((int)(k+1),srcW-1,0)][1]); // red

outputThreeDeminsionData[row][col][2] = (int)(coffiecent1 * input3DData[getClip((int)j,srcH-1,0)][getClip((int)k,srcW-1, 0)][2] +
coffiecent2 * input3DData[getClip((int)(j+1),srcH-1,0)][getClip((int)k,srcW-1,0)][2] +
coffiecent3 * input3DData[getClip((int)(j+1),srcH-1,0)][getClip((int)(k+1),srcW-1,0)][2] +
coffiecent4 * input3DData[getClip((int)j,srcH-1,0)][getClip((int)(k+1),srcW-1,0)][2]);// green

outputThreeDeminsionData[row][col][3] = (int)(coffiecent1 * input3DData[getClip((int)j,srcH-1,0)][getClip((int)k,srcW-1, 0)][3] +
coffiecent2 * input3DData[getClip((int)(j+1),srcH-1,0)][getClip((int)k,srcW-1,0)][3] +
coffiecent3 * input3DData[getClip((int)(j+1),srcH-1,0)][getClip((int)(k+1),srcW-1,0)][3] +
coffiecent4 * input3DData[getClip((int)j,srcH-1,0)][getClip((int)(k+1),srcW-1,0)][3]); // blue
}
}

return convertToOneDim(outputThreeDeminsionData, destW, destH);
}

private int getClip(int x, int max, int min) {
return x>max ? max : x<min? min : x;
}

/* <p> The purpose of this method is to convert the data in the 3D array of ints back into </p>
* <p> the 1d array of type int. </p>
*
*/
public int[] convertToOneDim(int[][][] data, int imgCols, int imgRows) {
// Create the 1D array of type int to be populated with pixel data
int[] oneDPix = new int[imgCols * imgRows * 4];

// Move the data into the 1D array. Note the
// use of the bitwise OR operator and the
// bitwise left-shift operators to put the
// four 8-bit bytes into each int.
for (int row = 0, cnt = 0; row < imgRows; row++) {
for (int col = 0; col < imgCols; col++) {
oneDPix[cnt] = ((data[row][col][0] << 24) & 0xFF000000)
| ((data[row][col][1] << 16) & 0x00FF0000)
| ((data[row][col][2] << 8) & 0x0000FF00)
| ((data[row][col][3]) & 0x000000FF);
cnt++;
}// end for loop on col

}// end for loop on row

return oneDPix;
}// end convertToOneDim

private double [][][] processOneToThreeDeminsion(int[] oneDPix2, int imgRows, int imgCols) {
double[][][] tempData = new double[imgRows][imgCols][4];
for(int row=0; row<imgRows; row++) {

// per row processing
int[] aRow = new int[imgCols];
for (int col = 0; col < imgCols; col++) {
int element = row * imgCols + col;
aRow[col] = oneDPix2[element];
}

// convert to three dimension data
for(int col=0; col<imgCols; col++) {
tempData[row][col][0] = (aRow[col] >> 24) & 0xFF; // alpha
tempData[row][col][1] = (aRow[col] >> 16) & 0xFF; // red
tempData[row][col][2] = (aRow[col] >> 8) & 0xFF;  // green
tempData[row][col][3] = (aRow[col]) & 0xFF;       // blue
}
}
return tempData;
}

}