图像处理之错切变换


图像处理之错切变换

一：基本数学知识：

图像错切变换在图像几何形变方面非常有用，常见的错切变换分为X方向与Y方向的

错切变换。对应的数学矩阵分别如下：



根据上述矩阵假设P(x1, y1)为错切变换之前的像素点，则错切变换以后对应的像素

P’(x2, y2)当X方向错切变换时：



当Y方向错切变换时：



二：程序实现基本思路

实现图像错切变换时，必须考虑图像将目标像素点坐标变为源相点坐标时小数部分对

像素值的影响，这里通过临近点插值算法实现了目标像素值的计算。根据目标像素计

算源像素的公式可以根据上面的数学公式运算以后分别求的x1,y1的值。由于错切以

后图像会在宽或者高上比原图像大，多出来的这些背景像素默认填充颜色为黑色。

类ShearFilter实现了图像水平或者垂直方向的错切变换，支持角度与背景颜色参数

设置。

三：编程关键点解析

Ø 计算错切以后图像的宽与高

[java]
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double angleValue = (angle/180.0d) * Math.PI;
outh = vertical ? (int)(height + width * Math.tan(angleValue)) : height;
outw = vertical ? width : (int)(width + height * Math.tan(angleValue));
System.out.println("after shear, new width : " + outw);
System.out.println("after shear, new height: " + outh);

double angleValue = (angle/180.0d) * Math.PI;
outh = vertical ? (int)(height + width * Math.tan(angleValue)) : height;
outw = vertical ? width : (int)(width + height * Math.tan(angleValue));
System.out.println("after shear, new width : " + outw);
System.out.println("after shear, new height: " + outh);

Ø 根据目标像素点坐标计算源像素点坐标

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double prow = vertical ? row + Math.tan(angleValue) * (col - width) : row;
double pcol = vertical ? col : col + Math.tan(angleValue) * (row - height);
int[] rgb = getPixel(inPixels, width, height, prow, pcol);

double prow = vertical ? row + Math.tan(angleValue) * (col - width) : row;
double pcol = vertical ? col : col + Math.tan(angleValue) * (row - height);
int[] rgb = getPixel(inPixels, width, height, prow, pcol);

Ø 临近点插值计算目标像素点像素值

[java]
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private int[] getPixel(int[] input, int width, int height,
double prow, double pcol) {
double row = Math.floor(prow);
double col = Math.floor(pcol);
if(row < 0 || row >= height) {
return new int[]{backgroundColor.getRed(),
backgroundColor.getGreen(),
backgroundColor.getBlue()};
}
if(col < 0 || col >= width) {
return new int[]{backgroundColor.getRed(),
backgroundColor.getGreen(),
backgroundColor.getBlue()};
}
double u = vertical ? (prow - row) : pcol - col;
int nextCol = (int)(col + 1);
int nextRow = (int)(row + 1);
if((col + 1) >= width) {
nextCol = (int)col;
}
if((row + 1) >= height) {
nextRow = (int)row;
}
int index1 = (int)(row * width + col);
int index2 = vertical ? (int)(nextRow * width + col) : (int)(row * width + nextCol);

int tr1, tr2;
int tg1, tg2;
int tb1, tb2;

tr1 = (input[index1] >> 16) & 0xff;
tg1 = (input[index1] >> 8) & 0xff;
tb1 = input[index1] & 0xff;

tr2 = (input[index2] >> 16) & 0xff;
tg2 = (input[index2] >> 8) & 0xff;
tb2 = input[index2] & 0xff;

int tr = (int)(tr1 * (1-u) + tr2 * u);
int tg = (int)(tg1 * (1-u) + tg2 * u);
int tb = (int)(tb1 * (1-u) + tb2 * u);

return new int[]{tr, tg, tb};
}

private int[] getPixel(int[] input, int width, int height,
double prow, double pcol) {
double row = Math.floor(prow);
double col = Math.floor(pcol);
if(row < 0 || row >= height) {
return new int[]{backgroundColor.getRed(),
backgroundColor.getGreen(),
backgroundColor.getBlue()};
}
if(col < 0 || col >= width) {
return new int[]{backgroundColor.getRed(),
backgroundColor.getGreen(),
backgroundColor.getBlue()};
}
double u = vertical ? (prow - row) : pcol - col;
int nextCol = (int)(col + 1);
int nextRow = (int)(row + 1);
if((col + 1) >= width) {
nextCol = (int)col;
}
if((row + 1) >= height) {
nextRow = (int)row;
}
int index1 = (int)(row * width + col);
int index2 = vertical ? (int)(nextRow * width + col) : (int)(row * width + nextCol);

int tr1, tr2;
int tg1, tg2;
int tb1, tb2;

tr1 = (input[index1] >> 16) & 0xff;
tg1 = (input[index1] >> 8) & 0xff;
tb1 = input[index1] & 0xff;

tr2 = (input[index2] >> 16) & 0xff;
tg2 = (input[index2] >> 8) & 0xff;
tb2 = input[index2] & 0xff;

int tr = (int)(tr1 * (1-u) + tr2 * u);
int tg = (int)(tg1 * (1-u) + tg2 * u);
int tb = (int)(tb1 * (1-u) + tb2 * u);

return new int[]{tr, tg, tb};
}

四：运行效果



五：类ShearFilter完整代码

[java]
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package com.gloomyfish.filter.study;

import java.awt.Color;
import java.awt.image.BufferedImage;
import java.awt.image.ColorModel;

public class ShearFilter extends AbstractBufferedImageOp {
private int outw;
private int outh;
private double angle;
private Color backgroundColor;
private boolean vertical;

public void setVertical(boolean vertical) {
this.vertical = vertical;
}

public ShearFilter()
{
backgroundColor = Color.BLACK;
vertical = false;
this.angle = 20;
}

public int getOutw() {
return outw;
}
public void setOutw(int outw) {
this.outw = outw;
}
public int getOuth() {
return outh;
}
public void setOuth(int outh) {
this.outh = outh;
}
public double getAngle() {
return angle;
}
public void setAngle(double angle) {
this.angle = angle;
}
public Color getBackgroundColor() {
return backgroundColor;
}
public void setBackgroundColor(Color backgroundColor) {
this.backgroundColor = backgroundColor;
}
@Override
public BufferedImage filter(BufferedImage src, BufferedImage dest) {
int width = src.getWidth();
int height = src.getHeight();

double angleValue = (angle/180.0d) * Math.PI;
outh = vertical ? (int)(height + width * Math.tan(angleValue)) : height;
outw = vertical ? width : (int)(width + height * Math.tan(angleValue));
System.out.println("after shear, new width : " + outw);
System.out.println("after shear, new height: " + outh);

int[] inPixels = new int[width*height];
int[] outPixels = new int[outh*outw];
getRGB( src, 0, 0, width, height, inPixels );
int index = 0;
for(int row=0; row<outh; row++) {
int ta = 0;
for(int col=0; col<outw; col++) {
double prow = vertical ? row + Math.tan(angleValue) * (col - width) : row;
double pcol = vertical ? col : col + Math.tan(angleValue) * (row - height);
int[] rgb = getPixel(inPixels, width, height, prow, pcol);
index = row * outw + col;
outPixels[index] = (ta << 24) | (rgb[0] << 16) | (rgb[1] << 8) | rgb[2];
}
}

if ( dest == null )
dest = createCompatibleDestImage( src, null );
setRGB( dest, 0, 0, outw, outh, outPixels );
return dest;
}

private int[] getPixel(int[] input, int width, int height,
double prow, double pcol) {
double row = Math.floor(prow);
double col = Math.floor(pcol);
if(row < 0 || row >= height) {
return new int[]{backgroundColor.getRed(), backgroundColor.getGreen(), backgroundColor.getBlue()};
}
if(col < 0 || col >= width) {
return new int[]{backgroundColor.getRed(), backgroundColor.getGreen(), backgroundColor.getBlue()};
}
double u = vertical ? (prow - row) : pcol - col;
int nextCol = (int)(col + 1);
int nextRow = (int)(row + 1);
if((col + 1) >= width) {
nextCol = (int)col;
}
if((row + 1) >= height) {
nextRow = (int)row;
}
int index1 = (int)(row * width + col);
int index2 = vertical ? (int)(nextRow * width + col) : (int)(row * width + nextCol);

int tr1, tr2;
int tg1, tg2;
int tb1, tb2;

tr1 = (input[index1] >> 16) & 0xff;
tg1 = (input[index1] >> 8) & 0xff;
tb1 = input[index1] & 0xff;

tr2 = (input[index2] >> 16) & 0xff;
tg2 = (input[index2] >> 8) & 0xff;
tb2 = input[index2] & 0xff;

int tr = (int)(tr1 * (1-u) + tr2 * u);
int tg = (int)(tg1 * (1-u) + tg2 * u);
int tb = (int)(tb1 * (1-u) + tb2 * u);

return new int[]{tr, tg, tb};
}

public BufferedImage createCompatibleDestImage(BufferedImage src, ColorModel dstCM) {
if ( dstCM == null )
dstCM = src.getColorModel();
return new BufferedImage(dstCM, dstCM.createCompatibleWritableRaster(outw, outh), dstCM.isAlphaPremultiplied(), null);
}

}

package com.gloomyfish.filter.study;

import java.awt.Color;
import java.awt.image.BufferedImage;
import java.awt.image.ColorModel;

public class ShearFilter extends AbstractBufferedImageOp {
private int outw;
private int outh;
private double angle;
private Color backgroundColor;
private boolean vertical;

public void setVertical(boolean vertical) {
this.vertical = vertical;
}

public ShearFilter()
{
backgroundColor = Color.BLACK;
vertical = false;
this.angle = 20;
}

public int getOutw() {
return outw;
}
public void setOutw(int outw) {
this.outw = outw;
}
public int getOuth() {
return outh;
}
public void setOuth(int outh) {
this.outh = outh;
}
public double getAngle() {
return angle;
}
public void setAngle(double angle) {
this.angle = angle;
}
public Color getBackgroundColor() {
return backgroundColor;
}
public void setBackgroundColor(Color backgroundColor) {
this.backgroundColor = backgroundColor;
}
@Override
public BufferedImage filter(BufferedImage src, BufferedImage dest) {
int width = src.getWidth();
int height = src.getHeight();

double angleValue = (angle/180.0d) * Math.PI;
outh = vertical ? (int)(height + width * Math.tan(angleValue)) : height;
outw = vertical ? width : (int)(width + height * Math.tan(angleValue));
System.out.println("after shear, new width : " + outw);
System.out.println("after shear, new height: " + outh);

int[] inPixels = new int[width*height];
int[] outPixels = new int[outh*outw];
getRGB( src, 0, 0, width, height, inPixels );
int index = 0;
for(int row=0; row<outh; row++) {
int ta = 0;
for(int col=0; col<outw; col++) {
double prow = vertical ? row + Math.tan(angleValue) * (col - width) : row;
double pcol = vertical ? col : col + Math.tan(angleValue) * (row - height);
int[] rgb = getPixel(inPixels, width, height, prow, pcol);
index = row * outw + col;
outPixels[index] = (ta << 24) | (rgb[0] << 16) | (rgb[1] << 8) | rgb[2];
}
}

if ( dest == null )
dest = createCompatibleDestImage( src, null );
setRGB( dest, 0, 0, outw, outh, outPixels );
return dest;
}

private int[] getPixel(int[] input, int width, int height,
double prow, double pcol) {
double row = Math.floor(prow);
double col = Math.floor(pcol);
if(row < 0 || row >= height) {
return new int[]{backgroundColor.getRed(), backgroundColor.getGreen(), backgroundColor.getBlue()};
}
if(col < 0 || col >= width) {
return new int[]{backgroundColor.getRed(), backgroundColor.getGreen(), backgroundColor.getBlue()};
}
double u = vertical ? (prow - row) : pcol - col;
int nextCol = (int)(col + 1);
int nextRow = (int)(row + 1);
if((col + 1) >= width) {
nextCol = (int)col;
}
if((row + 1) >= height) {
nextRow = (int)row;
}
int index1 = (int)(row * width + col);
int index2 = vertical ? (int)(nextRow * width + col) : (int)(row * width + nextCol);

int tr1, tr2;
int tg1, tg2;
int tb1, tb2;

tr1 = (input[index1] >> 16) & 0xff;
tg1 = (input[index1] >> 8) & 0xff;
tb1 = input[index1] & 0xff;

tr2 = (input[index2] >> 16) & 0xff;
tg2 = (input[index2] >> 8) & 0xff;
tb2 = input[index2] & 0xff;

int tr = (int)(tr1 * (1-u) + tr2 * u);
int tg = (int)(tg1 * (1-u) + tg2 * u);
int tb = (int)(tb1 * (1-u) + tb2 * u);

return new int[]{tr, tg, tb};
}

public BufferedImage createCompatibleDestImage(BufferedImage src, ColorModel dstCM) {
if ( dstCM == null )
dstCM = src.getColorModel();
return new BufferedImage(dstCM, dstCM.createCompatibleWritableRaster(outw, outh), dstCM.isAlphaPremultiplied(), null);
}

}

下半年事情比较多，博客一直没有更新，感谢众多网友的关注与留言

我会继续努力的！再次声明一下：请不要向我索取源码！谢谢！
代码我在整理中，最终我会开源让大家自己下载，请耐心等待！