之前,俺也发过不少快速高斯模糊算法.
俺一般认为,只要处理一千六百万像素彩色图片,在2.2GHz的CPU上单核单线程超过1秒的算法,都是不快的.
之前发的几个算法,在俺2.2GHz的CPU上耗时都会超过1秒.
而众所周知,快速高斯模糊有很多实现方法:
1.FIR (Finite impulse response)
https://zh.wikipedia.org/wiki/%E9%AB%98%E6%96%AF%E6%A8%A1%E7%B3%8A
2.SII (Stacked integral images)
http://dx.doi.org/10.1109/ROBOT.2010.5509400
http://arxiv.org/abs/1107.4958
3.Vliet-Young-Verbeek (Recursive filter)
http://dx.doi.org/10.1016/0165-1684(95)00020-E
http://dx.doi.org/10.1109/ICPR.1998.711192
4.DCT (Discrete Cosine Transform)
http://dx.doi.org/10.1109/78.295213
5.box (Box filter)
http://dx.doi.org/10.1109/TPAMI.1986.4767776
6.AM(Alvarez, Mazorra)
http://www.jstor.org/stable/2158018
7.Deriche (Recursive filter)
http://hal.inria.fr/docs/00/07/47/78/PDF/RR-1893.pdf
8.ebox (Extended Box)
http://dx.doi.org/10.1007/978-3-642-24785-9_38
9.IIR (Infinite Impulse Response)
https://software.intel.com/zh-cn/articles/iir-gaussian-blur-filter-implementation-using-intel-advanced-vector-extensions
10.FA (Fast Anisotropic)
http://mathinfo.univ-reims.fr/IMG/pdf/Fast_Anisotropic_Gquss_Filtering_-_GeusebroekECCV02.pdf
......
实现高斯模糊的方法虽然很多,但是作为算法而言,核心关键是简单高效.
目前俺经过实测,IIR是兼顾效果以及性能的不错的方法,也是半径无关(即模糊不同强度耗时基本不变)的实现.
英特尔官方实现的这份:
IIR Gaussian Blur Filter Implementation using Intel® Advanced Vector Extensions [PDF 513KB]
source: gaussian_blur.cpp [36KB]
采用了英特尔处理器的流(SIMD)指令,算法处理速度极其惊人.
俺写算法追求干净整洁,高效简单,换言之就是不采用任何硬件加速方案,实现简单高效,以适应不同硬件环境.
故基于英特尔这份代码,俺对其进行了改写以及优化.
最终在俺2.20GHz的CPU上,单核单线程,不采用流(SIMD)指令,达到了,处理一千六百万像素的彩色照片仅需700毫秒左右.
按照惯例,还是贴个效果图比较直观.
之前也有网友问过这个算法的实现问题.
想了想,还是将代码共享出来,供大家参考学习.
完整代码:
void CalGaussianCoeff(float sigma, float * a0, float * a1, float * a2, float * a3, float * b1, float * b2, float * cprev, float * cnext) {
float alpha, lamma, k;
if (sigma < 0.5f)
sigma = 0.5f;
alpha = (float)exp((0.726) * (0.726)) / sigma;
lamma = (float)exp(-alpha);
*b2 = (float)exp(-2 * alpha);
k = (1 - lamma) * (1 - lamma) / (1 + 2 * alpha * lamma - (*b2));
*a0 = k; *a1 = k * (alpha - 1) * lamma;
*a2 = k * (alpha + 1) * lamma;
*a3 = -k * (*b2);
*b1 = -2 * lamma;
*cprev = (*a0 + *a1) / (1 + *b1 + *b2);
*cnext = (*a2 + *a3) / (1 + *b1 + *b2);
}
void gaussianHorizontal(unsigned char * bufferPerLine, unsigned char * pRowInitial, unsigned char * pColumn, int Width, int Height, int Channels, int Nwidth, int a0a1, int a2a3, int b1b2, int cprev, int cnext)
{
int HeightStep = Channels*Height;
int lastWidth = Width - 1;
if (Channels == 3)
{
int prevOut[3];
prevOut[0] = (pRowInitial[0] * cprev) >> 8;
prevOut[1] = (pRowInitial[1] * cprev) >> 8;
prevOut[2] = (pRowInitial[2] * cprev) >> 8;
for (int x = 0; x < Width; ++x) {
prevOut[0] = ((pRowInitial[0] * (a0a1)) - (prevOut[0] * (b1b2))) >> 16;
prevOut[1] = ((pRowInitial[1] * (a0a1)) - (prevOut[1] * (b1b2))) >> 16;
prevOut[2] = ((pRowInitial[2] * (a0a1)) - (prevOut[2] * (b1b2))) >> 16;
bufferPerLine[0] = prevOut[0];
bufferPerLine[1] = prevOut[1];
bufferPerLine[2] = prevOut[2];
bufferPerLine += Channels;
pRowInitial += Channels;
}
pRowInitial -= Channels;
pColumn += HeightStep * lastWidth;
bufferPerLine -= Channels;
prevOut[0] = (pRowInitial[0] * cnext) >> 8;
prevOut[1] = (pRowInitial[1] * cnext) >> 8;
prevOut[2] = (pRowInitial[2] * cnext) >> 8;
for (int x = lastWidth; x >= 0; --x) {
prevOut[0] = ((pRowInitial[0] * (a2a3)) - (prevOut[0] * (b1b2))) >> 16;
prevOut[1] = ((pRowInitial[1] * (a2a3)) - (prevOut[1] * (b1b2))) >> 16;
prevOut[2] = ((pRowInitial[2] * (a2a3)) - (prevOut[2] * (b1b2))) >> 16;
bufferPerLine[0] += prevOut[0];
bufferPerLine[1] += prevOut[1];
bufferPerLine[2] += prevOut[2];
pColumn[0] = bufferPerLine[0];
pColumn[1] = bufferPerLine[1];
pColumn[2] = bufferPerLine[2];
pRowInitial -= Channels;
pColumn -= HeightStep;
bufferPerLine -= Channels;
}
}
else if (Channels == 4)
{
int prevOut[4];
prevOut[0] = (pRowInitial[0] * cprev) >> 8;
prevOut[1] = (pRowInitial[1] * cprev) >> 8;
prevOut[2] = (pRowInitial[2] * cprev) >> 8;
prevOut[3] = (pRowInitial[3] * cprev) >> 8;
for (int x = 0; x < Width; ++x) {
prevOut[0] = ((pRowInitial[0] * (a0a1)) - (prevOut[0] * (b1b2))) >> 16;
prevOut[1] = ((pRowInitial[1] * (a0a1)) - (prevOut[1] * (b1b2))) >> 16;
prevOut[2] = ((pRowInitial[2] * (a0a1)) - (prevOut[2] * (b1b2))) >> 16;
prevOut[3] = ((pRowInitial[3] * (a0a1)) - (prevOut[3] * (b1b2))) >> 16;
bufferPerLine[0] = prevOut[0];
bufferPerLine[1] = prevOut[1];
bufferPerLine[2] = prevOut[2];
bufferPerLine[3] = prevOut[3];
bufferPerLine += Channels;
pRowInitial += Channels;
}
pRowInitial -= Channels;
pColumn += HeightStep * lastWidth;
bufferPerLine -= Channels;
prevOut[0] = (pRowInitial[0] * cnext) >> 8;
prevOut[1] = (pRowInitial[1] * cnext) >> 8;
prevOut[2] = (pRowInitial[2] * cnext) >> 8;
prevOut[3] = (pRowInitial[3] * cnext) >> 8;
for (int x = lastWidth; x >= 0; --x) {
prevOut[0] = ((pRowInitial[0] * a2a3) - (prevOut[0] * b1b2)) >> 16;
prevOut[1] = ((pRowInitial[1] * a2a3) - (prevOut[1] * b1b2)) >> 16;
prevOut[2] = ((pRowInitial[2] * a2a3) - (prevOut[2] * b1b2)) >> 16;
prevOut[3] = ((pRowInitial[3] * a2a3) - (prevOut[3] * b1b2)) >> 16;
bufferPerLine[0] += prevOut[0];
bufferPerLine[1] += prevOut[1];
bufferPerLine[2] += prevOut[2];
bufferPerLine[3] += prevOut[3];
pColumn[0] = bufferPerLine[0];
pColumn[1] = bufferPerLine[1];
pColumn[2] = bufferPerLine[2];
pColumn[3] = bufferPerLine[3];
pRowInitial -= Channels;
pColumn -= HeightStep;
bufferPerLine -= Channels;
}
}
else if (Channels == 1)
{
int prevOut = (pRowInitial[0] * cprev) >> 8;
for (int x = 0; x < Width; ++x) {
prevOut = ((pRowInitial[0] * (a0a1)) - (prevOut * (b1b2))) >> 16;
bufferPerLine[0] = prevOut;
bufferPerLine += Channels;
pRowInitial += Channels;
}
pRowInitial -= Channels;
pColumn += HeightStep*lastWidth;
bufferPerLine -= Channels;
prevOut = (pRowInitial[0] * cnext) >> 8;
for (int x = lastWidth; x >= 0; --x) {
prevOut = ((pRowInitial[0] * a2a3) - (prevOut * b1b2)) >> 16;;
bufferPerLine[0] += prevOut;
pColumn[0] = bufferPerLine[0];
pRowInitial -= Channels;
pColumn -= HeightStep;
bufferPerLine -= Channels;
}
}
}
void gaussianVertical(unsigned char * bufferPerLine, unsigned char * pRowInitial, unsigned char * pColInitial, int Height, int Width, int Channels, int a0a1, int a2a3, int b1b2, int cprev, int cnext) {
int WidthStep = Channels*Width;
int lastHeight = Height - 1;
if (Channels == 3)
{
int prevOut[3];
prevOut[0] = (pRowInitial[0] * cprev) >> 8;
prevOut[1] = (pRowInitial[1] * cprev) >> 8;
prevOut[2] = (pRowInitial[2] * cprev) >> 8;
for (int y = 0; y < Height; y++) {
prevOut[0] = ((pRowInitial[0] * a0a1) - (prevOut[0] * b1b2)) >> 16;
prevOut[1] = ((pRowInitial[1] * a0a1) - (prevOut[1] * b1b2)) >> 16;
prevOut[2] = ((pRowInitial[2] * a0a1) - (prevOut[2] * b1b2)) >> 16;
bufferPerLine[0] = prevOut[0];
bufferPerLine[1] = prevOut[1];
bufferPerLine[2] = prevOut[2];
bufferPerLine += Channels;
pRowInitial += Channels;
}
pRowInitial -= Channels;
bufferPerLine -= Channels;
pColInitial += WidthStep * lastHeight;
prevOut[0] = (pRowInitial[0] * cnext) >> 8;
prevOut[1] = (pRowInitial[1] * cnext) >> 8;
prevOut[2] = (pRowInitial[2] * cnext) >> 8;
for (int y = lastHeight; y >= 0; y--) {
prevOut[0] = ((pRowInitial[0] * a2a3) - (prevOut[0] * b1b2)) >> 16;
prevOut[1] = ((pRowInitial[1] * a2a3) - (prevOut[1] * b1b2)) >> 16;
prevOut[2] = ((pRowInitial[2] * a2a3) - (prevOut[2] * b1b2)) >> 16;
bufferPerLine[0] += prevOut[0];
bufferPerLine[1] += prevOut[1];
bufferPerLine[2] += prevOut[2];
pColInitial[0] = bufferPerLine[0];
pColInitial[1] = bufferPerLine[1];
pColInitial[2] = bufferPerLine[2];
pRowInitial -= Channels;
pColInitial -= WidthStep;
bufferPerLine -= Channels;
}
}
else if (Channels == 4)
{
int prevOut[4];
prevOut[0] = (pRowInitial[0] * cprev) >> 8;
prevOut[1] = (pRowInitial[1] * cprev) >> 8;
prevOut[2] = (pRowInitial[2] * cprev) >> 8;
prevOut[3] = (pRowInitial[3] * cprev) >> 8;
for (int y = 0; y < Height; y++) {
prevOut[0] = ((pRowInitial[0] * a0a1) - (prevOut[0] * b1b2)) >> 16;
prevOut[1] = ((pRowInitial[1] * a0a1) - (prevOut[1] * b1b2)) >> 16;
prevOut[2] = ((pRowInitial[2] * a0a1) - (prevOut[2] * b1b2)) >> 16;
prevOut[3] = ((pRowInitial[3] * a0a1) - (prevOut[3] * b1b2)) >> 16;
bufferPerLine[0] = prevOut[0];
bufferPerLine[1] = prevOut[1];
bufferPerLine[2] = prevOut[2];
bufferPerLine[3] = prevOut[3];
bufferPerLine += Channels;
pRowInitial += Channels;
}
pRowInitial -= Channels;
bufferPerLine -= Channels;
pColInitial += WidthStep*lastHeight;
prevOut[0] = (pRowInitial[0] * cnext) >> 8;
prevOut[1] = (pRowInitial[1] * cnext) >> 8;
prevOut[2] = (pRowInitial[2] * cnext) >> 8;
prevOut[3] = (pRowInitial[3] * cnext) >> 8;
for (int y = lastHeight; y >= 0; y--) {
prevOut[0] = ((pRowInitial[0] * a2a3) - (prevOut[0] * b1b2)) >> 16;
prevOut[1] = ((pRowInitial[1] * a2a3) - (prevOut[1] * b1b2)) >> 16;
prevOut[2] = ((pRowInitial[2] * a2a3) - (prevOut[2] * b1b2)) >> 16;
prevOut[3] = ((pRowInitial[3] * a2a3) - (prevOut[3] * b1b2)) >> 16;
bufferPerLine[0] += prevOut[0];
bufferPerLine[1] += prevOut[1];
bufferPerLine[2] += prevOut[2];
bufferPerLine[3] += prevOut[3];
pColInitial[0] = bufferPerLine[0];
pColInitial[1] = bufferPerLine[1];
pColInitial[2] = bufferPerLine[2];
pColInitial[3] = bufferPerLine[3];
pRowInitial -= Channels;
pColInitial -= WidthStep;
bufferPerLine -= Channels;
}
}
else if (Channels == 1)
{
int prevOut = 0;
prevOut = (pRowInitial[0] * cprev) >> 8;
for (int y = 0; y < Height; y++) {
prevOut = ((pRowInitial[0] * a0a1) - (prevOut * b1b2)) >> 16;
bufferPerLine[0] = prevOut;
bufferPerLine += Channels;
pRowInitial += Channels;
}
pRowInitial -= Channels;
bufferPerLine -= Channels;
pColInitial += WidthStep*lastHeight;
prevOut = (pRowInitial[0] * cnext) >> 8;
for (int y = lastHeight; y >= 0; y--) {
prevOut = ((pRowInitial[0] * a2a3) - (prevOut * b1b2)) >> 16;
bufferPerLine[0] += prevOut;
pColInitial[0] = bufferPerLine[0];
pRowInitial -= Channels;
pColInitial -= WidthStep;
bufferPerLine -= Channels;
}
}
}
//本人博客:http://tntmonks.cnblogs.com/ 转载请注明出处.
void GaussianBlurFilter(unsigned char * inputBuffer, unsigned char * outputBuffer, int Width, int Height, int Channels, float gaussianSigma = 2.0f) {
float a0, a1, a2, a3, b1, b2, cprev, cnext;
CalGaussianCoeff(gaussianSigma, &a0, &a1, &a2, &a3, &b1, &b2, &cprev, &cnext);
int icprev = cprev * 256;
int icnext = cnext * 256;
int a0a1 = (a0 + a1) * 65536;
int a2a3 = (a2 + a3) * 65536;
int b1b2 = (b1 + b2) * 65536;
int bufferSizePerLine = (Width > Height ? Width : Height) * Channels;
unsigned char * bufferPerLine = (unsigned char*)malloc(bufferSizePerLine);
unsigned char * cacheData = (unsigned char*)malloc(Height * Width * Channels);
int WidthStep = Width * Channels;
for (int y = 0; y < Height; ++y) {
unsigned char * pRowInitial = inputBuffer + WidthStep * y;
unsigned char * pColumnInitial = cacheData + y * Channels;
gaussianHorizontal(bufferPerLine, pRowInitial, pColumnInitial, Width, Height, Channels, Width, a0a1, a2a3, b1b2, icprev, icnext);
}
int HeightStep = Height*Channels;
for (int x = 0; x < Width; ++x) {
unsigned char * pColInitial = outputBuffer + x*Channels;
unsigned char * pRowInitial = cacheData + HeightStep * x;
gaussianVertical(bufferPerLine, pRowInitial, pColInitial, Height, Width, Channels, a0a1, a2a3, b1b2, icprev, icnext);
}
free(bufferPerLine);
free(cacheData);
}
调用方法:
GaussianBlurFilter(输入图像数据,输出图像数据,宽度,高度,通道数,强度)
注:支持通道数分别为 1 ,3 ,4.
关于IIR相关知识,参阅 百度词条 "IIR数字滤波器"
http://baike.baidu.com/view/3088994.htm
天下武功，唯快不破。
本文只是抛砖引玉一下，若有其他相关问题或者需求也可以邮件联系俺探讨。
邮箱地址是:
gaozhihan@vip.qq.com
题外话:
很多网友一直推崇使用opencv,opencv的确十分强大,但是若是想要有更大的发展空间以及创造力.
还是要一步一个脚印去实现一些最基本的算法,扎实的基础才是构建上层建筑的基本条件.
俺目前只是把opencv当资料库来看,并不认为opencv可以用于绝大多数的商业项目.
若本文帮到您,厚颜无耻求微信扫码打个赏.
