半径无关快速高斯模糊实现(附完整C代码)

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 * lpRowInitial, unsigned char  * lpColumn, int width, int height, int Channels, int Nwidth, float a0a1, float a2a3, float b1b2, float  cprev, float cnext)
{
int HeightStep = Channels*height;
int WidthSubOne = width - 1;
if (Channels == 3)
{
float prevOut[3];
prevOut[0] = (lpRowInitial[0] * cprev);
prevOut[1] = (lpRowInitial[1] * cprev);
prevOut[2] = (lpRowInitial[2] * cprev);
for (int x = 0; x < width; ++x) {
prevOut[0] = ((lpRowInitial[0] * (a0a1)) - (prevOut[0] * (b1b2)));
prevOut[1] = ((lpRowInitial[1] * (a0a1)) - (prevOut[1] * (b1b2)));
prevOut[2] = ((lpRowInitial[2] * (a0a1)) - (prevOut[2] * (b1b2)));
bufferPerLine[0] = prevOut[0];
bufferPerLine[1] = prevOut[1];
bufferPerLine[2] = prevOut[2];
bufferPerLine += Channels;
lpRowInitial += Channels;
}
lpRowInitial -= Channels;
lpColumn += HeightStep * WidthSubOne;
bufferPerLine -= Channels;
prevOut[0] = (lpRowInitial[0] * cnext);
prevOut[1] = (lpRowInitial[1] * cnext);
prevOut[2] = (lpRowInitial[2] * cnext);

for (int x = WidthSubOne; x >= 0; --x) {
prevOut[0] = ((lpRowInitial[0] * (a2a3)) - (prevOut[0] * (b1b2)));
prevOut[1] = ((lpRowInitial[1] * (a2a3)) - (prevOut[1] * (b1b2)));
prevOut[2] = ((lpRowInitial[2] * (a2a3)) - (prevOut[2] * (b1b2)));
bufferPerLine[0] += prevOut[0];
bufferPerLine[1] += prevOut[1];
bufferPerLine[2] += prevOut[2];
lpColumn[0] = bufferPerLine[0];
lpColumn[1] = bufferPerLine[1];
lpColumn[2] = bufferPerLine[2];
lpRowInitial -= Channels;
lpColumn -= HeightStep;
bufferPerLine -= Channels;
}
}
else if (Channels == 4)
{
float prevOut[4];

prevOut[0] = (lpRowInitial[0] * cprev);
prevOut[1] = (lpRowInitial[1] * cprev);
prevOut[2] = (lpRowInitial[2] * cprev);
prevOut[3] = (lpRowInitial[3] * cprev);
for (int x = 0; x < width; ++x) {
prevOut[0] = ((lpRowInitial[0] * (a0a1)) - (prevOut[0] * (b1b2)));
prevOut[1] = ((lpRowInitial[1] * (a0a1)) - (prevOut[1] * (b1b2)));
prevOut[2] = ((lpRowInitial[2] * (a0a1)) - (prevOut[2] * (b1b2)));
prevOut[3] = ((lpRowInitial[3] * (a0a1)) - (prevOut[3] * (b1b2)));

bufferPerLine[0] = prevOut[0];
bufferPerLine[1] = prevOut[1];
bufferPerLine[2] = prevOut[2];
bufferPerLine[3] = prevOut[3];
bufferPerLine += Channels;
lpRowInitial += Channels;
}
lpRowInitial -= Channels;
lpColumn += HeightStep * WidthSubOne;
bufferPerLine -= Channels;

prevOut[0] = (lpRowInitial[0] * cnext);
prevOut[1] = (lpRowInitial[1] * cnext);
prevOut[2] = (lpRowInitial[2] * cnext);
prevOut[3] = (lpRowInitial[3] * cnext);

for (int x = WidthSubOne; x >= 0; --x) {
prevOut[0] = ((lpRowInitial[0] * a2a3) - (prevOut[0] * b1b2));
prevOut[1] = ((lpRowInitial[1] * a2a3) - (prevOut[1] * b1b2));
prevOut[2] = ((lpRowInitial[2] * a2a3) - (prevOut[2] * b1b2));
prevOut[3] = ((lpRowInitial[3] * a2a3) - (prevOut[3] * b1b2));
bufferPerLine[0] += prevOut[0];
bufferPerLine[1] += prevOut[1];
bufferPerLine[2] += prevOut[2];
bufferPerLine[3] += prevOut[3];
lpColumn[0] = bufferPerLine[0];
lpColumn[1] = bufferPerLine[1];
lpColumn[2] = bufferPerLine[2];
lpColumn[3] = bufferPerLine[3];
lpRowInitial -= Channels;
lpColumn -= HeightStep;
bufferPerLine -= Channels;
}
}
else if (Channels == 1)
{
float prevOut = (lpRowInitial[0] * cprev);

for (int x = 0; x < width; ++x) {
prevOut = ((lpRowInitial[0] * (a0a1)) - (prevOut  * (b1b2)));
bufferPerLine[0] = prevOut;
bufferPerLine += Channels;
lpRowInitial += Channels;
}
lpRowInitial -= Channels;
lpColumn += HeightStep*WidthSubOne;
bufferPerLine -= Channels;

prevOut = (lpRowInitial[0] * cnext);

for (int x = WidthSubOne; x >= 0; --x) {
prevOut = ((lpRowInitial[0] * a2a3) - (prevOut  * b1b2));
bufferPerLine[0] += prevOut;
lpColumn[0] = bufferPerLine[0];
lpRowInitial -= Channels;
lpColumn -= HeightStep;
bufferPerLine -= Channels;
}
}
}

void gaussianVertical(unsigned char * bufferPerLine, unsigned char * lpRowInitial, unsigned char * lpColInitial, int height, int width, int Channels, float a0a1, float a2a3, float b1b2, float  cprev, float  cnext) {

int WidthStep = Channels*width;
int HeightSubOne = height - 1;
if (Channels == 3)
{
float prevOut[3];
prevOut[0] = (lpRowInitial[0] * cprev);
prevOut[1] = (lpRowInitial[1] * cprev);
prevOut[2] = (lpRowInitial[2] * cprev);

for (int y = 0; y < height; y++) {
prevOut[0] = ((lpRowInitial[0] * a0a1) - (prevOut[0] * b1b2));
prevOut[1] = ((lpRowInitial[1] * a0a1) - (prevOut[1] * b1b2));
prevOut[2] = ((lpRowInitial[2] * a0a1) - (prevOut[2] * b1b2));
bufferPerLine[0] = prevOut[0];
bufferPerLine[1] = prevOut[1];
bufferPerLine[2] = prevOut[2];
bufferPerLine += Channels;
lpRowInitial += Channels;
}
lpRowInitial -= Channels;
bufferPerLine -= Channels;
lpColInitial += WidthStep * HeightSubOne;
prevOut[0] = (lpRowInitial[0] * cnext);
prevOut[1] = (lpRowInitial[1] * cnext);
prevOut[2] = (lpRowInitial[2] * cnext);
for (int y = HeightSubOne; y >= 0; y--) {
prevOut[0] = ((lpRowInitial[0] * a2a3) - (prevOut[0] * b1b2));
prevOut[1] = ((lpRowInitial[1] * a2a3) - (prevOut[1] * b1b2));
prevOut[2] = ((lpRowInitial[2] * a2a3) - (prevOut[2] * b1b2));
bufferPerLine[0] += prevOut[0];
bufferPerLine[1] += prevOut[1];
bufferPerLine[2] += prevOut[2];
lpColInitial[0] = bufferPerLine[0];
lpColInitial[1] = bufferPerLine[1];
lpColInitial[2] = bufferPerLine[2];
lpRowInitial -= Channels;
lpColInitial -= WidthStep;
bufferPerLine -= Channels;
}
}
else if (Channels == 4)
{
float prevOut[4];

prevOut[0] = (lpRowInitial[0] * cprev);
prevOut[1] = (lpRowInitial[1] * cprev);
prevOut[2] = (lpRowInitial[2] * cprev);
prevOut[3] = (lpRowInitial[3] * cprev);

for (int y = 0; y < height; y++) {
prevOut[0] = ((lpRowInitial[0] * a0a1) - (prevOut[0] * b1b2));
prevOut[1] = ((lpRowInitial[1] * a0a1) - (prevOut[1] * b1b2));
prevOut[2] = ((lpRowInitial[2] * a0a1) - (prevOut[2] * b1b2));
prevOut[3] = ((lpRowInitial[3] * a0a1) - (prevOut[3] * b1b2));
bufferPerLine[0] = prevOut[0];
bufferPerLine[1] = prevOut[1];
bufferPerLine[2] = prevOut[2];
bufferPerLine[3] = prevOut[3];
bufferPerLine += Channels;
lpRowInitial += Channels;
}
lpRowInitial -= Channels;
bufferPerLine -= Channels;
lpColInitial += WidthStep*HeightSubOne;
prevOut[0] = (lpRowInitial[0] * cnext);
prevOut[1] = (lpRowInitial[1] * cnext);
prevOut[2] = (lpRowInitial[2] * cnext);
prevOut[3] = (lpRowInitial[3] * cnext);
for (int y = HeightSubOne; y >= 0; y--) {
prevOut[0] = ((lpRowInitial[0] * a2a3) - (prevOut[0] * b1b2));
prevOut[1] = ((lpRowInitial[1] * a2a3) - (prevOut[1] * b1b2));
prevOut[2] = ((lpRowInitial[2] * a2a3) - (prevOut[2] * b1b2));
prevOut[3] = ((lpRowInitial[3] * a2a3) - (prevOut[3] * b1b2));
bufferPerLine[0] += prevOut[0];
bufferPerLine[1] += prevOut[1];
bufferPerLine[2] += prevOut[2];
bufferPerLine[3] += prevOut[3];
lpColInitial[0] = bufferPerLine[0];
lpColInitial[1] = bufferPerLine[1];
lpColInitial[2] = bufferPerLine[2];
lpColInitial[3] = bufferPerLine[3];
lpRowInitial -= Channels;
lpColInitial -= WidthStep;
bufferPerLine -= Channels;
}
}
else if (Channels == 1)
{
float prevOut = 0;
prevOut = (lpRowInitial[0] * cprev);
for (int y = 0; y < height; y++) {
prevOut = ((lpRowInitial[0] * a0a1) - (prevOut * b1b2));
bufferPerLine[0] = prevOut;
bufferPerLine += Channels;
lpRowInitial += Channels;
}
lpRowInitial -= Channels;
bufferPerLine -= Channels;
lpColInitial += WidthStep*HeightSubOne;
prevOut = (lpRowInitial[0] * cnext);
for (int y = HeightSubOne; y >= 0; y--) {
prevOut = ((lpRowInitial[0] * a2a3) - (prevOut * b1b2));
bufferPerLine[0] += prevOut;
lpColInitial[0] = bufferPerLine[0];
lpRowInitial -= Channels;
lpColInitial -= WidthStep;
bufferPerLine -= Channels;
}
}
}
//本人博客:http://tntmonks.cnblogs.com/ 转载请注明出处.
void  GaussianBlurFilter(unsigned char * input, unsigned char * output, int Width, int Height, int Stride, float GaussianSigma) {

int Channels = Stride / Width;
float a0, a1, a2, a3, b1, b2, cprev, cnext;

CalGaussianCoeff(GaussianSigma, &a0, &a1, &a2, &a3, &b1, &b2, &cprev, &cnext);

float a0a1 = (a0 + a1);
float a2a3 = (a2 + a3);
float b1b2 = (b1 + b2);

int bufferSizePerThread = (Width > Height ? Width : Height) * Channels;
unsigned char * bufferPerLine = (unsigned char*)malloc(bufferSizePerThread);
unsigned char * tempData = (unsigned char*)malloc(Height * Stride);
if (bufferPerLine == NULL || tempData == NULL)
{
if (tempData)
{
free(tempData);
}
if (bufferPerLine)
{
free(bufferPerLine);
}
return;
}
for (int y = 0; y < Height; ++y) {
unsigned char * lpRowInitial = input + Stride * y;
unsigned char * lpColInitial = tempData + y * Channels;
gaussianHorizontal(bufferPerLine, lpRowInitial, lpColInitial, Width, Height, Channels, Width, a0a1, a2a3, b1b2, cprev, cnext);
}
int HeightStep = Height*Channels;
for (int x = 0; x < Width; ++x) {
unsigned char * lpColInitial = output + x*Channels;
unsigned char * lpRowInitial = tempData + HeightStep * x;
gaussianVertical(bufferPerLine, lpRowInitial, lpColInitial, Height, Width, Channels, a0a1, a2a3, b1b2, cprev, cnext);
}

free(bufferPerLine);
free(tempData);
}

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.

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