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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