目录
[1 简介](#1 简介)
[2 算法原理](#2 算法原理)
[3 代码实现](#3 代码实现)
[4 演示Demo](#4 演示Demo)
[4.1 开发环境](#4.1 开发环境)
[4.2 功能介绍](#4.2 功能介绍)
[4.3 下载地址](#4.3 下载地址)
1 简介
BEEPS（Bias Elimination in Edge-Preserving Smoothing） 是一种基于偏微分方程（PDE）的边缘保留平滑滤波算法。它能够在平滑图像的同时有效消除偏差（Bias），从而更好地保留边缘和细节。BEEPS 滤波算法广泛应用于图像去噪、图像增强和医学图像处理等领域。
2 算法原理
BEEPS 滤波的核心思想是通过引入偏差消除项，改进传统的边缘保留平滑算法（如各向异性扩散）。其数学模型基于以下偏微分方程：
其中
-
I 是图像。
-
∇I 是图像的梯度。
-
c (∣∇I∣) 是扩散系数，控制滤波的强度。
-
是偏差消除项的权重。
-
扩散系数c (∣∇I∣) 通常定义为：
或
其中，k 是一个控制边缘敏感度的参数。
算法步骤：
-
计算图像的梯度 ∇I。
-
根据梯度计算扩散系数 c (∣∇I∣)。
-
使用扩散系数更新图像像素值。
-
重复上述步骤，直到达到指定的迭代次数。
3 代码实现
Anisotropic滤波算法的的C语言实现代码如下
cpp
double Gaussian(int u, int v, double sigma)
{
int t = -(u - v) * (u - v);
return exp((double)t / sigma);
}
int BEEPSHorizontal(unsigned char* srcPtr, int width, int height, unsigned char* outData, double sigma, int c)
{
unsigned char* F = (unsigned char*)malloc(sizeof(unsigned char) * width * height);
int *s = (int*)malloc(sizeof(int) * width);
int *v = (int*)malloc(sizeof(int) * width);
int pos = 0, X = 0, Y = 0;
int p = 0;
memset(F, 0, width * height);
memset(outData, 0, width * height);
memset(s, 0, width);
memset(v, 0, width);
unsigned char* D = outData;
for (int y = 0; y < height; y++)
{
for (int x = 0; x < width; x++)
{
X = width - 1 - x;
Y = height - 1 - y;
if (x == 0)
{
pos = x + y * width;
F[pos] = srcPtr[pos];
s[0] = srcPtr[pos];
p = X;
pos = p + Y * width;
v[p] = srcPtr[pos];
D[pos] = srcPtr[pos];
}
else
{
p = x;
pos = p + y * width;
s[p] = (int)(10.0 * Gaussian(srcPtr[pos], F[pos - 1], sigma));
F[pos] = CLIP3((((100 - s[p] * c) * srcPtr[pos] + s[p] * c * F[pos - 1]) / 100), 0, 255);
p = X;
pos = p + Y * width;
v[p] = (int)(10.0 * Gaussian(srcPtr[pos], D[pos + 1], sigma));
D[pos] = CLIP3((((100 - v[p] * c) * srcPtr[pos] + v[p] * c * D[pos + 1]) / 100), 0, 255);
}
}
}
for (int i = 0; i < height * width; i++)
{
D[i] = CLIP3(((10 * F[i] - (10 - c) * (srcPtr[i]) + 10 * D[i]) / (10 + c)), 0, 255);
}
free(F);
free(s);
free(v);
return 0;
}
int BEEPSVertical(unsigned char* srcPtr, int width, int height, unsigned char* outData, double sigma, int c)
{
unsigned char* F = (unsigned char*)malloc(sizeof(unsigned char) * width * height);
unsigned char* D = outData;
int* s = (int*)malloc(sizeof(int) * height);
int* v = (int*)malloc(sizeof(int) * height);
int pos = 0, X = 0, Y = 0;
memset(s, 0, height);
memset(v, 0, height);
for (int x = 0; x < width; x++)
{
for (int y = 0; y < height; y++)
{
X = width - 1 - x;
Y = height - 1 - y;
if (y == 0)
{
pos = x + y * width;
F[pos] = srcPtr[pos];
s[y] = srcPtr[pos];
pos = X + Y * width;
D[pos] = srcPtr[pos];
v[Y] = srcPtr[pos];
}
else
{
pos = x + y * width;
s[y] = (int)(10.0 * Gaussian(srcPtr[pos], F[pos - width], sigma));
F[pos] = CLIP3((((100 - s[y] * c) * srcPtr[pos] + s[y] * c * F[pos - width]) / 100), 0, 255);
pos = X + Y * width;
v[Y] = (int)(10.0 * Gaussian(srcPtr[pos], D[pos + width], sigma));
D[pos] = CLIP3((((100 - v[Y] * c) * srcPtr[pos] + v[Y] * c * D[pos + width]) / 100), 0, 255);
}
}
}
for (int i = 0; i < height*width; i++)
{
D[i] = CLIP3(((10 * F[i] - (10 - c) * (srcPtr[i]) + 10 * D[i]) / (10 + c)), 0, 255);
}
free(F);
free(s);
free(v);
return 0;
}
void BEEPSProcess(unsigned char* srcPtr, int width, int height, float sigma, float c)
{
float* GMAP = (float*)malloc(sizeof(float) * 256 * 256);
for (int j = 0; j < 256; j++)
{
for (int i = 0; i < 256; i++)
{
GMAP[i + j * 256] = Gaussian(i, j, sigma);
}
}
sigma = sigma > 50 ? 50 : sigma;
sigma = sigma * sigma * 2.0f;
float Lamba = 10.0f * (float)(1 - (sqrt(2.0f * c * c + 1) - 1) / (c * c));
unsigned char* pSrc = srcPtr;
unsigned char* hValue = (unsigned char*)malloc(sizeof(unsigned char) * width * height);
unsigned char* vValue = (unsigned char*)malloc(sizeof(unsigned char) * width * height);
unsigned char* dstValue = (unsigned char*)malloc(sizeof(unsigned char) * width * height);
BEEPSHorizontal(pSrc, width, height, hValue, sigma, Lamba);
BEEPSVertical(hValue, width, height, vValue, sigma, Lamba);
BEEPSVertical(pSrc, width, height, hValue, sigma, Lamba);
BEEPSHorizontal(hValue, width, height, dstValue, sigma, Lamba);
for (int i = 0; i < width * height; i++)
{
*pSrc++ = CLIP3(((vValue[i] + dstValue[i]) / 2), 0, 255);
}
free(hValue);
free(vValue);
free(dstValue);
}
int mxBeepsFilter(unsigned char* srcData, int nWidth, int nHeight, int nStride, float delta, float delta_s)
{
if (srcData == NULL)
{
return 0;
}
if (delta == 0 || delta_s == 0)
return 0;
unsigned char* yData = (unsigned char*)malloc(sizeof(unsigned char) * nWidth * nHeight);
unsigned char* cbData = (unsigned char*)malloc(sizeof(unsigned char) * nWidth * nHeight);
unsigned char* crData = (unsigned char*)malloc(sizeof(unsigned char) * nWidth * nHeight);
unsigned char* pSrc = srcData;
int Y, CB, CR;
unsigned char* pY = yData;
unsigned char* pCb = cbData;
unsigned char* pCr = crData;
for (int j = 0; j < nHeight; j++)
{
for (int i = 0; i < nWidth; i++)
{
RGBToYCbCr(pSrc[2], pSrc[1], pSrc[0], &Y, &CB, &CR);
*pY = Y;
*pCb = CB;
*pCr = CR;
pY++;
pCb++;
pCr++;
pSrc += 4;
}
}
BEEPSProcess(yData, nWidth, nHeight, delta, delta_s);
pSrc = srcData;
pY = yData;
pCb = cbData;
pCr = crData;
int R, G, B;
for (int j = 0; j < nHeight; j++)
{
for (int i = 0; i < nWidth; i++)
{
YCbCrToRGB(*pY, *pCb, *pCr, &R, &G, &B);
pSrc[0] = B;
pSrc[1] = G;
pSrc[2] = R;
pY++;
pCb++;
pCr++;
pSrc += 4;
}
}
free(yData);
free(cbData);
free(crData);
return 0;
}4 演示Demo
4.1 开发环境
-
Windows 10 Pro x64
-
Visual Studio 2015
4.2 功能介绍
演示程序主界面如下图所示，具有图像读取、显示、保存、双边滤波、表面模糊、导向滤波、局部均值方差滤波、各向异性扩散滤波、Smart Blur滤波、MeanShift滤波、BEEPS滤波、处理耗时等功能
原图
滤波效果图
4.3 下载地址
开发环境：
-
Windows 10 pro x64
-
Visual Studio 2015
下载地址：图像保边滤波之BEEPS滤波算法Demo
参考
图像视频滤镜与人像美颜美妆算法详解. 胡耀武、谭娟、李云夕. 电子工业出版社、2020-07