本文将介绍图像金字塔以及拉普拉斯融合的相关知识。
图像金字塔
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一般的的线性变换通过将一幅图像乘以transform函数分成不同的components。离散傅里叶变换、离散余弦变换、奇异值分解 和 小波变换 都以炙热的猎豹和其他奖采样变换为简单基础。
真实数字图像包括一系列物体和特征（不同scales、orientation和角度下的lines, shapes, patterns, edges）
the simple process for a pyramid with an arbitrary number of levels：
平滑图像->将图像进行下采样（常取采样率r=2） 而获得，同样的操作反复做，金字塔层数逐渐上升，空间采样密度逐渐下降。（如下图）这个多维表示就像一个金字塔，其中fi表示图像，li表示低通滤波结果，hi表示高通滤波结果。li / hi通过将图像与高通/低通滤波器卷积而得。
与之相反，金字塔重建通过上采样获得。
以图像金字塔为基础的双边滤波器是一个图像细节增强和操作的很好的框架。
图像融合（Image Blending）
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原理：
1.建立两幅图像的炙热的猎豹
2.求高斯金字塔（掩模金字塔-为了拼接左右两幅图像）
3. 进行拼接blendLapPyrs() ; 在每一层上将左右laplacian图像直接拼起来得结果金字塔resultLapPyr
4.重建图像: 从最高层结果图
//将左右laplacian图像拼成的resultLapPyr金字塔中每一层，从上到下插值放大并和下一层相加，即得blend图像结果（reconstructImgFromLapPyramid）
Code：
配置环境：
VS2010+opencv 2.3.1(2.2版本以上均可)
#include "opencv2/opencv.hpp"using namespace cv;/************************************************************************//* 说明：*金字塔从下到上依次为 [0,1，...，level-1] 层*blendMask 为图像的掩模*maskGaussianPyramid为金字塔每一层的掩模*resultLapPyr 存放每层金字塔中直接用左右两图Laplacian变换拼成的图像*//************************************************************************/class LaplacianBlending {private:Mat_<Vec3f> left;Mat_<Vec3f> right;Mat_<float> blendMask;vector<Mat_<Vec3f> > leftLapPyr,rightLapPyr,resultLapPyr;//Laplacian PyramidsMat leftHighestLevel, rightHighestLevel, resultHighestLevel;vector<Mat_<Vec3f> > maskGaussianPyramid; //masks are 3-channels for easier multiplication with RGBint levels;void buildPyramids() {buildLaplacianPyramid(left,leftLapPyr,leftHighestLevel);buildLaplacianPyramid(right,rightLapPyr,rightHighestLevel);buildGaussianPyramid();}void buildGaussianPyramid() {//金字塔内容为每一层的掩模assert(leftLapPyr.size()>0);maskGaussianPyramid.clear();Mat currentImg;cvtColor(blendMask, currentImg, CV_GRAY2BGR);//store color img of blend mask into maskGaussianPyramidmaskGaussianPyramid.push_back(currentImg); //0-levelcurrentImg = blendMask;for (int l=1; l<levels+1; l++) {Mat _down;if (leftLapPyr.size() > l)pyrDown(currentImg, _down, leftLapPyr[l].size());elsepyrDown(currentImg, _down, leftHighestLevel.size()); //lowest levelMat down;cvtColor(_down, down, CV_GRAY2BGR);maskGaussianPyramid.push_back(down);//add color blend mask into mask PyramidcurrentImg = _down;}}void buildLaplacianPyramid(const Mat& img, vector<Mat_<Vec3f> >& lapPyr, Mat& HighestLevel) {lapPyr.clear();Mat currentImg = img;for (int l=0; l<levels; l++) {Mat down,up;pyrDown(currentImg, down);pyrUp(down, up,currentImg.size());Mat lap = currentImg - up;lapPyr.push_back(lap);currentImg = down;}currentImg.copyTo(HighestLevel);}Mat_<Vec3f> reconstructImgFromLapPyramid() {//将左右laplacian图像拼成的resultLapPyr金字塔中每一层//从上到下插值放大并相加，即得blend图像结果Mat currentImg = resultHighestLevel;for (int l=levels-1; l>=0; l--) {Mat up;pyrUp(currentImg, up, resultLapPyr[l].size());currentImg = up + resultLapPyr[l];}return currentImg;}void blendLapPyrs() {//获得每层金字塔中直接用左右两图Laplacian变换拼成的图像resultLapPyrresultHighestLevel = leftHighestLevel.mul(maskGaussianPyramid.back()) +rightHighestLevel.mul(Scalar(1.0,1.0,1.0) - maskGaussianPyramid.back());for (int l=0; l<levels; l++) {Mat A = leftLapPyr[l].mul(maskGaussianPyramid[l]);Mat antiMask = Scalar(1.0,1.0,1.0) - maskGaussianPyramid[l];Mat B = rightLapPyr[l].mul(antiMask);Mat_<Vec3f> blendedLevel = A + B;resultLapPyr.push_back(blendedLevel);}}public:LaplacianBlending(const Mat_<Vec3f>& _left, const Mat_<Vec3f>& _right, const Mat_<float>& _blendMask, int _levels)://construct function, used in LaplacianBlending lb(l,r,m,4); left(_left),right(_right),blendMask(_blendMask),levels(_levels) { assert(_left.size() == _right.size()); assert(_left.size() == _blendMask.size()); buildPyramids();//construct Laplacian Pyramid and Gaussian Pyramid blendLapPyrs();//blend left & right Pyramids into one Pyramid }; Mat_<Vec3f> blend() { return reconstructImgFromLapPyramid();//reconstruct Image from Laplacian Pyramid }};Mat_<Vec3f> LaplacianBlend(const Mat_<Vec3f>& l, const Mat_<Vec3f>& r, const Mat_<float>& m) {LaplacianBlending lb(l,r,m,4);return lb.blend();}int main() {Mat l8u = imread("left.png");Mat r8u = imread("right.png");imshow("left",l8u); imshow("right",r8u);Mat_<Vec3f> l; l8u.convertTo(l,CV_32F,1.0/255.0);//Vec3f表示有三个通道，即 l[row][column][depth]Mat_<Vec3f> r; r8u.convertTo(r,CV_32F,1.0/255.0);/***************** void convertTo( OutputArray m, int rtype, double alpha=1, double beta=0 ) const;******************//* Performs linear transformation on every source array element:dst(x,y,c) = scale*src(x,y,alpha)+beta.Arbitrary combination of input and output array depths are allowed(number of channels must be the same), thus the function can be usedfor type conversion *///create blend mask matrix mMat_<float> m(l.rows,l.cols,0.0);//将m全部赋值为0m(Range::all(),Range(0,m.cols/2)) = 1.0;//取m全部行&[0,m.cols/2]列，赋值为1.0Mat_<Vec3f> blend = LaplacianBlend(l, r, m);imshow("blended",blend);waitKey(0);return 0;}
效果图：