一、重映射简介
重映射，就是把一幅图像中某位置的像素放置到另一图像指定位置的过程。即：
在重映射过程中，图像的大小也可以同时发生改变。此时像素与像素之间的关系就不是一一对应关系，因此在重映射过程中，可能会涉及到像素值的插值计算。
Remap(
InputArray src, 输入图像（灰度图或真彩图均可）
OutputArray dst, 输出图像（要求大小和xmap,ymap相同，通道数目及数据类型和src相同）
InputArray map1, x 映射表 CV_32FC1/CV_32FC2
InputArray map2, y 映射表
int interpolation, 选择的插值方法，常见线性插值，可选择立方等
int borderMode, BORDER_CONSTANT
const Scalar borderValue color
)
头文件 quick_opencv.h：声明类与公共函数
#pragma once
#include <opencv2\opencv.hpp>
using namespace cv;
class QuickDemo {
public:
...
void remap_Demo(Mat& image1);
void MLS(Mat& src, std::vector<Point> p, std::vector<Point> q);
void MLS(Mat& src, int* p, int* q, int rows, int cols);
};
主函数调用该类的公共成员函数
#include <opencv2\opencv.hpp>
#include <quick_opencv.h>
#include <iostream>
using namespace cv;
int main(int argc, char** argv) {
Mat src = imread("D:\\Desktop\\pandas_small22.png");
if (src.empty()) {
printf("Could not load images...\n");
return -1;
}
QuickDemo qk;
qk.remap_Demo(src);
vector<Point> p{
Point(30, 147), Point(147, 147), Point(268, 147), Point(112, 148),
Point(186, 148), Point(98, 316), Point(211, 316)
};
vector<Point> q{
Point(28, 209), Point(126, 143), Point(282, 26), Point(71, 236),
Point(136, 240), Point(79, 313), Point(190, 310)
};
qk.MLS(src1, p, q);
int p_array[7][2] = { {30, 147}, {147, 147}, {268, 147}, {112, 148}, {186, 148}, {98, 316}, {211, 316} };
int q_array[7][2] = { {28, 209}, {126, 143}, {282, 26}, {71, 236}, {136, 240}, {79, 313}, {190, 310} };
qk.MLS(src1, (int *)p_array, (int*)q_array, 7, 2);
waitKey(0);
destroyAllWindows();
return 0;
}
源文件 quick_demo.cpp：实现类与公共函数
void update_map(Mat& image, int index, Mat& x_map, Mat& y_map) {
int height = image.rows;
int width = image.cols;
double h_41 = height * 0.25;
double h_43 = height * 0.75;
double w_41 = width * 0.25;
double w_43 = width * 0.75;
for (int h = 0; h < height; h++) {
float* x_ptr = x_map.ptr<float>(h);
float* y_ptr = y_map.ptr<float>(h);
for (int w = 0; w < width; w++) {
switch (index)
{
case 0:
if (h > h_41 && h < h_43 && w>w_41 && w < w_43) {
*x_ptr++ = 2 * (w - w_41 + 0.5);
*y_ptr++ = 2 * (h - h_41 + 0.5);
}
else
{
*x_ptr++ = 0;
*y_ptr++ = 0;
}
break;
case 1:
*x_ptr++ = width - w - 1;
*y_ptr++ = h;
break;
case 2:
*x_ptr++ = w;
*y_ptr++ = height - h - 1;
break;
case 3:
*x_ptr++ = width - w - 1;
*y_ptr++ = height - h - 1;
break;
}
}
}
}
void QuickDemo::remap_Demo(Mat& image) {
Mat dst, x_map, y_map;
int index = 0;
x_map.create(image.size(), CV_32FC1);
y_map.create(image.size(), CV_32FC1);
int c = 0;
while (true)
{
c = waitKey(400);
if ((char)c==27){
break;
}
index = c % 4;
update_map(image,index, x_map, y_map);
remap(image, dst, x_map, y_map, INTER_LINEAR, BORDER_CONSTANT, Scalar(255, 0, 0));
imshow("remap", dst);
}
}
如上两个函数，update_map，用于更新remap的具体映射方法，remap_Demo为调用函数。
二、图像扭曲
MLS算法 图像扭曲 Image Deformation Using Moving Least Squares 论文。
最小二乘法（MLS）对图像进行变形 python 实现
Point NewPoint(Point V, vector<Point> p, vector<Point> q){
vector<float>W;
Point p_star, q_star = Point(0, 0);
for (int i = 0; i <= p.size() - 1; i++){
float temp;
if (p[i] == V){
temp = INT_MAX;
}else{
temp = 1.0 / (((p[i].x - V.x) * (p[i].x - V.x)) + ((p[i].y - V.y) * (p[i].y - V.y)));
}
W.push_back(temp);
}
float px = 0, py = 0, qx = 0, qy = 0, W_sum = 0;
for (int i = 0; i <= W.size() - 1; i++){
px += W[i] * p[i].x;
py += W[i] * p[i].y;
qx += W[i] * q[i].x;
qy += W[i] * q[i].y;
W_sum += W[i];
}
p_star.x = px / W_sum;
p_star.y = py / W_sum;
q_star.x = qx / W_sum;
q_star.y = qy / W_sum;
vector<Point> p_hat, q_hat;
for (int i = 0; i <= p.size() - 1; i++){
p_hat.push_back(p[i] - p_star);
q_hat.push_back(q[i] - q_star);
}
Mat pi_hat_t_ = Mat::zeros(2, 1, CV_32FC1);
Mat_<float> pi_hat_t = pi_hat_t_;
Mat pi_hat_ = Mat::zeros(1, 2, CV_32FC1);
Mat_<float> pi_hat = pi_hat_;
Mat M_1_ = Mat::zeros(2, 2, CV_32FC1);
Mat_<float> M_1 = M_1_;
for (int i = 0; i <= p_hat.size() - 1; i++){
pi_hat_t.at<float>(0, 0) = p_hat[i].x;
pi_hat_t.at<float>(1, 0) = p_hat[i].y;
pi_hat.at<float>(0, 0) = p_hat[i].x;
pi_hat.at<float>(0, 1) = p_hat[i].y;
M_1 += pi_hat_t * W[i] * pi_hat;
}
Mat_<float> M_1_inv = M_1.inv();
M_1 = M_1_inv;
Mat pj_hat_t_ = Mat::zeros(2, 1, CV_32FC1);
Mat_<float> pj_hat_t = pj_hat_t_;
Mat qj_hat_ = Mat::zeros(1, 2, CV_32FC1);
Mat_<float> qj_hat = qj_hat_;
Mat M_2_ = Mat::zeros(2, 2, CV_32FC1);
Mat_<float> M_2 = M_2_;
for (int j = 0; j <= q.size() - 1; j++){
pj_hat_t.at<float>(0, 0) = p_hat[j].x;
pj_hat_t.at<float>(1, 0) = p_hat[j].y;
qj_hat.at<float>(0, 0) = q_hat[j].x;
qj_hat.at<float>(0, 1) = q_hat[j].y;
M_2 += W[j] * pj_hat_t * qj_hat;
}
Mat_<float> M = M_1 * M_2;//ok
//cout << "M = " << M << endl;
Point x_p_star = V - p_star;
Mat M_x_p_star_ = Mat::zeros(1, 2, CV_32FC1);
Mat_<float> M_x_p_star = M_x_p_star_;
M_x_p_star.at<float>(0, 0) = x_p_star.x;
M_x_p_star.at<float>(0, 1) = x_p_star.y;
Mat M_q_star_ = Mat::zeros(1, 2, CV_32FC1);
Mat_<float> M_q_star = M_q_star_;
M_q_star.at<float>(0, 0) = q_star.x;
M_q_star.at<float>(0, 1) = q_star.y;
Mat_<float> Lv = M_x_p_star * M + M_q_star;
return Point(Lv.at<float>(0, 0), Lv.at<float>(0, 1));
}
void QuickDemo::MLS(Mat& src, std::vector<Point> p, std::vector<Point> q){
double time0 = static_cast<double>(getTickCount());
Mat dst = Mat::zeros(src.rows, src.cols, CV_8UC3);
for (int i = 0; i < src.rows; i++){
for (int j = 0; j < src.cols; j++){
Point old = Point(j, i);
Point new_point = NewPoint(old, p, q);
//cout << "old = " << old << "\tnew = " << new_point << endl;
dst.at<Vec3b>(i, j) = src.at<Vec3b>(abs(new_point.y), abs(new_point.x));
}
}
double time1 = static_cast<double>(getTickCount());
cout << "Total cost time is " << ((time1 - time0) / getTickFrequency()) << "seconds" << endl;
imshow("dst_msl", dst);
}
重载函数文章来源：https://www.toymoban.com/news/detail-639895.html
Point NewPoint(Point V, float* W, int* p, int* q , float* p_hat, float* q_hat, int rows, int cols) {
Point p_star, q_star = Point(0, 0);
float temp = 0;
float px = 0, py = 0, qx = 0, qy = 0, W_sum = 0;
for (int i = 0; i < rows; i++) {
int p_0 = *(p + i * cols);
int p_1 = *(p + i * cols + 1);
if (!(p_0 == V.x && p_1 == V.y)) {
temp = 1.0 / (((p_0 - V.x) * (p_0 - V.x)) + ((p_1 - V.y) * (p_1 - V.y)));
}else {
temp = INT_MAX;
}
W[i] = temp;
px += temp * p_0;
py += temp * p_1;
qx += temp * (*(q + i * cols));
qy += temp * (*(q + i * cols + 1));
W_sum += temp;
}
p_star.x = px / W_sum;
p_star.y = py / W_sum;
q_star.x = qx / W_sum;
q_star.y = qy / W_sum;
for (int i = 0; i < rows; i++) {
*(p_hat + i * cols) = *(p + i * cols) - p_star.x;
*(p_hat + i * cols + 1) = *(p + i * cols + 1) - p_star.y;
*(q_hat + i * cols) = *(q + i * cols) - p_star.x;
*(q_hat + i * cols + 1) = *(q + i * cols + 1) - p_star.y;
}
// ====================================
Mat pi_hat_t_ = Mat::zeros(2, 1, CV_32FC1);
Mat_<float> pi_hat_t = pi_hat_t_;
Mat pi_hat_ = Mat::zeros(1, 2, CV_32FC1);
Mat_<float> pi_hat = pi_hat_;
Mat M_1_ = Mat::zeros(2, 2, CV_32FC1);
Mat_<float> M_1 = M_1_;
// ====================================
Mat pj_hat_t_ = Mat::zeros(2, 1, CV_32FC1);
Mat_<float> pj_hat_t = pj_hat_t_;
Mat qj_hat_ = Mat::zeros(1, 2, CV_32FC1);
Mat_<float> qj_hat = qj_hat_;
Mat M_2_ = Mat::zeros(2, 2, CV_32FC1);
Mat_<float> M_2 = M_2_;
// ====================================
for (int i = 0; i < rows; i++) {
float p_hat_x = *(p_hat + i * cols);
float p_hat_y = *(p_hat + i * cols + 1);
pi_hat_t.at<float>(0, 0) = p_hat_x;
pi_hat_t.at<float>(1, 0) = p_hat_y;
pi_hat.at<float>(0, 0) = p_hat_x;
pi_hat.at<float>(0, 1) = p_hat_y;
M_1 += pi_hat_t * W[i] * pi_hat;
pj_hat_t.at<float>(0, 0) = p_hat_x;
pj_hat_t.at<float>(1, 0) = p_hat_y;
qj_hat.at<float>(0, 0) = *(q_hat + i * cols);
qj_hat.at<float>(0, 1) = *(q_hat + i * cols + 1);
M_2 += pj_hat_t * W[i] * qj_hat;
}
Mat_<float> M_1_inv = M_1.inv();
M_1 = M_1_inv;
Mat_<float> M = M_1 * M_2;
//=====================================
//
// 如下为总公式计算
//
//======================================
Point x_p_star = V - p_star;
Mat M_x_p_star_ = Mat::zeros(1, 2, CV_32FC1);
Mat_<float> M_x_p_star = M_x_p_star_;
M_x_p_star.at<float>(0, 0) = x_p_star.x;
M_x_p_star.at<float>(0, 1) = x_p_star.y;
Mat M_q_star_ = Mat::zeros(1, 2, CV_32FC1);
Mat_<float> M_q_star = M_q_star_;
M_q_star.at<float>(0, 0) = q_star.x;
M_q_star.at<float>(0, 1) = q_star.y;
Mat_<float> Lv = M_x_p_star * M + M_q_star;
return Point(Lv.at<float>(0, 0), Lv.at<float>(0, 1));
}
void QuickDemo::MLS(Mat& src, int* p, int* q, int rows, int cols) {
double time0 = static_cast<double>(getTickCount());
Mat dst = Mat::zeros(src.rows, src.cols, CV_8UC3);
assert(7 == rows); // 若断言失败请修改如下三个数组的长度为rows
float W[7] = { 0 }; // 权重长度为p数组长度：rows=7
float p_hat[7][2] = { 0 }; // p_hat长度为p数组长度：rows=7
float q_hat[7][2] = { 0 }; // q_hat长度为p数组长度：rows=7
for (int i = 0; i < src.rows; i++) {
for (int j = 0; j < src.cols; j++) {
Point new_point = NewPoint(Point(j, i), W, p, q, (float*)p_hat, (float*)p_hat, rows, cols);
//cout << "old = " << old << "\tnew = " << new_point << endl;
dst.at<Vec3b>(i, j) = src.at<Vec3b>(abs(new_point.y), abs(new_point.x));
//cout << "src.at<uchar> = " << src.at<Vec3b>(new_point.y,new_point.x) << endl;
}
}
double time1 = static_cast<double>(getTickCount());
cout << "Total cost time is " << ((time1 - time0) / getTickFrequency()) << "seconds" << endl;
imshow("dst_msl", dst);
}
————
鸣谢与拓展阅读：
使用范例 记录四图像处理之瘦脸 MLS算法 C++实现
OpenCV局部变形算法探究添加链接描述
基于移动最小二乘（MLS）的图像扭曲刚性变形python实现
使用重映射实现图像的局部扭曲 来实现 图像增强。文章来源地址https://www.toymoban.com/news/detail-639895.html
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