Article directory
1. Introduction to remapping
Remapping is the process of placing pixels at a certain position in one image to a specified position in another image. That is:
during the remapping process, the size of the image can also change at the same time. At this time, the relationship between pixels is not a one-to-one correspondence, so the interpolation calculation of pixel values may be involved in the remapping process.
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
)
Header file quick_opencv.h: Declare classes and public functions
#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);
};
The main function calls the public member functions of the class
#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;
}
Source file quick_demo.cpp: Implementing classes and public functions
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);
}
}
The above two functions, update_map, are used to update the specific mapping method of remap, and remap_Demo is the calling function.
2. Image distortion
MLS algorithm image distortion Image Deformation Using Moving Least Squares paper.
The least square method (MLS) deforms the image python implementation
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);
}
overloaded function
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);
}
————
Acknowledgments and further reading:
Use example records to record four image processing face-slimming MLS algorithms C++ implementation
OpenCV local deformation algorithm exploration Add link description Image distortion
based on moving least squares (MLS) Rigid deformation Python implementation Use remapping to achieve image local distortion to achieve Image enhancement.