參考資料
- 國立臺灣大學-Image Morphing-Homework
- 圖像處理（十）基於特徵線的圖像變形-Siggraph 1992
- Face Morphing on Animation Producing-ntu-csie
- 2D Image Morphing Algorithms
基於特徵的圖像變形算法，來源於1992年的一篇論文。它是分別在兩幅圖像中分別選擇相應的特徵對（特徵線段對），然後根據原始像素與每個特徵的相對位置，映射原始像素，再取加權平均得出最終的像素值。
如下圖是特徵線段對爲2個的情況：
特徵線段可以是交互產生的，也可以是自動檢測的。
圖像變形採用的是雙線性插值的反向映射算法。
具體的算法推演，博客開頭列出的資料1和2已經講得很明白了，而且給出了算法實現的僞代碼，以及基於OpenCV1的C代碼。
這篇博客所做的工作是將上述C代碼，完全翻譯爲C++代碼。模塊解耦清晰，沒有一大堆煩人的全局變量，易於理解。
改寫後的代碼基於OpenCV2。運行程序的使用方法與原程序同，見參考資料2。
廢話不多說了，貼代碼。
代碼實現
主函數文件 Main.cpp
#include<string.h>
#include"Morpher.h"
int main()
{
Morpher morpher;
morpher.main();
return EXIT_SUCCESS;
}頭文件 Morpher.h，包含幾個類的定義。
#include <stdio.h>
#include <stdlib.h>
#include <iostream>
#include <vector>
#include <string>
#include <math.h>
#include <opencv2/opencv.hpp>
#include <opencv2/highgui/highgui.hpp>
using namespace std;
using namespace cv;
class Line
{
public:
//起點、終點、中點、線長、角度
Point2f P=Point2f(0.f,0.f);
Point2f Q = Point2f(0.f, 0.f);
Point2f M = Point2f(0.f, 0.f);
double len{0};
float degree{0};
//參數a,b,p
double a=1.0;
double b=2.0;
double p=1.0;
public:
Line() :P(Point2f(0.f, 0.f)), Q(Point2f(0.f, 0.f)){};
//由P,Q座標得到中點，線長，角度信息
void PQtoMLD();
void MLDtoPQ();
void show();
double Getu(Point2f X);
double Getv(Point2f X);
Point2f Get_Point(double u, double v);
double Get_Weight(Point2f X);
};
class LinePair
{
public:
Line leftLine;
Line rightLine;
vector<Line> warpLine;
public:
//生成中間過渡的線段集合
void genWarpLine(int frame_count);
};
class Image
{
public:
//過渡幀序號
int frame_index;
Mat left_image;
Mat right_image;
Mat new_image;
public:
Image(int frame_index,string leftImageName,string rightImageName);
//雙線性插值
Vec3b bilinear(Mat image, double X, double Y);
//生成過渡圖像幀
void Warp(int frame_count, string new_image_name, vector<LinePair> pairs);
};
class Morpher
{
public:
vector<LinePair> pairs;
LinePair curLinePair;
//計數，交互式畫線要用到
int counter = 0;
//設置動畫的過渡幀，比如1爲50%，3爲25%，50%，75%
int frame_count = 1;
Mat leftImage;
Mat rightImage;
Mat leftImageTmp;
Mat rightImageTmp;
//顯示相關。畫線的顏色、線寬、偏移
Scalar color = Scalar(0, 255, 0);
int thickness = 2;
int shift = 0;
//按鍵值，用於控制
int key;
string first_image_name;
string second_image_name;
string new_image_name;
public:
void show_pairs();
//捕獲左圖像上的鼠標動作
static void on_mousel(int event, int x, int y, int flag, void* param);
//捕獲右圖像上的鼠標動作
static void on_mouser(int event, int x, int y, int flag, void* param);
//運行morph
void runWarp();
void main();
};實現文件 Morpher.cpp，類函數的具體實現。
#include"Morpher.h"
void Line::PQtoMLD()
{
M.x = (P.x + Q.x) / 2;
M.y = (P.y + Q.y) / 2;
float tmpx = Q.x - P.x;
float tmpy = Q.y - P.y;
len = sqrt(tmpx*tmpx + tmpy*tmpy);
degree = atan2(tmpy, tmpx);
return;
}
void Line::MLDtoPQ()
{
float tmpx = 0.5*len*cos(degree);
float tmpy = 0.5*len*sin(degree);
Point2f tmpP;
Point2f tmpQ;
tmpP.x = M.x - tmpx;
tmpP.y = M.y - tmpy;
tmpQ.x = M.x + tmpx;
tmpQ.y = M.y + tmpy;
P = tmpP;
Q = tmpQ;
return;
}
void Line::show()
{
printf("P(%lf,%lf) Q(%lf,%lf) M(%lf,%lf)\n \tlen=%lf degree=%f\n", P.x, P.y, Q.x, Q.y, M.x, M.y, len, degree);
return;
}
double Line::Getu(Point2f X)
{
double X_P_x = X.x - P.x;
double X_P_y = X.y - P.y;
double Q_P_x = Q.x - P.x;
double Q_P_y = Q.y - P.y;
double u = ((X_P_x * Q_P_x) + (X_P_y * Q_P_y)) / (len * len);
return u;
}
double Line::Getv(Point2f X)
{
double X_P_x = X.x - P.x;
double X_P_y = X.y - P.y;
double Q_P_x = Q.x - P.x;
double Q_P_y = Q.y - P.y;
double Perp_Q_P_x = Q_P_y;
double Perp_Q_P_y = -Q_P_x;
double v = ((X_P_x * Perp_Q_P_x) + (X_P_y * Perp_Q_P_y)) / len;
return v;
}
Point2f Line::Get_Point(double u, double v)
{
double Q_P_x = Q.x - P.x;
double Q_P_y = Q.y - P.y;
double Perp_Q_P_x = Q_P_y;
double Perp_Q_P_y = -Q_P_x;
double Point_x = P.x + u * (Q.x - P.x) + ((v * Perp_Q_P_x) / len);
double Point_y = P.y + u * (Q.y - P.y) + ((v * Perp_Q_P_y) / len);
Point2f X;
X.x = Point_x;
X.y = Point_y;
return X;
}
double Line::Get_Weight(Point2f X)
{
double d = 0.0;
double u = Getu(X);
if (u > 1.0)
d = sqrt((X.x - Q.x) * (X.x - Q.x) + (X.y - Q.y) * (X.y - Q.y));
else if (u < 0)
d = sqrt((X.x - P.x) * (X.x - P.x) + (X.y - P.y) * (X.y - P.y));
else
d = abs(Getv(X));
double weight = pow(pow(len, p) / (a + d), b);
return weight;
}
void LinePair::genWarpLine(int frame_count)
{
while (leftLine.degree - rightLine.degree>3.14159265)
rightLine.degree = rightLine.degree + 3.14159265;
while (rightLine.degree - leftLine.degree>3.14159265)
leftLine.degree = leftLine.degree + 3.14159265;
for (int i = 0; i<frame_count; i++)
{
double ratio = (double)(i + 1) / (frame_count + 1);
Line curLine;
curLine.M.x = (1 - ratio)*leftLine.M.x + ratio*rightLine.M.x;
curLine.M.y = (1 - ratio)*leftLine.M.y + ratio*rightLine.M.y;
curLine.len = (1 - ratio)*leftLine.len + ratio*rightLine.len;
curLine.degree = (1 - ratio)*leftLine.degree + ratio*rightLine.degree;
curLine.MLDtoPQ();
warpLine.push_back(curLine);
}
return;
}
Image::Image(int index, string leftImageName, string rightImageName)
{
frame_index = index;
left_image = imread(leftImageName);
right_image = imread(rightImageName);
Size ImageSize = Size(left_image.cols, left_image.rows);
new_image.create(ImageSize, CV_8UC3);
}
Vec3b Image::bilinear(Mat image, double X, double Y)
{
int width = image.cols;
int height = image.rows;
int x_floor = (int)X;
int y_floor = (int)Y;
int x_ceil = x_floor + 1;
int y_ceil = y_floor + 1;
double a = X - x_floor;
double b = Y - y_floor;
if (x_ceil >= width - 1)
x_ceil = width - 1;
if (y_ceil >= height - 1)
y_ceil = height - 1;
Vec3b output_scalar;
Vec3b leftdown = image.at<Vec3b>(y_floor, x_floor);
Vec3b lefttop = image.at<Vec3b>(y_ceil, x_floor);
Vec3b rightdown = image.at<Vec3b>(y_floor, x_ceil);
Vec3b righttop = image.at<Vec3b>(y_ceil, x_ceil);
for (int i = 0; i < 3; i++)
{
output_scalar.val[i] = (1 - a)*(1 - b)*leftdown.val[i] + a*(1 - b)*rightdown.val[i] + a*b*righttop.val[i] + (1 - a)*b*lefttop.val[i];
}
return output_scalar;
}
void Image::Warp(int frame_count, string new_image_name, vector<LinePair> pairs)
{
double ratio = (double)(frame_index + 1) / (frame_count + 1);
Mat ori_leftImage, ori_rightImage;
ori_leftImage = left_image;
ori_rightImage = right_image;
int width = new_image.cols;
int height = new_image.rows;
for (int x = 0; x < width; x++)
{
for (int y = 0; y < height; y++)
{
Point2f dst_point;
dst_point.x = x;
dst_point.y = y;
double leftXSum_x = 0.0;
double leftXSum_y = 0.0;
double leftWeightSum = 0.0;
double rightXSum_x = 0.0;
double rightXSum_y = 0.0;
double rightWeightSum = 0.0;
for (int i = 0; i < pairs.size(); i++){
Line src_line = pairs[i].leftLine;
Line dst_line = pairs[i].warpLine[frame_index];
double new_u = dst_line.Getu(dst_point);
double new_v = dst_line.Getv(dst_point);
Point2f src_point = src_line.Get_Point(new_u, new_v);
double src_weight = dst_line.Get_Weight(dst_point);
leftXSum_x = leftXSum_x + (double)src_point.x * src_weight;
leftXSum_y = leftXSum_y + (double)src_point.y * src_weight;
leftWeightSum = leftWeightSum + src_weight;
src_line = pairs[i].rightLine;
new_u = dst_line.Getu(dst_point);
new_v = dst_line.Getv(dst_point);
src_point = src_line.Get_Point(new_u, new_v);
src_weight = dst_line.Get_Weight(dst_point);
rightXSum_x = rightXSum_x + (double)src_point.x * src_weight;
rightXSum_y = rightXSum_y + (double)src_point.y * src_weight;
rightWeightSum = rightWeightSum + src_weight;
}
double left_src_x = leftXSum_x / leftWeightSum;
double left_src_y = leftXSum_y / leftWeightSum;
double right_src_x = rightXSum_x / rightWeightSum;
double right_src_y = rightXSum_y / rightWeightSum;
if (left_src_x<0)
left_src_x = 0;
if (left_src_y<0)
left_src_y = 0;
if (left_src_x >= width)
left_src_x = width - 1;
if (left_src_y >= height)
left_src_y = height - 1;
if (right_src_x<0)
right_src_x = 0;
if (right_src_y<0)
right_src_y = 0;
if (right_src_x >= width)
right_src_x = width - 1;
if (right_src_y >= height)
right_src_y = height - 1;
Vec3b left_scalar = bilinear(ori_leftImage, left_src_x, left_src_y);
Vec3b right_scalar = bilinear(ori_rightImage, right_src_x, right_src_y);
Vec3b new_scalar;
new_scalar.val[0] = (1 - ratio)*left_scalar.val[0] + ratio*right_scalar.val[0];
new_scalar.val[1] = (1 - ratio)*left_scalar.val[1] + ratio*right_scalar.val[1];
new_scalar.val[2] = (1 - ratio)*left_scalar.val[2] + ratio*right_scalar.val[2];
new_image.at<Vec3b>(y, x) = new_scalar;
}
}
char win_name[16];
char img_name[50];
sprintf(img_name, "%s_%d.jpg", new_image_name.c_str(), frame_index);
imshow(img_name, new_image);
imwrite(img_name,new_image);
return;
}
void Morpher::runWarp()
{
for (int i = 0; i<frame_count; i++)
{
Image curImage = Image(i, first_image_name, second_image_name);
printf("warping %d...\n", i);
curImage.Warp(frame_count,new_image_name, pairs);
}
}
void Morpher::show_pairs()
{
int len = pairs.size();
printf("pairs size=%d\n", len);
for (int i = 0; i<len; i++)
{
printf("leftLine:");
pairs[i].leftLine.show();
printf("rightLine:");
pairs[i].rightLine.show();
printf("\n");
}
}
void Morpher::on_mousel(int event, int x, int y, int flag, void* param)
{
Morpher* pm = (Morpher*)param;
int& counter=pm->counter;
LinePair& curLinePair = pm->curLinePair;
Mat& leftImage = pm->leftImage;
Mat& leftImageTmp = pm->leftImageTmp;
Scalar& color = pm->color;
int& thickness = pm->thickness;
int& shift = pm->shift;
if (counter % 2 == 0 && pm->counter > 0)
{
curLinePair.warpLine.clear();
if (event == CV_EVENT_LBUTTONDOWN || event == CV_EVENT_RBUTTONDOWN){
printf("Left image( %d, %d) ", x, y);
printf("The Event is : %d ", event);
printf("The flags is : %d ", flag);
printf("The param is : %d\n", param);
curLinePair.leftLine.P.x = x;
curLinePair.leftLine.P.y = y;
cout << "P:" << curLinePair.leftLine.P.x << '\t' << curLinePair.leftLine.P.y << endl;
}
if (event == CV_EVENT_LBUTTONUP || event == CV_EVENT_RBUTTONUP){
printf("Left image( %d, %d) ", x, y);
printf("The Event is : %d ", event);
printf("The flags is : %d ", flag);
printf("The param is : %d\n", param);
curLinePair.leftLine.Q.x = x;
curLinePair.leftLine.Q.y = y;
curLinePair.leftLine.PQtoMLD();
cout <<"P:"<< curLinePair.leftLine.P.x <<'\t'<< curLinePair.leftLine.P.y << endl;
cout << "Q:" << curLinePair.leftLine.Q.x << '\t' << curLinePair.leftLine.Q.y << endl;
line(leftImage, curLinePair.leftLine.P, curLinePair.leftLine.Q, color, thickness, CV_AA, shift);
leftImageTmp = leftImage.clone();
counter--;
}
if (flag == CV_EVENT_FLAG_LBUTTON || flag == CV_EVENT_FLAG_RBUTTON){
curLinePair.leftLine.Q.x = x;
curLinePair.leftLine.Q.y = y;
leftImage.release();
leftImage = leftImageTmp.clone();
line(leftImage, curLinePair.leftLine.P, curLinePair.leftLine.Q, color, thickness, CV_AA, shift);
imshow("left", leftImage);
}
}
else
{
//cout << "you have selected the wrong image" << endl;
}
}
void Morpher::on_mouser(int event, int x, int y, int flag, void* param)
{
Morpher* pm = (Morpher*)param;
int& counter = pm->counter;
LinePair& curLinePair = pm->curLinePair;
Mat& rightImage = pm->rightImage;
Mat& rightImageTmp = pm->rightImageTmp;
int& frame_count = pm->frame_count;
vector<LinePair>& pairs = pm->pairs;
Scalar& color = pm->color;
int& thickness = pm->thickness;
int& shift = pm->shift;
if (counter % 2 == 1 && counter > 0)
{
if (event == CV_EVENT_LBUTTONDOWN || event == CV_EVENT_RBUTTONDOWN){
printf("right image( %d, %d) ", x, y);
printf("The Event is : %d ", event);
printf("The flags is : %d ", flag);
printf("The param is : %d\n", param);
curLinePair.rightLine.P.x = x;
curLinePair.rightLine.P.y = y;
}
if (event == CV_EVENT_LBUTTONUP || event == CV_EVENT_RBUTTONUP){
printf("right image( %d, %d) ", x, y);
printf("The Event is : %d ", event);
printf("The flags is : %d ", flag);
printf("The param is : %d\n", param);
curLinePair.rightLine.Q.x = x;
curLinePair.rightLine.Q.y = y;
curLinePair.rightLine.PQtoMLD();
line(rightImage, curLinePair.rightLine.P, curLinePair.rightLine.Q, color, thickness, CV_AA, shift);
rightImageTmp = rightImage.clone();
counter--;
curLinePair.genWarpLine(frame_count);
pairs.push_back(curLinePair);
printf("\n");
pm->show_pairs();
counter = 0;
}
if (flag == CV_EVENT_FLAG_LBUTTON || flag == CV_EVENT_FLAG_RBUTTON){
curLinePair.rightLine.Q.x = x;
curLinePair.rightLine.Q.y = y;
rightImage.release();
rightImage = rightImageTmp.clone();
line(rightImage, curLinePair.rightLine.P, curLinePair.rightLine.Q, color, thickness, CV_AA, shift);
imshow("right", rightImage);
}
}
else
{
//cout << "you have selected the wrong image" << endl;
}
}
void Morpher::main()
{
first_image_name = "test_img/1.jpg";
second_image_name = "test_img/2.jpg";
new_image_name = "morph";
//設置動畫的過渡幀數，比如1爲50%，3爲25%，50%，75%
frame_count = 3;
leftImage = imread(first_image_name);
rightImage = imread(second_image_name);
leftImageTmp = leftImage.clone();
rightImageTmp = rightImage.clone();
namedWindow("left", 1);
moveWindow("left", 10, 10);
namedWindow("right", 1);
moveWindow("right", 300, 10);
setMouseCallback("left", on_mousel, this);
setMouseCallback("right", on_mouser, this);
imshow("left", leftImage);
imshow("right", rightImage);
while (true)
{
key = waitKey(0);
if (key == 'c')
counter =counter + 2;
else if (key == 'w')
runWarp();
else if (key == 'q')
break;
}
imwrite("left_marked.jpg",leftImage);
imwrite("right_marked.jpg", rightImage);
return;
}
運行方法及效果
在Morpher類成員函數main()的實現裏，指定兩幅輸入圖像的路徑字符串。指定輸出圖像的名稱字符串。指定變形過渡的幀數。這裏設爲3。
first_image_name = "test_img/1.jpg";
second_image_name = "test_img/2.jpg";
new_image_name = "morph";
//設置動畫的過渡幀數，比如1爲50%，3爲25%，50%，75%
frame_count = 3;按下“C”鍵交互式的在兩幅圖像上畫出對應特徵線。每選取一對，按一次“C”鍵。
按下“W”鍵，開始warping…
0%:
25%:
50%:
75%:
100%:
其它：
