Affine transformation implementation

         To deal with the affine transformation task, it is necessary to obtain three coordinate points of the target area of two images (（x11,y11）,（x21,y21）,（x31,y31） And （x12,y12）,（x22,y22）,（x32,y32）), Three points define a plane , By solving 6 Equations obtained 6 Parameters .

         Equation form ：

                x1=x2*a+y2*b+k1;

                y1=x2*c+y2*d+k2;

         adopt opencv Self contained cv2.getAffineTransform() Function to obtain the parameter matrix M, And function cv2.warpAffine() Obtain the image after affine transformation .

test

ptsa.jpg

ptsb.jpg

 res.jpg

         The implementation will ptsa Replace the two triangle colors with ptsb The color of the , keep ptsa It's the same shape . Without getting ptsb In the case of color , Use affine transformation to transform ptsb The shape in changes directly to ptsa, Then change the transformed ptsb The coordinates in and ptsa Correspond and replace .

There are ways to deal with it 2 Kind of ：

1、 Reduce the circumscribed rectangle of the triangle area to the same size , After affine transformation, the target area of the image can be directly replaced with the original image .

2、 Do not shrink , The parameter matrix is obtained by direct affine transformation M（a,b,k1,c,d,k2）, All coordinates of the target area need to be M Mapping transformation （ The above equation ） To the original .

Method 1 implementation code ：

import cv2
import numpy as np

imga=cv2.imread('img/pica.jpg')
imgb=cv2.imread('img/picb.jpg')

ptsa=np.float32([[100,200],[250,100],[300,250]])#ptsa Three point coordinates of the left triangle area of 
ptsb=np.float32([[50,120],[150,50],[120,130]])#ptsb Three point coordinates of the left triangle area of 

ptsa_=np.float32([[250,100],[300,250],[400,150]])#ptsa Three point coordinates of the right triangle area 
ptsb_=np.float32([[150,50],[120,130],[220,80]])#ptsb Three point coordinates of the right triangle area 

# np.float32([[0,70*rh],[100*rw,0],[70*rw,80*rh]])

def IsTrangleOrArea(x1, y1, x2, y2, x3, y3):
    return abs((x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2)) / 2.0)


def IsInside(x1, y1, x2, y2, x3, y3, x, y):
    #  triangle ABC The area of 
    ABC = IsTrangleOrArea(x1, y1, x2, y2, x3, y3)

    #  triangle PBC The area of 
    PBC = IsTrangleOrArea(x, y, x2, y2, x3, y3)

    #  triangle ABC The area of 
    PAC = IsTrangleOrArea(x1, y1, x, y, x3, y3)

    #  triangle ABC The area of 
    PAB = IsTrangleOrArea(x1, y1, x2, y2, x, y)

    return (ABC == PBC + PAC + PAB)


def warpTriangle(ptsa,ptsb,imga,imgb):
    r1=cv2.boundingRect(ptsa)
    r2=cv2.boundingRect(ptsb)
    roia=imga[r1[1]:r1[1]+r1[3],r1[0]:r1[0]+r1[2],:]
    roib=imgb[r2[1]:r2[1]+r2[3],r2[0]:r2[0]+r2[2],:]

    rate_h=roia.shape[0]/roib.shape[0]
    rate_w=roia.shape[1]/roib.shape[1]
    roib=cv2.resize(roib,(0,0),fx=rate_w,fy=rate_h)
    nptsa=[]
    nptsb=[]
    for i in range(3):
        nptsa.append([ptsa[i,0]-r1[0],ptsa[i,1]-r1[1]])
        nptsb.append([(ptsb[i, 0] - r2[0])*rate_w, (ptsb[i, 1] - r2[1])*rate_h])

    # print(ptsa)
    # print(ptsb)
    # print(nptsa)
    # print(nptsb)
    nptsa=np.array(nptsa,dtype=np.float32)
    nptsb=np.array(nptsb,dtype=np.float32)
    M=cv2.getAffineTransform(nptsb,nptsa)
    dst=cv2.warpAffine(roib,M,(roib.shape[1],roib.shape[0]))


    res=imga.copy()
    # print(ptsa[0,0], ptsa[0,1], ptsa[1,0], ptsa[1,1],ptsa[2,0], ptsa[2,1])
    print(r1[0],r1[0]+r1[2],r1[1], r1[1] + r1[3])
    for i in range(r1[1],r1[1]+r1[3]):
        for j in range(r1[0], r1[0] + r1[2]):
            if IsInside(ptsa[0,0], ptsa[0,1], ptsa[1,0], ptsa[1,1],ptsa[2,0], ptsa[2,1],j,i):
                res[i,j,:]=dst[i-r1[1],j-r1[0],:]

    return res


    # cv2.imshow('roia',roia)
    # cv2.imshow('dst',dst)


res=warpTriangle(ptsa,ptsb,imga,imgb)
res=warpTriangle(ptsa_,ptsb_,res,imgb)
cv2.imshow('res',res)
cv2.imshow('imgb',imgb)
cv2.imshow('imga', imga)
cv2.imwrite('res.jpg',res)
cv2.waitKey()

application ：

Because the pixels in the rectangular area are traversed in the process of image processing , Affine transformation requires 3 Point coordinates （ That is, a triangle ）, The transformed image Some areas It cannot be directly replaced with the original drawing , The effective area is just inside the triangle , So we need to use the area method to replace the effective area . If the situation is complex , You need to split the target area into multiple triangular areas （ Get the coordinates of three points ） Perform affine transformation respectively . At the same time, attention should be paid to boundary treatment .

Affine transformation principle reference ：

What is affine transformation (Affine Transformation) - Alexander - Blog Garden

【OpenCV Learning notes 】 The affine transformation of （Affine Transformation）_ Little by little, little by little, little by little ~ The blog of -CSDN Blog _ Affine transformation

Affine transformation principle of image and c++ Realization （ rotate , translation , The zoom , The offset , Combination transformation ）_ Xiao Wu ~~ The blog of -CSDN Blog _c++ Affine transformation