Image Affinement and Real-time Object Detection

The homography transformation is based on the following formulae[4]:
homography formula

A Homography is a transformation ( a 3×3 matrix ) that maps the points

in one image to the corresponding points in the other image.[5]

$H = \left[ \begin{array}{ccc} h_{00} & h_{01} & h_{02} \\ h_{10} & h_{11} & h_{12} \\ h_{20} & h_{21} & h_{22} \end{array} \right]$

$\left[ \begin{array}{c} x_1 \\ y_1 \\ 1 \end{array} \right] &= H \left[ \begin{array}{c} x_2 \\ y_2 \\ 1 \end{array} \right] &= \left[ \begin{array}{ccc} h_{00} & h_{01} & h_{02} \\ h_{10} & h_{11} & h_{12} \\ h_{20} & h_{21} & h_{22} \end{array} \right] \left[ \begin{array}{c} x_2 \\ y_2 \\ 1 \end{array} \right]$

homography example

Image Alignment Using Homography

Image Alignment using Homography

Translation[6]

Rotation[6]

Affine Transformation[6]

Perspective Transformation[6]

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How to find angle between two images[10]

cv::Point3d findOrientation(const cv::Mat& src){      cv::Moments m = cv::moments(src, true);      double cen_x=m.m10/m.m00;      double cen_y=m.m01/m.m00;     double m_11= 2*m.m11-m.m00*(cen_x*cen_x+cen_y*cen_y);// m.mu11/m.m00;         double m_02=m.m02-m.m00*cen_y*cen_y;// m.mu02/m.m00;     double m_20=m.m20-m.m00*cen_x*cen_x;//m.mu20/m.m00;         double theta = m_20==m_02?0:atan2(m_11, m_20-m_02)/2.0;    //  theta = (theta / PI) * 180.0; //if you want in radians.(or vice versa, not sure)    return cv::Point3d(cen_x,cen_y,theta);}