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Affine transformation blog post portal (the paid column with an asterisk):
- Image Affine Transformation Principle 1: Detailed explanation of the ins and outs of homogeneous coordinates
- Image affine transformation principle 2: matrix transformation, linear transformation and image linear transformation matrix
- Image affine transformation principle 3: affine transformation type and transformation matrix detailed explanation
- Image affine transformation principle 4: combination transformation and corresponding transformation matrix
- Image affine transformation principle 5: OpenCV-Python implementation of combined transformation matrix
For detailed instructions, please refer to " https://blog.csdn.net/LaoYuanPython/article/details/113804210 Image Affine Transformation Principle 2: Matrix Transformation, Linear Transformation and Image Linear Transformation Matrix ".
Second, the transformation matrix
Assuming that the origin of the coordinates in the two-dimensional rectangular coordinate system is o, the coordinates of a point v in the image are (x, y), and the coordinates of the transformed point v'are (x', y'). The linear transformation of all two-dimensional images can be expressed as:
The rotation transformation matrix is:
The miscut transformation matrix is: the
scaling transformation matrix is:
Three, summary
This section introduces the transformation matrix of image rotation, miscutting, and scaling transformation. Image rotation, miscutting, and scaling transformation can be represented by a matrix left multiplication vector, and this representation is essentially a matrix transformation, according to the definition of linear transformation and Matrix addition, number multiplication, and multiplication can prove that matrix transformation is linear transformation.
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For more basic mathematical knowledge of image processing, please refer to the column " Artificial Intelligence Mathematical Foundation https://blog.csdn.net/laoyuanpython/category_10382948.html "
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