Transformation Concept in OpenCV

c++, computer-vision, image-processing, opencv

Solution

1) It is not a question about OpenCV but rather about mathematics. Applying affine transformation to point (x,y) means the following:

x_new = a*x + b*y + c;
y_new = d*x + e*y + f;

And so affine transform has 6 degrees of freedom: a, b, c, d, e, f. They are stored in 2x3 matrix: a, b, c in the first row, and d, e, f in the second row. You can apply transform to a point by multiplying of matrix and vector.

Perspective transform of (x,y) would be:

z = g*x + h*y + 1;
x_new = (a*x + b*y + c)/z;
y_new = (d*x + e*y + f)/z;

As you can see it has 8 degrees of freedom that are stored in 3x3 matrix. Third row is g, h, 1.

See also homogeneous coordinates for more information about why this representation is so convenient.

2) Affine transformation is also called 'weak perspective' transformation: if you are looking at some scene from different perspective but size of the scene is small relatively to distance to the camera (i.e. parallel lines remain more or less parallel), than you may use affine transform. Otherwise perspective transform will be required.

Problem

I am new to opencv. and I am right now going through with the concept of Image Transformation in OpenCV. So my question is, 1) Why does Affine Transformation use 2*3 matrix and perspective transformation use 3*3 matrix? 2) When to use Affine transformation and Perspective transformation over each other? Any Suggestions?

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