Matrix Transformation for image-CodePudding

I am working on an image processing project in python in which I am required to change the coordinate system

I thought it is analogous to matrix transformation and tried but it is not working, I have taken the coordinates of the red dots

CodePudding user response：

Simply subtract by 256 and divide by 512. The connection is that you see values of 256 get mapped to 0. Therefore, 0 gets mapped to -256, 256 gets mapped to 0 and 512 gets mapped to 256. However, you further need the values to be in the range of [-0.5, 0.5]. Dividing everything by 512 finishes this off.

Therefore the relationship is:

out = (in - 256) / 512 = (in / 512) - 0.5

Try some values from your example input above to convince yourself that this is the correct relationship.

If you want to form this as a matrix multiplication, this can be interpreted as an affine transform with scale and translation, but no rotation:

    [ 1/512 0   -0.5 ]
K = [   0 1/512 -0.5 ]
    [   0   0     1  ]

Take note that you will need to use homogeneous coordinates to achieve the desired result.

For example:

(x, y) = (384, 256)

[X]   [ 1/512 0   -0.5 ][384]
[Y] = [   0 1/512 -0.5 ][256]
[1]   [   0   0     1  ][ 1 ]

[X]   [384/512 - 0.5]   [ 0.25 ]
[Y] = [256/512 - 0.5] = [   0  ]
[1]   [      1      ]   [   1  ]

Simply remove the last coordinate to get the final answer of (0.25, 0).