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I was looking at the following link:

http://www.dimensions-math.org/Dim_CH5_E.htm

The section 6 deals with conformal mapping of the image for different kinds of transformations. I tried to reproduce them in mathematica for the transformation [itex]z \rightarrow z^2[/itex].

I followed the following algorithm:

1. Take an image and obtain the values for all pixels, say (x,y)=0.2.

2. Then I transformed the coordinates according to the transformation [itex](x,y)\rightarrow (x^2-y^2, 2xy)[/itex].

3. The previously stored pixel values are now assigned to these new coordinates.

4. Get the new image.

The problem I am facing is that the dimension of the image changes from [itex]m \times n \rightarrow m^2 \times n^2 [/itex] after the transformation. But I know the pixel values for only m n points. Thus I don't have enough points to generate the final image.

Can you suggest a way out of this difficulty or any other algorithm to generate the images.

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# Conformal mapping of images

Can you offer guidance or do you also need help?

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