Image transform polar to cartesian

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I am making a project for my college that involves image manipulation or conversion from polar to cartesian in Visual Studio C#. I tried finding solution on web for my problem but haven't been able to find anything relevant. If someone can help or provide a terminology so that I can search web and find it myself I would be thankful.

So basicly in the next image is depicited the transformation I need to perform. The image on the left is input, and the image on the right is the output.

http://www.deviantpics.com/images/2014/11/26/Untitled0anK9.png

Anybody has any idea?

This is the pic that I have to transform for it to look like I am looking at it from the front.

deviantpics.com/images/2014/11/26/Slika2.jpg

This is what I did until today.

deviantpics.com/images/2014/11/26/Slika222222.png

The final problem is that I have to analyze the object and symbols on him and compare it to the picture and symbol of the last object (symbol comparison, in this case stars).

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