I want your guidance in following problem.

I have a Rectangle with a known height and width. (aspect ration is fixed) It has a plane surface. Something like cardboard. Or Rectangle Drawn on wall.

I am now taking image of this rectangle from webcam.

After taking image of this rectangle from webcam, rectangle occupy small area on image and that is in a form of quadrilateral inside image. I can calculate the XY location of Rectangle from image , So I have Following Matrix

Co-ordinate on image -> Actual real world co-ordinate

_______________________________________

X1 Y1 -> 0 , 0

X2 Y2 -> width, 0

X3 Y3 -> 0, height

X4 Y4 -> width, height

________________________________________

width and height of rectangle is known because I can measure this real object

X1 Y1 to X4 Y4 are 4 co-ordinate of this object in image. Because it is a projective transformation, this will be in a shaped of quadrilateral.

Now I want to know a matrix operation or any formula, by which I can convert a given X Y of image into corresponding co-ordinate on rectangle.

I think, this is known as homography. seeing on web, i can find complex description and formulas which i am unable to understand.

May you give me exact formula for how to do it.

Thanks !

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│ Narendra Sisodiya

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http://narendrasisodiya.com
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