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Given the convex quadrilateral Q. The problem is to determine if $\exists$ a rectangle and a camera perspective projection matrix M (3x4), so that Q = M*R.

My question is similar: Mapping Irregular Quadrilateral to a Rectangle but not exactly duplicate.

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kelin
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Every strictly convex quadrilateral (with angles strictly less than $180^\circ$) is the perspective projection of a rectangle.

In the projective plane, identify the two points where opposite sides of the quadrilateral intersect. It is always possible with a projective transformation to move two different points to points that are $90^\circ$ apart on the line at infinity. This transformation takes the entire original quadrilateral to a rectangle.

hmakholm left over Monica
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    Thank you for the answer. Can you clarify what does "points that are 90∘90∘ apart on the line at infinity" mean? I could not understand this with my low English. – kelin Jul 27 '16 at 13:48
  • Do you need a constructive way to find the rectangle and the point of view V ? I mean by that, that given 4 points $P_k(x_k,y_k)$ in the xOy plane, you want to know the coordinates of V as functions of the $x_k$ and $y_k$ and points $Q_k(X_k,Y_k)$ that can be candidates for being the vertices of the rectangle ? – Jean Marie Jul 27 '16 at 14:29
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    @JeanMarie, actually no. I'm just finding a way to filter out quadrilaterals detected on image, which are not rectangles. – kelin Jul 27 '16 at 14:52