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    <p>You need more information, that transformed figure could come from any parallelogram given an arbitrary perspective.</p> <p>So I guess you need to do some kind of calibration first.</p> <p><strong>Edit:</strong> for those who said that I was wrong, here goes the mathematical proof that there are infinite combinations of rectangles/cameras that yield to the same projection:</p> <p>In order to simplify the problem (as we only need the ratio of the sides) let's assume that our rectangle is defined by the following points: <code>R=[(0,0),(1,0),(1,r),(0,r)]</code> (this simplification is the same as transforming any problem to an equivalent one in an affine space).</p> <p>The transformed polygon is defined as: <code>T=[(tx0,ty0),(tx1,ty1),(tx2,ty2),(tx3,ty3)]</code></p> <p>There exists a transformation matrix <code>M = [[m00,m01,m02],[m10,m11,m12],[m20,m21,m22]]</code> that satisfies <code>(Rxi,Ryi,1)*M=wi(txi,tyi,1)'</code></p> <p>if we expand the equation above for the points,</p> <p>for <code>R_0</code> we get: <code>m02-tx0*w0 = m12-ty0*w0 = m22-w0 = 0</code></p> <p>for <code>R_1</code> we get: <code>m00-tx1*w1 = m10-ty1*w1 = m20+m22-w1 = 0</code></p> <p>for <code>R_2</code> we get: <code>m00+r*m01-tx2*w2 = m10+r*m11-ty2*w2 = m20+r*m21+m22-w2 = 0</code></p> <p>and for <code>R_3</code> we get: <code>m00+r*m01-tx3*w3 = m10+r*m11-ty3*w3 = m20 + r*m21 + m22 -w3 = 0</code></p> <p>So far we have 12 equations, 14 unknown variables (9 from the matrix, 4 from the <code>wi</code>, and 1 for the ratio <code>r</code>) and the rest are known values (<code>txi</code> and <code>tyi</code> are given).</p> <p>Even if the system weren't underspecified, some of the unknowns are multiplied among themselves (<code>r</code> and <code>mi0</code> products) making the system non linear (you could transform it to a linear system assigning a new name to each product, but you'll end still with 13 unknowns, and 3 of them being expanded to infinite solutions).</p> <p>If you can find any flaw in the reasoning or the maths, please let me know.</p>
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    1. POproportions of a perspective-deformed rectangle
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    1. COBut he knows its a rectangle. i.e. scanned documents.
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    2. CO@Neil N So what? Maybe now the rectangles are not parallelograms and I haven't noticed...
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    3. CObecause rectangles have all 90 degree corners, which takes the possible rotations down from infinity to one (well technically two if you consider he could be looking at the back side). A huge difference.
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