3D reconstruction from a 2D image
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Damon Pierre-Marie
il 9 Nov 2017
Commentato: Ayush singhal
il 22 Mag 2021
Hello,
I have some difficulties to reconstruct a 3D scene from a 2D image. I would like to create a top view of scene removing the perspective, in other words, realize an inverse perspective mapping. Let's assume we know the camera position, orientation and its parameters. Moreover we consider all the captured points lie on the same plane XY. Then, it is easy to prove that a pixel at a (u,v) location in the image will move to the coordinate (X,Y,0) in the 3D space with:
X=-((u*P(3,4)-P(1,4))*(v*P(3,1)-P(2,1)) + (v*P(3,4)-P(2,4))*(P(1,1)-u*P(3,1)))/((u*P(3,2)-P(1,2))*(v*P(3,1)-P(2,1)) + (v*P(3,2)-P(2,2))*(P(1,1)-u*P(3,1)));
Y=(X*(u*P(3,2)-P(1,2)) + (u*P(3,4)-P(1,4)))/(P(1,1)-u*P(3,1));
P is the projection matrix such that: P=[KR KT] with K,R and T respectively the intrinsic, rotation and translation matrices.
Once all the 3D locations of each pixel are computed, I would like to display the XY plane with the color information of the original pixel as if it was a 2D image.
However, a pixel (u,v) can mapped in 3D space to a non integer location meaning that I get a non-regular scatter plot were each (X,Y) point contain a color information. I tried to divide the XY plane into small windows and then compute the average color of all points into each squares but it is very slow.
Please find my code enclosed. Some help would be appreciated!
Thank you in advance, Pm
8 Commenti
mostafa TAIBI
il 13 Feb 2020
another question if you allow, for the 3d reconstruction is that you take all the pixels of the image after you use the formula to calculate X and Y?
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Matt J
il 9 Nov 2017
Modificato: Matt J
il 9 Nov 2017
Once all the 3D locations of each pixel are computed, I would like to display the XY plane with the color information of the original pixel as if it was a 2D image.
I don't think you need to be doing the work of mapping and interpolating the coordinates. I think it should be as simple as
Image2 = imwarp(Image1,projective2d(P(:,[1,2,4]).'))
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