How to compute the homography

Dear Community,

I have some issue to getting the trasnform image for homography

I want to apply the homography to an image, I do have homography martix from the general formulation

H = R+1/d*n*t'

H = rotation_matrix + t.* Normal

H =

         0   -1.0000         0
   -0.3420         0   -0.9397
    5.9397    5.0000    4.6580

The basic concept of idea is to trying get image from vitrual camera, so the question I that how I can get the image from virtual camera ?

As you can see figure below , I have perspective image but I want to use inverse perspective mapping

Thanking you so much

Answer 1

[darova]

Hi, that green trapezoid is what you want. Can be found as line intersections of plane

But having all those point on a plane (in 3D) dont know how to convert them into 2D (to get that trapezoid in XY):

And how to convert image (pixels position) having that trapezoid?

See attached files

[Sushil Sharma]

Thank you so much darova for your answer

But having all those point on a plane (in 3D) dont know how to convert them into 2D (to get that trapezoid in XY):

Well, I want to know that how do you convert then into 2D in XY plane, I saw plot and really intresting, actually I need that answer, It will really appricate, if you provide my answer

Thanks once agian

[darova]

Create vectors Nx, Ny first:

NX = cross([0 0 1],-NZ);   % camera X-axis 
NX = NX/norm(NX);
NY = cross(NX, NZ);        % camera Y-axis
NY = NY/norm(NY);

Then using dot product convert each point in 2D:

Where, P = (x,y,z) - point on plane

[Sushil Sharma]

Thank you so much darova for your answer,

I get some idea, now I understand how to deal with situation,

Really apppericate for your help,

I wish in future you will clear my doubt as you did now

Thanks in advance

Answer 2

[Matt J]

tform = projective2d(H);

newImage = imwarp(oldImage,tform);

[Omar Ali]

how i can apply it on input image?

[Matt J]

That's what this line does

newImage = imwarp(oldImage,tform);