Homography (Perspective) Transform: Desmos Visualization [E4]

[@liyilin399]

Hi ，thank you very much for your explanation, it helped me a lot, I want to use homography to correct a picture taken with a tilted camera, how do I calculate the value of h32 if I only know the tilted angle of the camera. Thank you for your answer.

[@pratikian]

@@liyilin399 could you email me the problem. I will have to understand what do you mean by tilted angle.

[@liyilin399]

@@pratikian thanks for answering my question!!! what is your email address?

[@utkarshkathuria2931]

Around 5:20 you say that this system is homogeneous, but as soon as we start to use 1inspite of third coordinate it becomes inhomogeneous. Is it right?

[@utkarshkathuria2931]

Also can you please explain how four points define a projective transformation. I try to read it from books but still couldn't get their meaning

[@pratikian]

@@utkarshkathuria2931 the system is not homogenous these co-ordinates that we use (x,y,1) these are called homogeneous co-ordinates. For more details of homogenous you can watch this video of mine kzbin.info/www/bejne/i4DJkpxtmclnY9U You can watch it from 2.29 min I will mail you a book that can clear a lot of concepts.

[@pratikian]

@@utkarshkathuria2931 to explain this I would suggest you to see this video on image registration. kzbin.info/aero/PLFXza2AmUJa-RJZJj3b5Wm76I9k_QthWC The concept is like this the homography matrix has 9 parameters of which we can fix one parameter as 1. So we have 8 parameters that we need to find out in the homography matrix. So in other sense you have 8 variables whose value you want to find out. Now if you select 1 point that gives you 2 equations. (You can look at the video how 1 point gives 2 equations) since you have 8 variables. You need minimum 8 equation So that you can get the solution. Hence if we have 4 points we will get 8 equations and we can define a homography matrix with it. In the video I have explained affine as well as homography. You can look at both of them for better clarity. Hope that helps

[@utkarshkathuria2931]

@@pratikian So what I get is homogenous coordinates are always in 3dimensions and if I have to go back to two dimensions divide the first and second components by the third component. Then how to define non-homogenous coordinates. Aren't they also in two dimensions?

[@pratikian]

@@utkarshkathuria2931 yes non homogenous co-ordinates are nothing but the simple x and y co-ordinates. In 2 dimentions homogeneous co-ordinates are given by (x,y,w) but essentially they are 2 dimention (x/w,y/w) this you can extend to the 3 dimentions. For 3 dimentions homogeneous co-ordinates are (X,Y,Z,W) where essentially they are (X/W , Y/W , Z/W)

[@shivamkaushik6637]

thanks for desmos link

[@shivamkaushik6637]

nice explanation

[@disnexuno]

thank you

[@ajinvinodk321]

thank uu

[@Xerox482]

yup dark mode is good :)

[@pratikian]

Thanks for the feedback

[@divyamgoel9183]

dark mode is lit !!