COMP558
Assignment1
Common mistakes
Grader: Florian Shkurti 

Q1:
The most common mistake in this question was that instead of projecting
3D scene points on the plane Z=f like this: 

[x_pixel, y_pixel, 1] = K * [X Y Z]'

in some submissions people were trying to reverse the axes of the pixel
sensor plane, so that a positive displacement in the 3D axes corresponded
to a positive displacement on the sensor plane axis. Doing this is not 
necessary because it is expected that the 3D scene will be reversed when 
being projected onto the sensor plane. To avoid thinking about this inversion
you can think of the sensor plane as being placed in front of the origin of 
the camera.  
 
Q2: 
While there were several problems in the solutions of this question, there
didn't exist a theme among all the mistakes, and the question was in general
well-done. 

One point worth mentioning is that some students mentioned that they were
getting different signs for tilt depending on the choice of points on the image. 
This might have to do with the fact that atan() has range [-pi/2, pi/2]
while acos() has range [0, pi]. Also be aware of the existence of atan2()
in which you can basically decide the quadrant you want the resulting angle
to be in.  

Q3: 
One of the common issues in this question was that when reporting Z0=D/C
as a length you need to make sure that it is positive, which many people
didn't worry about.

Another issue was that many submissions used fsolve() or fzero(), which are
useful when trying to find minima of nonlinear functions, or roots of nonlinear
equations. These functions are in general sensitive to their initial conditions,
and it doesn't make sense to use them when you can derive the formula for the
solution of the system by hand, although it is cool that people were aware of 
their existence. 

Q4: 
The most common mistake here was that instead of projecting 3D points 
on the plane Z=Zsensor, most submissions projected them on Z=f. Zsensor
and f are in general very close so the results at the end would be almost the 
same. So, instead of using

K = [f*mx    0     px;
      0     f*my   py;
      0      0     1]

a technically more correct thing to do would be

K = [Zsensor*mx    0         px;
      0         Zsensor*my   py;
      0            0         1]

Keep in mind that both the pinhole and the thin lens model, are simply approximations
of how cameras work, and not perfect models. The second K is a better approximation than 
the first K. 

Another point worth mentioning is that, since the exercise said "assume a thin lens model,"
some submissions used the following projection equations: 

(Xi, Yi, Zi) = (f*X0/(Z0 - f), f*Y0/(Z0 - f), f*Z0/(Z0-f))

This is not correct because this equation projects a 3D point (X0, Y0, Z0) to the plane Zi
where the conjugate point would have zero blur. This plane Zi might or might not be the sensor 
plane.