Question about handdetector module

[shimiaoli]

Hi, @moberweger ,
In handdetector.py module, line 192, while project to 2D:
xstart = int(numpy.floor((com[0] * com[2] / self.fx - size[0] / 2.) / com[2]*self.fx))
Only when I take Zstart = Zcom (=com[2]) , I can derive out the same equation and cancel out ux.
However, I think it should be Zstart = Zcom - size[2]/2 ? Or you have made an approximation Zstart ~= Zcom here ?
Thanks.

[moberweger]

@shimiaoli
So assume com3D is the com point in 3D (com3D=(com[0]+ux) * com[2] / fx). Then a metric cube is extracted around this point, which has z-coordinates com3D[2] +/- size[2]/2 (handdetector.py L190-191). Then, we calculate the top and bottom projections around the 3D point com3D by com3D[0] +/- size[0]/2 for the x-axis, ie the top and bottom side of the cube. The z-coordinate stays the same, since we only add on the x-axis. This way, the 2D crop (2D projections of these sides of the cube) is taken around the com3D point with z=com3D[2]. Otherwise the crop would be larger if we take the top and bottom part from the back side of the cube or smaller from the front side, ie z=com3D[2] +/- size[2]. Also, the different sizes would depend on the distance of com3D to the camera, which should be irrelevant for the hand pose and would make the problem harder. Using this parametrization ux cancels and one should derive the used equation.

[jakeoung]

Sorry, but could I have a question? How do we cancel out ux? My derivation is like this: (I assume com3D=(com[0]-ux) * com[2] / fx)

((com[0] - ux) * com[2] / self.fx - size[0] / 2.) / com[2]*self.fx)

Here, I don't know how to cancel out $ux$.

[moberweger]

Hi @jakeoung
So the derivation could go like this:

Since
com3D=(com[0]-ux) * com[2] / fx <--> com[0] = com3D * fx / com[2] + ux

we plug in and derive
((com[0] - ux) * com[2] / fx - size[0] / 2.) / com[2]*fx + ux = com[0] - size[0] / 2. * fx / com[2]

[jakeoung]

Hello @moberweger,
I am very thankful for your reply. I can understand it now!