View Full Version : simulate depth sensor
barcode
11092015, 02:16 AM
hi.
i have to simulate a depth sensor (RGB + depth).
as of the moment i have to use opengl2.
to do that i have to get the z buffer and the rgbimage.
as far as i found out i can get the zbuffer's values with:
glReadPixels(0, 0, w, h, GL_DEPTH_COMPONENT, GL_FLOAT, depht_buffer);
my questions:
1. is my method correct?
2. is there a better way to get the zbuffer?
3. as far as i know the zbuffer's values are nonlinear in [0, 1] with 0==clipNear and 1==clipFar.
how can i transform the zbuffer's values to a linear scale? (e.g. a value delta of 0.1 is the same distance independent of the corresponding values.)
thanks for any help.
/edit: fixed an error
GClements
11092015, 05:06 AM
1. is my method correct?
Yes.
2. is there a better way to get the zbuffer?
Not if you're limited to OpenGL 2 (and don't have the ARB_framebuffer_object extension).
3. as far as i know the zbuffer's values are nonlinear in [0, 1] with 0==clipNear and 1==clipFar.
how can i transform the zbuffer's values to a linear scale? (e.g. a value delta of 0.1 is the same distance independent of the corresponding values.)
If the clipspace coordinates don't have constant W, the depthbuffer values will be nonlinear with respect to eyespace Z. For a perspective projection, clipspace W is typically equal to eyespace Z.
The values in the depth buffer are equal to (Z/W+1)/2, where Z and W are the clipspace Z and W, linearly interpolated across the primitive.
If you know how both clipspace Z and W relate to eyespace Z (i.e. you know the projection matrix and you also know that eyespace W is always 1), then you can obtain eyespace Z from the depth values.
For a projection matrix of the form
[ ? ? ? ? ]
[ ? ? ? ? ]
[ 0 0 A B ]
[ 0 0 1 0 ]
and assuming Weye = 1, you have
Zclip = A*Zeye + B
Wclip = Zeye
Conversion to NDC involves dividing clipspace X,Y,Z by W:
Zndc = Zclip/Wclip
= (A*Zeye+B)/(Zeye)
= (A+B/Zeye)
Finally, NDC Z (which lies in the range 1 to +1) is converted to depth (in the range 0 to 1) by
depth = (Zndc+1)/2
= (1AB/Zeye)/2
(Actually, it can be slightly more complex than that if the depth range is changed with glDepthRange()).
Solving for Zeye gives
depth = (1AB/Zeye)/2
2*depth = 1AB/Zeye
B/Zeye = 1A2*depth
Zeye = B/(1A2*depth)
If the matrix is a typical perspective matrix (generated with e.g. gluPerspective(), glFrustum(), or equivalent), then
A = (zNear+zFar)/(zNearzFar)
B = 2*zNear*zFar/(zNearzFar)
In which case, the equation for Zeye becomes
Zeye = zFar*zNear/(depth*zNear + (1depth)*zFar);
or
Zeye = zFar*zNear/(zFar + depth*(zNear  zFar));
Note that typically A and B are both negative, and Zeye is negative for anything that's visible, with Zeye becoming increasingly negative as you get farther from the viewpoint (i.e. +Zeye is pointing out of the screen).
barcode
12042015, 05:28 AM
hi.
first thanks for your help.
with your equation for Zeye i was able to implement the depth cam and it worked good enough (since it was used on small distances and an error was assumed).
now the depth data is used to generate a point cloud and is used for simultaneous localization and mapping.
when we tried this we noticed flat surfaces are curved. (since Zeye is not the distance beween camera and object)
how i understood it:
in cam coord


cam< Zeye > ^
 \  
 \  missing part for distance
 distance  
 \  v
 >object
1) am i correct with my assumption of Zeye unequal distance(cam,obj) ?
2) if that's the case i need Xeye and Yeye to calculate the distance. How can i get them?
3) is there a better way to calculate the distance between the camera and an object.
thanks again for any help.
GClements
12042015, 11:03 AM
1) am i correct with my assumption of Zeye unequal distance(cam,obj) ?
As your diagram suggests, Zeye is the distance in front of the viewpoint, not the distance from the viewpoint. The distance from the viewpoint is the magnitude of the eyespace position vector (Xeye,Yeye,Zeye).
2) if that's the case i need Xeye and Yeye to calculate the distance. How can i get them?
They can be determined from the window coordinates (i.e. the row and column indices within the data returned by glReadPixels).
Given window coordinates (Xwin,Ywin), where (0,0) is the lowerleft corner of the window, (width,height) is the upperleft corner and (0.5,0,5) is the centre of the lowerleft pixel, the conversion from NDC to window coordinates is given by the viewport transformation, set with glViewport(Xv,Yv,Wv,Hv) (the first time a context is bound to a window, the viewport is automatically set to cover the entire window as if by glViewport(0,0,width,height); thereafter, the viewport must be set explicitly if the window is resized).
The conversion from NDC to window coordinates is
Xwin = (Xndc + 1)*(Wv/2) + Xv
Ywin = (Yndc + 1)*(Hv/2) + Yv
so the inverse conversion (from window coordinates to NDC) is
Xndc = (XwinXv)*(2/Wv)1
Yndc = (YwinYv)*(2/Hv)1
Conversion from clip coordinates to NDC involves division by W, i.e.
Xndc = Xclip/Wclip
Yndc = Yclip/Wclip
Zndc = Zclip/Wclip
so the inverse is
Xclip = Xndc * Wclip
Yclip = Yndc * Wclip
Zclip = Zndc * Wclip
For a perspective transformation, Wclip is proportional to Zeye, which you've already calculated. Typically, it's equal to Zeye. If you've managed to calculate Zeye correctly from Zndc, then you must already know Wclip.
Conversion from eye coordinates to clip coordinates is given by the projection matrix. In the general case, you would need to invert that matrix. But a projection matrix generated by gluPerspective() or glFrustum() always has the form
[Sx 0 Kx 0]
[ 0 Sy Ky 0]
[ ? ? ? ?]
[ ? ? ? ?]
so the conversion is
Xclip = Sx * Xeye + Kx * Zeye
Yclip = Sy * Yeye + Ky * Zeye
and the inverse is
Xeye = (Xclip  Kx * Zeye) / Sx
Yeye = (Yclip  Ky * Zeye) / Sy
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