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How is depth determined from a disparity image?

KB Number: 10102

Last Revision Date: 5/14/2015

Created Date: 3/5/2014

This article details how users can determine the depth of a pixel based on the disparity image.

The easy answer is one should use one of:

`triclopsRCD8ToXYZ()`

`triclopsRCD16ToXYZ()`

`triclopsRCDFloatToXYZ()`

to determine the 3d position of a pixel in a disparity image.

`triclopsRCD8ToXYZ()`

is used when subpixel interpolation disabled and the user obtains a disparity value from the 8 bit TriclopsImage structure.

`triclopsRCD16ToXYZ()`

is used when subpixel interpolation is enabled and the user obtains a disparity value from the 16 bit TriclopsImage16 structure.

`triclopsRCDFloatToXYZ()`

is used when one obtains the disparity measure from other means, such as doing your own feature-based stereo.

The underlying equation that performs this conversion is:

`Z = fB/d`

where

Z = distance along the camera Z axis

f = focal length (in pixels)

B = baseline (in metres)

d = disparity (in pixels)

After Z is determined, X and Y can be calculated using the usual projective camera equations:

`X = uZ/f`

Y = vZ/f

where

u and v are the pixel location in the 2D image

X, Y, Z is the real 3d position

Note: u and v are not the same as row and column. You must account for the image center. You can get the image center using the triclopsGetImageCenter() function. Then you find u and v by:

`u = col - centerCol`

v = row - centerRow

Note: If u, v, f, and d are all in pixels and X,Y,Z are all in the meters, the units will always work i.e. pixel/pixel = no-unit-ratio = m/m.

**How accurate is it?**

Accuracy for stereo vision is difficult to exactly quantify, since the accuracy depends on the accuracy of the correlation match, which can depend on the image texture. However, a good 'rule of thumb' is to expect a 0.2 matching error in disparity matching. The PGR stereo vision calibration process minimizes the RMS pixel error between the observed and predicted locations of a set of calibration points, as dictated by the camera’s intrinsic and extrinsic values. The calibration of Digiclops and Bumblebee systems is usually within 0.08 pixels RMS error; the rest of the error is attributed to the stereo matching algorithm.

To determine the error at a particular Z value, do the following:

Assume `Z = 1.0m`

d = fB/Z

Since fB is a constant, you can determine the d value for this Z.

The error in Z would then be:

`delta Z = |Z - Z'|`

where `Z' = fB/(d+e)`

where e is the error in matching. So the whole equation works out to:

`delta Z = | fB/d - fB/(d+e) |`