Understanding depth values in 3D point cloud

Question

I have problems understanding the depth (Z) value in 3D point cloud resulted from 3d sparse reconstruction like this example in MATLAB: http://www.mathworks.com/help/vision/ug/sparse-3-d-reconstruction-from-multiple-views.html

I have attached a picture showing the reconstructed 3D point cloud in the above example. I have put some datatips on the figure so we know the (x,y,z) coordinates of the points. here are my questions:

1- what does the Z value in point cloud represent? is it the distance in millimeters from the camera? if that's the case then it does not make sense based on the picture I attached since I am sure the distance of the sphere and checkerboard from the camera must be greater than 200 mm. Or maybe it is from some reference point in space? then what is this reference point? and how can I make a 3D point cloud that the Z values indicate the distance from the camera?

2- why is there negative values for Z? what does that mean in terms of distance to the camera?

I appreciate if someone can explain.

Answer 1

In this example the world coordinates are defined by the checkerboard. The checkerboard defines the X-Y plane, and the Z-axis points into the checkerboard, as explained in the documentation:

Since your 3D points are above the checkerboard, they have negative Z-coordinates.

Answer 2

Your (x,y,z) coordinates are in world units, which are completely disconnected from metric values (unless you build a scale between world and metric, there are various methods to do it). So the z value tells you about the depth of each point in world coordinates.

If you have the pose of each camera, and you multiply each point by the camera projection matrix, you will get the (x',y',z') points in camera coordinates. At that point, if z' is negative, it means it's behind the camera.