Converting screen coordinates + depth into spatial coordinates for OpenPose…or anything else really

Depth cameras are wonderful things but they typically only give a distance associated with each (x, y) coordinate in screen space. To convert to spatial coordinates involves some calculation. One thing to note is that I am ignoring camera calibration which is required to get best accuracy. See this page for details of how to use calibration data in iOS for example. I have implemented this calculation for the iPad TrueDepth camera and also the ZED stereo camera to process OpenPose joint data and it seems to work but I cannot guarantee complete accuracy!

The concept for the conversion is shown in the diagram above. One can think of the 2D camera image as being mapped to a screen plane – the blue plane in the diagram. The width and height of the plane are determined by its distance from the camera and the camera’s field of view. Using the iPad as an example, you can get the horizontal and vertical camera field of view angles (hFOV and vFOV in the diagram) like this:

hFOV = captureDevice.activeFormat.videoFieldOfView * Float.pi / 180.0
vFOV = atan(height / width * tan(hFOV))
tanHalfHFOV = tan(hFOV / 2) 
tanHalfVFOV = tan(vFOV / 2)

where width and height are the width and height of the 2D image. This calculation can be done once at the start of the session since it is defined by the camera itself.

For the Stereolabs ZED camera (this is a partial code extract):

#include <sl_zed/Camera.hpp>

sl::Camera zed;
sl::InitParameters init_params;

// set up params here
if ( != sl::SUCCESS) {

sl::CameraInformation ci = zed.getCameraInformation();
sl::CameraParameters cp = ci.calibration_parameters.left_cam;
hFOV = cp.h_fov;
vFOV = cp.v_fov;
tanHalfHFOV = tan(hFOV / 2);
tanHalfVFOV = tan(vFOV / 2);

To pick up the depth value, you just look up the hit point (x, y) coordinate in the depth buffer. For the TrueDepth camera and the ZED, this seems to be the perpendicular distance from the center of the camera to the plane defined by the target point that is perpendicular to the camera look at point – the yellow plane in the diagram. Other types of depth sensors might give the radial distance from the center of the camera to the hit point which will obviously require a slightly modified calculation. Here I am assuming that the depth buffer contains the perpendicular distance – call this spatialZ.

What we need now are the tangents of the reduced angles that correspond to the horizontal and vertical angle components between the ray from the camera to the screen plane hit point and the ray that is the camera’s look at point. – call these angles ThetaX (horizontal) and ThetaY (vertical). Given the perpendicular distance to the yellow plane, we can then easily calculate the spatial x and y coordinates using the field of view tangents previously calculated:

tanThetaX = (x - Float32(width / 2)) / Float32(width / 2) * tanHalfHFOV
tanThetaY = (y - Float32(height / 2)) / Float32(height / 2) * tanHalfVFOV

spatialX = spatialZ * tanThetaX
spatialY = spatialZ * tanThetaY

The coordinates (spatialZ, spatialY, spatialZ) are in whatever units the depth buffer uses (often meters) and in the camera’s coordinate system. To convert the camera’s coordinate system to world coordinates is a standard operation given the camera’s pose in the world space.

Registering virtual and real worlds with rt-xr, ARKit and Unity

One of the goals for rt-xr is to allow augmented reality users within a space to collaborate with virtual reality users physically outside of the space, with the VR users getting a telepresent sense of being physically within the same space. To this end, VR users see a complete model of the space (my office in this case) including augmentations while physically present AR users just see the augmentations. Some examples of augmentations are virtual whiteboards and virtual sticky notes. Both AR and VR users see avatars representing the position and pose of other users in the space.

Achieving this for AR users requires that their coordinate system corresponds with that of the virtual models of the room. For iOS, ARKit goes a long way to achieving this so the rt-xr app for iOS has been extended to include ARKit and work in AR mode. The screen capture above shows how coordinate systems are synced. A known location in physical space (in this case, the center of the circular control of the fan controller) is selected by touching the iPad screen on the exact center of the control. This identifies position. To avoid multiple control points, the app is currently started in the correct pose so that the yaw rotation is zero relative to the model origin. It is pretty quick and easy to do. The video below shows the process and the result.

After starting the app in the correct orientation, the user is then free to move to click on the control point. Once that’s done, the rt-xr part of the app starts up and loads the virtual model of the room. For this test, the complete model is being shown (i.e. as for VR users rather than AR users) although in real life only the augmentations would be visible – the idea here was to see how the windows lined up. The results are not too bad all things considered although moving or rotating too fast can cause some drift. However, collaborating using augmentations can tolerate some offset so this should not be a major problem.

There are just a couple of augmentations in this test. One is the menu switch (the glowing M) which is used to instantiate and control augmentations. There is also a video screen showing the snowy scene from the driveway camera, the feed being generated by an rt-ai design.

Next step is to test out VR and AR collaboration properly by displaying the correct AR scene on the iOS app. Since VR collaboration has worked for some time, extending it to AR users should not be too hard.

MobileNet SSD object detection with Unity, ARKit and Core ML

This iOS app is really step 1 on the road to integrating Core ML enabled iOS devices with rt-ai Edge. The screenshot shows the MobileNet SSD object detector running within the ARKit-enabled Unity app on an iPad Pro. If anyone wants to try this, code is here. I put this together pretty quickly so apologies if it is a bit rough but it is early days. Detection box registration isn’t perfect as you can see (especially for the mouse) but it is not too bad. This is probably a field of view mismatch somewhere and will need to be investigated.

Next, this code needs to be integrated with the Manifold C# Unity client. Following that, I will need to write the PutManifold SPE for rt-ai Edge. When this is done, the video and object detection data stream from the iOS device will appear within an rt-ai Edge stream processing network and look exactly the same as the stream from the CYOLO SPE.

The app is based on two repos that were absolutely invaluable in putting it together:

Many thanks to the authors of those repos.

An rt-xr SpaceObjects tour de force

rt-xr SpaceObjects are now working very nicely. It’s easy to create, configure and delete SpaceObjects as needed using the menu switch which has been placed just above the light switch in my office model above.

The video below shows all of this in operation.

The typical process is to instantiate an object, place and size it and then attach it to a Manifold stream if it is a Proxy Object. Persistence, sharing and collaboration works for all relevant SpaceObjects across the supported platforms (Windows and macOS desktop, Windows MR, Android and iOS).

This is a good place to leave rt-xr for the moment while I wait for the arrival of some sort of AR headset in order to support local users of an rt-xr enhanced sentient space. Unfortunately, Magic Leap won’t deliver to my zip code (sigh) so that’s that for the moment. Lots of teasers about the HoloLens 2 right now and this might be the best way to go…eventually.

Now the focus moves back to rt-ai Edge. While this is working pretty well, it needs to have a few bugs fixed and also add some production modes (such as auto-starting SPNs when server nodes are started). Then begins the process of data collection for machine learning. ZeroSensors will collect data from each monitored room and this will be saved by ManifoldStore for later use. The idea is to classify normal and abnormal situations and also to be proactive in responding to the needs of occupants of the sentient space.

Latest rt-xr toy: shared virtual whiteboards

Since the sticky note idea now works, I thought that it would be fun to do a freehand version – a virtual whiteboard. It’s working pretty reasonably now. I placed a big whiteboard in my virtual office as you can see above to show how two or more occupants of the space can work together on a shared virtual whiteboard. The video below shows how this works.

The screen on the left is the desktop rt-xrViewer app, the screen on the left is the Mixed Reality Portal showing the Windows Mixed Reality rt-xrViewer app. The mouse is used to draw on the whiteboard in the desktop app (blue lines), motion controllers are used for the WMR app (red lines).

This also shows the new interaction rays. They sort of emanate from where the nose of the avatar should be.

They help give a sense of what the virtual occupants are doing. Otherwise, writing on the whiteboard seems a bit ghostly.

Whiteboards are actually proxy objects, driven from a special server that’s part of the SharingServer. The whiteboard itself is a completely dumb graphical asset. This makes it ideal for packaging as a Unity assetbundle and downloading at runtime rather than having to be built into the app. The required standard scripts included with rt-xrViewer are attached after a proxy object is instantiated.

This is the first time that proxy objects have supported interaction, opening the door to more interesting proxy objects in the future.

Multi-platform interaction styles for rt-xr and Unity

The implementation of sticky notes in rt-xr opened a whole can of worms but really just forced the development of a set of capabilities that will be needed for the general case where occupants of a sentient space can download assets from anywhere, instantiate them in a space and then interact with them. In particular, the need to be able to create a sticky note, position it and add text to it when being used on the supported platforms (Windows and mac OS desktop, Android, iOS and Windows Mixed Reality) required a surprising amount of work. I decided to standardize on a three button mouse model and map the various interaction styles into mouse events. This means that the bulk of the code doesn’t need to care about the interaction style (mouse, motion controller, touch screen etc) as all the complexity is housed in one script.

The short video below shows this in operation on a Windows desktop.

It ended up running a bit fast but that was due to the video recorder setup – I can’t really do things that fast!

I am still just using opaque devices – where is my HoloLens 2 or Magic Leap?!!! However, things should map across pretty well. Note how the current objects are glued to the virtual walls. Using MR devices, the spatial maps would be used for raycasting so that the objects would be glued to the real walls. I do need to add a mode where you can pull things off walls and position them arbitrarily in space but that’s just a TODO right now.

What doesn’t yet work is sharing of these actions. When an object is moved, that move should be visible to all occupants of the space. Likewise, when a new object is created or text updated on a sticky note, everyone should see that. That’s the next step, followed by making all of this persistent.

Anyway, here is how interaction works on the various platforms.

Windows and mac OS desktop

For Windows, the assumption is that three button (middle wheel) mouse is used. The middle button is used to grab and position objects. The right mouse button opens up the menu for that object. The left button is used for selection and resizing. On the Mac, which doesn’t have a middle button, the middle button is simulated by holding down the Command key which maps the left button into the middle button.

Navigation is via the SpaceMouse on both platforms.

Windows Mixed Reality

The motion controllers have quite a few controls and buttons available. I am using the Grab button to grab and position objects. The trigger is used for selection and resizing while the menu button is used to bring up the object menu. Pointing at the sticky note and pressing the trigger causes the virtual keyboard to appear.

Navigation uses the standard joystick-based teleport system.

Android and iOS

My solution here is a little ugly. Basically, the number of fingers used for a tap and/or hold dictates which mouse button the action maps to. A single touch means the left mouse button, two touches means the right mouse button while three touches means the middle button. It works but it is pretty amusing trying to get three simultaneous touches on an object to initiate a grab on a small screen device like a phone!

Navigation is via single or dual touch. Single touch and slide moves in x and y directions. Dual touch and slide rotates around the y axis. Since touches are used for other things, navigation touches need to be made away from objects or else they will be misinterpreted. Probably there is a better way of doing this. However, in the longer term, see-through mode using something like ARCore or ARKit will eliminate the navigation issue which is only a problem in VR (opaque) mode. I assume the physical occupants of a space will use see-through mode with only remote occupants using VR mode.

I haven’t been using ARCore or ARKit yet, mainly because they haven’t seemed good enough to create a spatial map that is useful for rt-xr. This is changing (ARKit 2 for example) but the question is whether it can cope with multiple rooms. For example, objects behind a real wall should not be visible – they need to be occluded by the spatial map. The HoloLens can do this however and is the best available option right now for multi-room MR with persistence.