This edition of Point Grey's Insights newsletter showcases how the Bumblebee^® stereo vision camera was used in the Bounded Hough Transform (BHT).

What is the Bounded Hough Transform?

The Bounded Hough Transform (BHT) is an algorithm that tracks in real-time the pose of objects in the data sequence returned from a Bumblebee^® stereovision sensor. Real-time tracking is a challenging problem due to the large number of possible values (i.e., the pose space) that an object's pose can have. The pose space of a 3D object is actually six dimensional, containing 3 translational and 3 rotational dimensions, which leads to a huge number of possible object poses in any frame. 

Click on the image below to view the entire tracking sequence.

An example of real-time tracking

The key to the BHT algorithm's speed is based on two factors:

1) Using the knowledge of the previous frame's pose to limit the search in the current frame. Given the 30 fps maximum frame rate of the Bumblebee^®, and assuming reasonable limits to the interframe motion of the object, the search for the object's pose in the current frame can be limited to a small bounded region around the previous frame's pose.

2) Tracking is done in discrete rather than continuous space. Lets consider just one translational dimension of the object's pose, i.e. the x-axis. If the x-axis is a discrete grid, then the current x-value will have one of only 3 possible values relative to the previous pose, i.e., the same grid element, the element to the left, or the element to the right. If we extend this reasoning to all 6 dimensions, then at each frame there are only 3⁶ = 729 possible pose values to consider.

The end result is both fast (it runs at ~500 Hz on a 2GHz Pentium) and robust. The input to the algorithm is a surface model of the object to be tracked and its initial pose.  The output is an estimate of the object's pose at each frame. The object does not require any geometric features and can be freeform as long as it is rigid and has sufficient texture to extract surface points. 

The above work was co-authored by Michael Greenspan, Piotr Jasiobedzki and Limin Shang.  For more information on the Bumblebee^®, contact sales@ptgrey.com.

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