We use the image motion to estimate the hand movement. This task can be accomplished by either feature tracking or by computing the full optic flow. The image flow detection technique we use is based on the sum-of-squared-differences optic flow. The sensor acquisition procedure (grabbing images) and uncertainty in image processing mechanisms for determining features are factors that should be taken into consideration when we compute the uncertainty in the optic flow.

One can model an arbitrary 3-D motion in terms of stationary-scene/moving-viewer as shown in Figure 11. The optical flow at the image plane can be related to the 3-D world as indicated by the following pair of equations for each point in the image plane [20] :

where and are the image velocity at image location , and are the translational and rotational velocity vectors of the observer, and is the unknown distance from the camera to the object. In this system of equations, the only knowns are the 2-D vectors and , if we use the formulation with uncertainty then basically the 2-D vectors are random variables with a known probability distribution. A number of techniques can be used to linearize the system of equations and to solve for the motion and structure parameters as random variables [4,5,31].

Tue Nov 22 21:30:54 MST 1994