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].
