There   is  an   additional   way   in  which   a cross-

(a)

maintained across iterations  of the vision  system  in a similar manner as before。 If a newly detected segment is found to contain a  tracked  feature window, then the segment is assumed  to correspond to the object for which the feature window was originally selected。 The accuracy of this correspon- dence mechanism can be increased by relying on multiple feature windows。 Figure 5 illustrates how feature window cross-correlation provides  a method of successfully corresponding figure segments in a situation where the adjacency method would have failed。

4。2。 Cross-correlation  optimizations

As with figure segmentation, subsampling can increase the speed of the cross-correlation correspon- dence methods。 Subsampling can be applied in two ways:

• When searching the feature’s neighborhood for displacements that minimize the SSD measure of Eg。 (8), we consider only a subsampled number of displacements。 This reduces the number of SSD calculations  that  are performed。

• When performing the SSD summation in Eq。 (8) over the feature window, we consider only a subsampled number of the ig and ip terms。 This reduces  the time that each  SSD calculation  takes。

(a) The detection module produces two figure segments。 A feature window is found for each。

(b) After tracking the feature windows, the current window locations can be matched to newly detected figure segments。

Fig。 S。 Feature window method  of correspondence。

Fig。 6。 The Minnesota robotic visual  tracker。

If the motion of an object of interest is rapid enough to cause its projection to move beyond Nil j before the tracking algorithm is able to complete its search, then the tracking algorithm  will  fail。 However, if we  try  to  solve  the  previous problem by increasing the size of N ( ) then the search time increases, possibly making the problem worse。 To provide a balance between these two situations, our system increases the size of Np ,(t) proportionally to increases in the neighborhood search subsampling, forming a sequence of pyramiding levels。 Our algorithm  dynamically  uses  a pyramiding  level that

is based upon the magnitude of the figure segment’s previous displacement。 27

Subsampling uses a methodical, non-intelligent means of selecting candidate displacements  (e。g。 every third displacement  from  the neighborhood)。 An alternative method of selecting candidate dis- placements is to use a gradient descent  search strategy like the one that was  used  for feature window  selection  (see  Section  3。2。3)。  Reducing the

number of summation terms by the subsampling method does not take into account  the  fact  that previous SSD measures  have  been  computed  in  all but the first case。 Because the cross-correlation correspondence algorithm is searching for the minimum SSD measure,‘ our system can stop accumulating summation terms if the current summation value exceeds a previously  computed SSD measure。 There is a heuristic which says the following: i, and ip indices that are closer to  the center  of  the  window   lt'„ (,)  tend  to  increase  the

summation  result  more  than  those  on  the   periph-

ery 27  Since  we  will  need  to  add  fewer  terms  if the