208 round speckles as above, an ROI would need at least three speckles to be fully constrained. By adding  extra dimensions to speckles,  it is possible to reduce the number needed to constrain an ROI. For this  reason, we use ovals, or clusters of ovals, as the basic s hapes for our speckle pattern. A single oval in an  ROI limits it to one of two angular orientations. Local solving methods, with frame rates appropriately  matched to device motion, should be capable of successfully tracking such an  ROI. Global methods  (such  as DICe , discussed below ), or test environments with insufficient framerates, may have more trouble and  require more constraint . 

This leads to perhaps the ultimate consideration of speckle design, which is the aperture problem. An ROI  must be uniquely identifiable within the search area of the algorithm. This implies that it should be nonrepetitive over that area. This was accomplished by designing a pattern that extends beyond the intended  area of the region of interest. Non- repetition was verified by subjecting it to correlation tests against  translated versions of itself.   For certain miniature mechanism components with complex shapes, pattern optimization was not enough to enable robust, automated tracking, and thus drove the development and incorporation of DICe for this purpose.  

Benefits of DICe  as the proposed tracking algorithm   The first and most substantial improvement is that subsets in D ICe can be of arbitrary shape. In our  application, with irregularly (non- square) regions of interest , this allows the use of  more of a component’s  surface for matching. Conformal subsets are subsets with geometries that correspond to the outline of a  particular part or region, therefore including more fiducials/speckles than traditional square subsets . An  example of a conformal subset vs. a traditional square subset is shown in Figure 2.  This results in an  improvement in accuracy since more information is available within each conformal subset . As a bonus,  this also enables the tracking of objects that are partially obscured, since even if part of a conformal subset leaves the field of view or becomes blocked by another object, there remains enough pixel  information in the subset to successfully correlate.  

Note that in Figure 2  it would be possible to place the markings and subsets in such a way that they fall  completely within the boundary of the object of interest. If attempting to do that with a traditional square subset, the result would be either a smaller subset (yielding less information to correlate resulting in lower   accuracy) or a subset that extends beyond the boundary  (leading to possible de- correlation and  erroneous tracking).    A second benefit to employing the algorithms in DICe is the ability to use simplex (as opposed to  gradient) optimization, providing improved performance in low contrast images. However, this change in  matching methods means that patterns optimized for the gradient approach of software like VIC -2D, with  as many speckle edges as possible,  do not perform as well in the DICe simplex method , which prefers  larger areas of constant color . The lack of gradient dependence makes the simplex method useful for  data sets that are impossible to analyze with the traditional  Lucas -Kanade type algorithms;  for example,  objects without speckles, images w ith low c ontrast, and small subset size.  However, the robustness  comes at a cost –  a substantial increase in processing time when compared to VIC -2D.   The following examples demonstrate the applicability of conformal subsets and illustrate their advantages . 

Example 1: Synthetic rotation of an oddly shaped object of interest   In this example, an image data set is constructed using a synthetic sequence of images so that the exact solution is known and the error of various methods can be computed. A reference image is synthetical ly  rotated through an angle of 10 degrees. This motion is then tracked using both square subsets and a  conformal subset. The synthetic image, subsets, and results are shown in Figure 2 . The magenta and  green curves show the rotation error for the square subsets vs. the blue line, which shows the conformal subset results. In some cases, for example at a rotation of two degrees, the error in the square subsets is