specimen. 2) The matching of two images taken by the two 
cameras respectively at the same time. With type 1) 
matching, the difference of the shapes of the same dot in 
two images was mainly caused by the deformation. With 
type 2) matching, the difference is mainly introduced by the 
angle of projection. However, viewing a dot in the image as 
a density distribution function, the transformation of one 
function into the other is mainly one of the translation of 
both X and Y axes. Therefore, the characteristic parameters 
used to describe a dot must be, first of all, translation 
invariants. In this experiment, central moments of the first 
four orders of each dot were calculated as the dot's 
signature. 
Hoo-7moo.  M10-Ho1-0 
Hao = M90 - Hoox? 
611 = M11 - HooxXy 
Ho2 = Mo2 - Hooÿ* 
30 = Mgo - 3m90X + 2p00x° 
os = Mo3 - 3mo2ÿ + 2Ho0ÿ*, 
Jio] 7 mo] - mggy - 2m11x * 2uo0x2y 
119 7 m]9 - mogy - 2m11y * 2uo0xy? 
400 12° 
here, Hpq7 | J(x-X)Pty-y)8f(x.y)dxdy 
-00 
co tee 
mpg = j [xPy f (x. y) dxdy 
-00 
and x-mjo/moo, y = Mo1/M00 
In addition to these, size is an important part of the signature 
of a dot. However, during the experiment, the size, as well 
as other factors of the signature, changes from image to 
image, due to both the projection angles and the 
deformation of the specimen. Fortunately, a valid 
assumption of this experiment is that the "distortion" of the 
shape of a dot in two images is always moderate within 
small intervals of time between image taking during 
deformation, and with almost identical projection angles, 
i.e., with the two cameras kept as vertical to the specimen as 
possible. Therefore, though they are not exactly invariants 
in all the images, this set of characteristic values, including 
central moments and size, comprise a reasonably good 
signature of a dot. 
Because of the digital nature of the images, it is easy to see 
that dots with a larger size have richer signature 
information. For example, in the extreme case, dots 
consisting of a single pixel are all the same in shape. For 
this reason, as the first iteration of image matching, the 
biggest dots in both images are selected and matched first 
by their signatures. However, as discussed above, the 
signature factors are not exactly invariants. As a 
consequence, the matching obtained only by signature is 
not absolutely dependable. An angle test is carried out for 
the matched dots in the first iteration by checking the 
difference between the angles formed by any three dots in 
the first image and the angles formed by the three 
    
correspondingly matched dots in the second image. If the 
difference is not smaller than a predefined threshold, the 
matching of one pair of the matched dots will be judged as 
unacceptable and deleted from the list of matched dots. The 
angle-test for the first iteration must be done very strictly 
since the matched dots are going to serve as "seeds" in the 
following iterations of matching. 
After the first matching of the largest dots in the image, a 
window of adjustable size is opened for each of the two 
matched dots in each image respectively. Other unmatched 
dots which fall into the window in two images are matched. 
Asin the first matching, at the end of all the dots in a pair of 
windows, the "angle-test" is carried out to delete the 
matches with significant difference in the angles. The 
threshold to determine if the angle difference is tolerable is 
dynamic. The more similar a pair of dots are in terms of 
their signature factors, the looser the threshold will be. In 
other words, the pair of dots that are very different in their 
signature have to pass very strict tests on the angle they 
form in order to be a match. 
The dots which are matched in the second matching in turn 
serve as "seeds" in the third iteration of matching, and so 
on. The matched dots are no longer considered in the 
following iterations. The entire matching process comes to 
an end when all the possible pairs of dots are matched. 
After the entire matching process, only the heights at the 
dots, or more precisely, the heights at the center of the dots, 
will be solved accurately with intersection. The heights of 
other points, if of interest, will be determined through 
interpolation. 
After matching the dots in the image, the image coordinates 
are put into the input data file for a least squares adjustment. 
4. RESULTS TO DATE 
Sample results are listed in Table 1. These results are for a 
two camera station solution which utilizes three types of 
object points, namely, object control points, object check 
points, and object random dots which will define the final 
surface deformation of the specimen. 
The determination of the interior and exterior orientation 
parameters for each camera were based on seven (7) known 
points which were located on the surface of the model. For 
these points the average absolute residuals in inches 
between known and final adjusted X, Y and Z coordinates 
were 0.0024, 0.0021, and 0.0006. An additional eight (8) 
check points were included in the solution. The weights of 
these points were zero and thus the solution was free to seek 
the best fit coordinates for these points. The average 
absolute residuals in inches in X, Y and Z for these points 
were 0.0295, 0.0301, and 0.0517. 
There were no checks on the computed coordinates for the 
132random dots; however, the average standard deviations 
in X, Y and Zin inches were 0.0062, 0.0062, and 0.0269 for 
the listed results in Table 1. In general theresults in X and Y 
are better than in the Z direction.