The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
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defined techniques measuring the similarity of the local area 
surrounding a feature. The image matching technique was 
intended to precisely locate tie points during image-to-image 
registration and estimate the accuracy of the local 
image-to-image transformation. The choice was based on 
Normalized Cross Correlation (NCC), which returns the 
similarity of two windows of pixels (Equation 1). Two highly 
similar windows centered on comers indicate that the comers 
match. The matching result is the position in the test image 
with the highest correlation score. 
Y(I(x,y)-IXJ(x,y)-J) 
(1) 
Where: 
A*>y) 
and -j 
Mx,y) 
I(x, y) is the value of a pixel from window 1. 
J(x, y) is the value of a pixel from window 2. 
N is the total number of pixels in window 1 or window 2. 
2.3 Reconstruction 
A shorter baseline between stereo images is better for reducing 
occlusions and increasing the reliability of matching. However, 
because a smaller baseline produces larger errors along depth 
direction, a larger baseline with an intersection angle near 90 
degrees is needed to improve accuracy. Ideally, the system 
would combine the advantages of short baseline and large 
baseline. Our hypothesis is as follows. First, intermediate 
images between two images with an appropriate baseline for 
best accuracy should be used for better matching. Second, 
tracking conjugate points through all images and reconstructing 
a point intersected by conjugate light rays from stereo images 
with an appropriate baseline can achieve an automatic 
matching procedure for generating accurate output of a 
reconstructed surface model. 
By using stereo imaging, 3D object points can be derived by 
the intersection of conjugate light rays which are defined by the 
conjugate points, the IOP of the camera, and the EOP of the 
image. A set of randomly distributed points can be obtained by 
using the intersection process. A well-reconstructed 3D facial 
model established from these random points requires an 
interpolation method. Thus, Thin Plate Spline is used in this 
stage. Thin Plate Spline (TPS) is an interpolation method that 
finds a "minimally bended" smooth surface that passes through 
all given points. The thin plate spline is the two-dimensional 
analog of the cubic spline in one dimension and is the 
fundamental solution to the biharmonic equation. The TPS can 
represent the surface through a mathematical function where 
the facial surface can be resampled and modeled with regularly 
spaced points. 
2.4 Registration 
Cheng and Habib (2007) introduced an automated surface 
matching algorithm for registering 3D geographic datasets 
constructed relative to two reference frames. The Modified 
Iterated Hough Transform (MIHT) is coupled with the Iterative 
Closest Patch (ICPatch) algorithm to improve the convergence 
rate of the matching strategy as it relates to the nature of 
acquired surface models. This algorithm can be used to model 
surfaces with randomly distributed points when it is unknown 
how they correspond with each other. 
Considering the characteristics of collected surface models, 3D 
points can be used to represent the first surface (Si) while 
triangular patches can be used to define the second surface (S 2 ). 
3D similarity transformation is used for describing the 
mathematical relationship or mapping function between the 
reference frames associated with the two surfaces. Seven 
parameters are involved in 3D similarity transformation, 
including three translations, one scale, and three rotational 
angles. A coplanarity constraint (Figure 3) is used here as the 
similarity measure in this algorithm. The enclosed volume of a 
transformed point and the corresponding patch should be zero 
if the point belongs to the same plane as the patch (Equation 2). 
V = 
X, 
Y, 
z, 
R 
R 
R 
x n 
y 
z nn 
pa 
pa 
pa 
X p b 
Z p b 
X 
r 
z 
pc 
pc 
pc 
V 
z , 
are 
= 0 
(2) 
point from Si, and p a , p h , p c denote the coordinates of the 
three vertices of the conjugate patch from S2 
Figure 3. Similarity measure for relating conjugate primitives 
in two facial models. 
The MIHT approach is a voting procedure that derives the most 
probable solutions of the transformation parameters needed for 
the best alignment of two surface models by considering all the 
possible matches between points in Si and patches in S 2 . The 
MIHT also determines the correspondence between conjugate 
surface elements in the involved facial models. To improve the 
performance of the MIHT, the ICPatch is used to fine tune the 
estimated transformation parameters and corresponding 
elements in the involved facial models by using only matched 
point-patch pairs obtained from MIHT. This algorithm does not 
deform the surfaces and can perform registration and matching 
in a one-step procedure. 
3. EXPERIMENTS 
The proposed approach employs a low-cost imaging system to 
capture overlapping imagery, which are then used to derive a 
3D facial model. The generated 3D model is then registered 
and matched with available 3D models in a central database for 
personal verification or identification purposes. A Canon EOS 
Digital camera (8 mega pixels; pixel size: 6.5 micrometers) was 
used in this study to capture images of two persons. The camera 
was accurately calibrated, checked for stability and mounted on 
a tripod. A test field with a set of 3D points which were 
previously measured was constructed to compute the position 
and orientation of the camera at the time of exposure. To reduce 
the motion caused by human operation, image capturing was 
remotely controlled. A pattern was projected onto the face 
during image acquisition by using a Sony projector to enable 
easier identification of a dense set of points. For each person,