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to design a pattern with distinct Spots, both in shape and 
dimension. A set of cross lines with varying orientation 
and number of lines and squares have been used in the 
implemented system. 
Edge detection and vectorization are performed after 
image grabbing only at defined windows in the image. 
The feature extraction step attempts to detect, recognise 
and "measure" the projected lines onto the object. Edge 
detection is accomplished with Sobel operators 
calculating the magnitude and gradient orientation. 
Orientation histograms are computed from gradient 
orientation data for small sliding windows. The histogram 
analysis defines the number and orientation of edges in 
the window aiming target recognition and labelling. Edge 
pixels are then classified using three grouping steps: 6-, 
p-, and xy-grouping. After edge grouping a least squares 
line fitting is performed (Tommaselli and Tozzi, 1996). 
The intersection of the adjusted straight lines defines the 
cross line center or the center of the Square. 
Least squares matching was also implemented to enable 
an alternative method for point detection, mainly 
detection of the central and peripheral squares. 
The process of feature extraction is applied to small 
search windows. The first window to be scanned is a 
large area around the center of the image. In this search 
window a square must be detected. Once the central 
square is detected, peripheral squares surrounding the 
object must be detected. With these set of points located 
in the image, smaller search windows can be computed 
for the star shaped points. The last step is the search 
for the crosses within each small area defined by 
previously located points. Squares and cross lines can be 
recognised either by template matching or analysing the 
number and orientation of connected straight lines in the 
orientation histogram. 
2.2 Accuracy of Feature Extraction 
Experiments using real images, which were collected 
with the projected pattern over flat surfaces and other 
scenes were conducted. The least squares matching 
works properly with flat surfaces attending sub-pixel 
accuracy requirements. 
However, the projected features are deformed in real 
surfaces and objects (a leg, or a torso, for example) and 
the least squares matching may fail. Even deformed 
geometric shapes (crosses) are still intersections of lines. 
As such, the adjusted straight line equations provided 
good results in these cases. 
The experiments have shown an accuracy of 1/4 of the 
pixel size with the 6-o grouping method. Similar results 
were obtained with the least squares matching, but only 
with flat surfaces. 
The results described above can be drastically improved. 
Trinder et al (1995) reported simulated experiments with 
precision of the order of 0.01 pixel. 
369 
3. PHOTOGRAMMETRIC INTERSECTION 
The concept of our approach is to avoid inner calibration 
of the projector. Only each straight line equation of the 
projected bundle is computed instead of the inner 
orientation parameters of the projector (Tommaselli et al, 
1995). 
The mathematical model is based on the collinearity 
equations (eq. (1)), considering the global reference 
system coincident with the photogrammetric reference of 
the camera. 
oy 
Rss 
(1) 
AM 
M s anzi 
where f is the camera focal length; 
X; y; are the image coordinates; 
Xi Yu Z; are the point coordinates in the object 
space; 
The parametric equations of a projected straight line are 
given by: 
X =X, + A, 
Y, 7» Y, « Am, (2) 
Z, = 25 + An, 
where: X,, Y,, Z, are the coordinates of the perspective 
center of the projector; 
l, m, n; are the direction cosines of the 
projected straight line; 
À; is a parameter; 
Equations (2) combined with (1) gives the basic 
equations of the mathematical model: 
X = NL Mh 
or (3) 
prf Y, * Am, 
Z,+ An 
The inner orientation parameters of the camera and the 
elements of the projected straight line (Xv Yo 5l mg ny 
were previously computed in the calibration step (section 
4). The parameter À; is unknown and must be computed 
for each straight line using the least squares method. For 
each projected straight line two observation equations 
are generated with only one unknown (A) and a least 
squares solution can be computed recursively, using 
equations (4). 
3V=-N'U (4) 
A = +82 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996