CREHT. 
acted with 
' into sub- 
ure 3. 
inny oper- 
  
      
ER 
Figure 3. Lines found after RHT. 
4. FEATURE MATCHING 
In this chapter, the term feature means a 2D object in 
image space, which has characteristic properties 
belonging to the object, notation deriving from pattern 
recognition field. And this should not be confused with 
3D linear features mentioned earlier. The feature 
matching then simply means solving the correspon- 
dence problem between features from different frames. 
When measuring images of a video sequence, the 
displacement of the current feature between consecu- 
tive frames cannot be too big. For this reason Hough 
parameters are good feature descriptors of a 2D image 
feature, both the length of the arc as well as the 
average strength of edges are suitable for the task. In 
case of line, the spatial coordinates of starting and 
ending point of the line are distinguished descriptors. 
Matching of features between consecutive frames can 
be a ambiguous process. The first stage is to construct 
all combinations of feature pairs and to calculate 
similarity measures between them. The correlation 
between feature vectors presents one good measure. 
Often some kind of normalization is needed for 
correlation coefficients. Based on these similarity 
measures weights for each feature pair are 
determined. 
Finding the correct feature pairs for the features of 
the first frame from the second frame, i.e. feature 
matching, can be done in many, different ways. One 
method widely used in any sort of situations is the 
probabilistic relaxation. The idea of this method is 
that the nodes near proximity effect on weights of the 
node. Relaxation is then an iterative process. The 
result can although depend on the order in which the 
nodes are updated. 
À problem occurs when occluding particles appear. In 
a such case, some heuristic threshold value has to be 
set for a similarity measure to eliminate the affect. 
Also geometrical constraints like epipolar constraint 
can stabilize the matching. The assumption is that 
camera movement is smooth between the frames. This 
223 
may restrict the search space and make the matching 
more robust. 
5. FEATURE MODELING 
Three dimensional form fitting can be done by using 
two dimensional image observations from two or 
multiple images, whose pose differ from each other for 
solving three dimensional parameters of the features. 
That means linear 3D features like lines, circles, 
ellipses, parabolas, hyperbolas, and b-splines are used 
instead of points to reconstruct the object. In 
photogrammetry D. Mulawa’ presented the idea in his 
dissertation thesis in. There he used this kind of three 
dimensional parametric form of the features to depict 
shape and size of the objects. The idea of doing form 
fitting in three dimensional space means that no 
subpixel line detection is needed in image space. The 
whole estimation can be done in three dimensional 
space using original pixel observations. 
The parametric presentation is very compact. The 
general form of curve can be presented as a set of 
points. In a case of a three dimensional curve its trace 
consists a certain set of points P;. 
(1) 
In the parametric formulation we can find a common 
set of parameters u; on which all points of curve are 
dependent. The general formulation of parametric 
presentation can be given as, 
x(u;) 
P; = P(u;) - | y(u,) 
z(u;) 
u; = set of parameters of feature i 
(2) 
All parametric presentations are not unique without 
involving some constrains. For modeling purpose also 
constrains between features are possible. Constrains 
e.g. intersection of lines in three dimensional space, 
parallelism of lines etc., set by the operator can 
simplify and stabilize the estimation in the object 
reconstruction part. 
To have a direct relation between image observation 
and three dimensional feature parameters gives us lot 
of redundancy in the estimation. We can have as many 
observation as edge points detected to determine the 
parameter values. The number of parameters is 
always small compared to number of observations we 
can have. And specially in our case with multiple video 
frames we can have massive number of observations 
connected to a single feature. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996