2.4.1 Homomorphic Filtering 
In order to improve the reliability of point detection in the 
matching process, we perform a modified homomorphic filter 
to reduce the effects of non-homogenous illumination as well as 
specular reflectance caused by moisture on the wound surface. 
The image function I(x,y) can be written as a product 
E,E(x,y).R(x,y), where E, is the desired constant illumination, 
E is the function of lighting and R is the reflectance. The idea is 
compressing the brightness from lighting conditions that 
generates some low frequencies, while enhancing the contrast 
from reflectance properties of the object that generates some 
high frequencies so as to reduce variations of the lighting while 
details will be reinforced, thus permitting a better observation 
in the dark zones of the image. The ad-hoc transfer function 
which is convolved is considered as (Kasser and Egels, 2002): 
H(0,,0,) - Enron. ee + À. (2) 
2 it 
-$4/0; to, 0, 
l+e 
Parameters s, @, and 4 govern the shape of the filter. This filter 
shows very good improvement in the final results (see 
section 4). 
2.4.2 Image Segmentation 
As the binarization of the images accelerates the matching 
process and is also required for connected component labelling 
in the next stage, we aim to find an optimal value for 
thresholding the image. For this purpose a locally adaptive 
TopHat filter is applied as B—/-O in which / is the image 
function, O is morphological opening operator, and B is the 
image Background. In cases in which the difference between 
the pixel value and its corresponding background value is 
small, the pixel is set to the same value as the previous pixel 
result. The region size in which the local average is to be 
calculated is dependent on the size of expected foreground 
features. This region size should be large enough to enclose a 
feature completely, but not so large as to average across 
background nonuniformity. It is also critical to determine how 
much of a deviation from the average to tolerate before a 
different threshold is selected. A low level for this deviation 
will result in many erroneous detections, a high level will leave 
some true features undetected. The selection of the threshold is 
made with the aid of the noise estimation. 
2.4.3 Point Detection 
For the extraction of the pattern features, we implement a 
connected component labelling procedure. This method is 
region-based and exploits pixel connectivities. Considering the 
binary image containing a set of objects corresponding to ON 
regions on an OFF background, when a pixel is found to be 
ON, neighbouring pixels are tested. Four situations can arise: 
None of these neighbours is ON, and the current pixel is set to a 
new label; one of the neighbours is ON, and the current pixel is 
given the same label; more than one neighbour is ON and 
labelled equivalently, so the current pixel is given the same 
label; finally, two or more neighbours are ON, but labelled 
differently, so the current pixel is set to one of the labels. When 
this pass is done, centroids of the regions are computed. When 
a contour point is encountered, the scan is interrupted and a 
filling routine is initiated. This procedure has the advantage of 
being unaffected by noise, leading to a robust estimate of the 
centroids. 
3. GEOMETRIC MATCHING 
The Geometric Matching procedure in MEDPHOS exploits the 
trifocal constraint to establish robust correspondences between 
three or more perspective images of a scene. The epipolar line 
constraint is fortunately independent of the shape of the object 
(Faugeras, 2001). Our method requires neither image pyramids 
nor interactive seed points for generating approximate values, 
but provides a solution which is independent of the availability 
of initial values or knowledge on the object shape; only a very 
rough apriori estimation on the minimum and maximum depth 
is required. Moreover, the length of the epipolar lines is 
basically unrestricted, and ambiguities due to multiple 
candidates are solved by means of the concepts of trifocal 
geometry, thus avoiding any smoothing effects introduced by 
surface fitting or patch size in area-based techniques. We 
assume only a set of three or more discrete, disparate, and 
monocular views. The method is robust against missing points. 
It is also evident from (1) that rather than in a two-camera 
model, the number of ambiguities does not depend on the 
length of the epipolar lines any longer (Maas, 1997). In general, 
our matching process consists of two stages which form a 
useful approach for making the final decision, i.e. local 
matching, and global matching. In the local matching stage, for 
every feature in the Source Image, an attempt is made to find a 
set of candidate match features in the Target Image that satisfy 
certain constraints and have similar local attribute properties. In 
this step correspondence hypotheses are being generated, i.e. 
finding initial matches between features from different images 
based on geometry, and radiometric and topologic similarities. 
The compatibility between the extracted features leads to a 
preliminary list of correspondences, including their weights. In 
the global matching stage, a scheme for imposing overall 
consistency among the local matches is exploited to 
disambiguate multiple local match feature candidates and to 
pick out the correct corresponding triplets. In other words, at 
this stage we are looking for the evaluation of the hypotheses. 
3.1 Image Correspondence 
A series of attributes P; in a series of images are said to be 
corresponding or homologous if all P;s are projections of the 
same physical entity. 
3.1.1 The Trifocal Geometry 
The correspondence between each image pair (ij) can be 
described by the Fundamental matrices F;. Given two 
corresponding points m; and m, in two images both in a 
homogeneous coordinate system, the following relationship 
exists (Faugeras, 2001): 
mb Fim, =0 (3) 
If the position x; of the camera nodal of the first image turns to 
the position x; of the camera nodal of the second image through 
3D rotation R and translation 7, then the relationship between 
x, and x; is expressed by: 
xL EX, =0 (4) 
in which E is called Essential matrix being a function of R and 
T (Mori, et al, 2001). The two above equations are called 
Epipolar equations. Considering the accuracy of the 
measurements and the purity of the lenses, this formulation 
should be modified as follows to compensate for the 
uncertainties (Seitz and Kim, 2002): 
m5 Fm, SE (5) 
—266— 
ot 
the 
th: 
lir 
i 
  
Ho OT ^n HHT Qu 
m. 
Tr