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selected randomly from various wounds and is displayed axis lies along that of minimum variance and another
in Figure 1 for the purpose of illustration. along that of the maximum. The optimum rotated
coordinate axes may be shown to lie in the directions
The concept of identifying the tissue types based on
pigmentation involves first building a reference base, that of the orthogonal eigenvectors of Ci, and scaled by the
is, a labeled set of clusters in the HSI space, based on inverse of the respective eigenvalues. The theoretical
a large number of pixels per category from many wound considerations outlined in the preceding result in the
images as judged by an experienced plastic surgeon. Prior following distance metric between the observation‑vector
to calculating the HSI parameters, the RGB components x and a cluster “i” with mean µ: i
T
must be calibrated to account for variations due to 2 3 2 3 3 [(x −µ ) e k ] 2
i
“local” or “global” factors. Local variations occur due d ( ,x µ= Π) ( j =1 λ ) { ∑ λ + 3} (3)
j
[11]
i
=1
k
to variations in the angle and the distance of the camera th k
from the wound. Global variation arises due to factors Where e and γ are the k eigenvectors and the
k
k
like ambient light. All of the wound images were taken by eigenvalue of C. Note that γ happens to be the variance
k
i
the same camera under similar conditions. Ignoring local of the sample points in the direction of e . Scaling
k
variations, the RGB components have been calibrated for the transformed axes by the inverse of the respective
global variations, as suggested by Wannous et al. by eigenvalues is, therefore, logical. The relation of this
[11]
exploiting the white patches available in the vicinity of approach to statistical decision theory is seen when one
the wound in some of the images. The corrected values notes that the minimum (Euclidean) distance classification
were used to compute the values of H, S, and I. Each pixel in the new space amounts to maximum likelihood
[19]
within the wound is represented by a 3‑element vector classification after fitting Gaussian density to the data.
(a point) in the HSI space. Points corresponding to a given Classification of a color pixel specified by the vector x
tissue type or pigmentation, as decided by an expert of HSI values is performed by assigning it to the cluster
based on its color, form a cluster. having the smallest value of d (x, µ)
i
Classification
Classification by distance‑based approaches is considered RESULTS
as the clusters were found to be fairly distinct.
The reference clusters were built by using 48 reference
The first approach is based on the Mahalanobis images of chronic wounds of various types, acquired
distance (MD). This measure recognizes that some under daylight, by a digital camera (Sony DSC P9) with
[21]
variables may suffer larger variance than the others flash. About 9,000 pixels (>1,000/category) were assigned
due to differences in numerical values, variances and to one of the eight categories. Samples of the eight types
their inter‑relationships (if any). Indeed, MD takes into of tissue and pigmentation are displayed in Figure 1. The
account the shape of each of the clusters, information calibrated RGB values of each of the pixels were recorded
about which is embedded in the covariance matrix. The against the category. The calibration factors were
expression for MD between the observation vector x and 1.0162 (red), 1 (green) and 1.016 (blue). After rejecting
a cluster “i” with mean µ and covariance matrix C , is the pixels (with I > 233) associated with reflections
i
i
given by: from flash, the values of H, S and I, associated with
each pixel, were computed, and that of H was modified
d 2 ( , )x µ i =x µ ( − i ) C i -1 (x µ − i ) (2) (as per Equation 1).
Note that the contours of constant density Views of the clusters in two different orientations are
(three‑dimensional histogram) are hyperellipsoids of displayed in Figure 2. It is very important to observe the
constant MD from µ. [22]
i presence of eight clusters and that they are fairly distinct.
Another method, the RCS method, is considered based on HGT and UGT lie within a narrow hue (red) but spread
its philosophy, its success in machine vision applications, only over saturation. Not surprisingly, they are close
[19]
and for the sake of comparison. It uses a metric derived to each other. In fact, the appearance or disappearance
by transforming the coordinates of the cluster space, of various colors over time allows one to assess the
such that the intra‑class samples are clustered closely, evolution of the wound toward a state of healing or
and inter‑class samples are separated. The transformation otherwise. To assist in a quantitative understanding of the
involves rotation and scaling of the axes, such that one clusters, the values of inter‑cluster distance are displayed
in Table 1. The inter‑cluster distance, based on the MD
[23]
measure, between clusters i and j, is given by:
d ij 2 x i j (x i − ( , ) x = j T ij −1 (x i − ) x C j ) x (4)

where x and x are the means of the clusters i and j,
j
i
respectively, and C is the pooled covariance matrix. The
ij
pooled covariance matrix was computed based on the data
associated with both of the clusters i and j (considered as
one group), rather than considering it to be a weighted
Figure 1: A sample each, of the eight categories of tissue
types/pigmentation, selected randomly from various wound‑beds average of the covariance matrices associated with the
Plast Aesthet Res || Vol 2 || Issue 5 || Sep 15, 2015 263