Ambient Diagnostics - Ambient Intelligence for Scientific Discovery - page 231

5.2 Fractal Dimensions

Fractal Dimension is another characterization of the texture on the tongue sur-
face. Differential Box-Counting Dimension (DBCD) is an estimator of Hausdorff-
Besicovitch dimension [8]. Like many other estimators of fractal dimension,
DBCD is estimated by examining the relationship between a measure and the
scale at which the measure was taken. DBCD is calculated on black and white
images, where one value (for example, black) is taken to represent the object and
the other value (white in this case) is taken to represent the background [28].
The image being measured was divided into equal sized squares. For a given
size square ( r x r pixels), the number of boxes containing any pixels belonging
to the image, N ( r ), is counted. This was done for several scales (several different
r values), after which the relationship between log( N ) and log( r ) was calculated
by finding the best-fit line between all r , N ( r ) data points. The best-fit line
corresponds to the relation:

N ( r )= k · r −Db (7)

The constant k is not important, but Db , the box dimension, is an estimator
of fractal dimension. The implementation created for this project takes as a
parameter an initial window size r to begin measuring. This window size was
doubled repeatedly as long as the window size did not exceed the image size.
Db was then calculated from the measurements taken at these scales. To adapt
tongue images to be feasible for this algorithm, tongues were first converted
to gray scale, using MatLab's rgb2gray function, and then from gray scale to
black while running a Canny edge-detector on the gray scale image. The black
and white image was analyzed using the DBCD algorithm described above.

5.3 Crack Detection

We also developed an algorithm to find and isolate cracks in the tongue. Cracks
in the tongue can be an indicator of abnormality. Other crack detectors and clas-
sifiers [45, 46] have also been based on threshold and morphological operations
in the primary stages. The system, outlined by Ukai [45], was used for detect-
ing cracks in tunnel walls, and worked by using dynamic binarization (adaptive
thresholding), dilation and erosion, eliminating particles, and analyzing the re-
maining particles. The interesting part of this system is its use of spatial fre-
quency filters to distinguish between normal wall joints and cracks. It should
be noted that this system appears to rely on hand-tuned parameters for each
stage, which may be okay for its usage (provided that the equipment used to
capture the input data, and the general properties of the walls do not change). A
detector and classifier of cracks, described by Nieniewski et al [46], was used for
analyzing cracked regions of ferrite. This system used morphological operations,
bi-level thresholding, and a feature-based parallel K-nearest neighbor classifier
[10]. This system was mainly intended for separating out cracks that are defects
from grooves that occur from grinding. The morphological parts quickly gener-
ated all candidates for cracks, and the K-nearest neighbor classifier is used to