Let I be a gray level image with the size NXM. We start
with a pre-processing step where edge emphasizing lter is
used and all high probability back ground pixels are turned
to zero. In the next step we calculate the centroid and the
diameter of the preprocessed shape. We use the values D
and C to draw a circle with the center C and diameter D.
n points taken uniformly distant on the ring are used as
view points to generate a vector of weighted distribution of
pixels on relative area. The number of pixels in each area
weighted by the gray level of each pixel is used to generate a
log-polar histogram of the shape gray value pixels measured
using the view points on the ring as reference points. In
our experiments, we have used 5 and 12 bins for logr and
respectively. This histogram is dened to be the histogram
of the view point rj on the given ring. The vector with size
n where each coordinate is the histogram H(rj) of the view
point rj is a feature vector describing the given shape I. This
denition can be seen as an extension of the known shape
context. In this denition we use the circle with it's view
points to replace contour points which is a robust represen-
tation of low quality shapes. To get the maximum benet
of the gray level information we use the gray level values of
each pixel to calculate a weighted distribution of the pixels.
As expected, high values which are foreground pixels with
high probability, contributes more value to the histogram in
the related area. As in the binary case, Concatenating all
H(rj)0s of each view point rj in the ring R will generate one
feature vector FV (L) representing a full descriptor of the
shape S from the layer L, i.e., FV (L) = fH(rj)gmj
=1.