Image Segmentation - Bezier and Splines in Image Processing and Machine Vision - page 45

M

j =1 |

N

B ij | /B

i =1

− h ij

IQI = . (2.25)

MN

The condition in equation (2.19) follows a psycho-visual criterion. A low value
of a psycho-visually produces a good quality of image. Note that for an ordi-
nary least square approximation using polynomial surface, the error over the
boundary points normally is higher than that over the interior points. There-
fore, any polynomial with order determined relative to an error function mea-
sured over the boundary points is expected to provide a good approximation
for the interior points.

2.4.4 Algorithms

Method 1: Variable order global approximation
Here we determine the order of the global approximation over data points in
each subimage obtained under different thresholds. A schematic description
of the global approximation scheme is given below. We assume that there are
k number of thresholds for an image and N 1 ,N 2 , ··· N k are the number of

regions in these k subimages.
Algorithm global approx ( input image, th, a , p )
begin

step 1: compute the weights as the gradients of the image;
step 2: find an acceptable subimage corresponding to a threshold th
obtained during segmentation by Algorithm Cond threshold
(assuming W(i,j)=1

i,j);
step 3: find the value of IQI of the subimage using equation (2.25);
step 4: set the order of the polynomial, p = 1;
step 5: approximate the subimage with weights as computed in
step 1.
step 6: find IQI of the approximated image.
step 7: if

∀

a then return p
and goto step 8 else set p = p+1 and goto step 5;
step 8: stop;

| ( IQI ) subimage − ( IQI ) approximated |≤

end ;
Method 2: Variable/fixed-order local approximation
If the variable order global approximation over subimages does not provide
good approximation for some regions in a subimage, then we do local cor-
rection. The global approximation is performed over each of the k subimages
using a variable order polynomial function. The residual error surface patches
are computed using the globally approximated surface s pp ( u, v ) and the orig-
inal input surface (here, the input subimage). Let us denote l -th error surface
patch of the i -th subimage by e i l ( u, v ). Considering N i error surface patches
that need local correction in the i -th subimage, we see that