Convolution and Correlation – Some Case Studies - Digital Communication: Principles and System Modelling - page 227

B.2.1 Case Study: Pattern (Shape Feature) Matching Between Two
Objects Using Cross-Correlation

Here the objective is to match two different objects using the shape (boundary)
feature only [1]. The matching must be invariant of scale, translation and rotation.
Firstly we have taken two rectangles of different size and orientation as shown in
Fig. B.9 a. The distance of boundary from centroid (in rectangle that is the cross
point of diagonals) of each object is taken and put into one array. This array can
now behave as a one dimensional sequence. The sequences are plotted (Fig. B.9 b)
for different rectangles of different scale and orientation. Then the cross correlation
coefficient is calculated. We found form our program that, for two rectangles the
cross-correlation coefficient is 0.9919, i.e., very close to 1.
Next we have taken two objects. One is rectangle and the other is a triangle.
The same method is being followed. We have again found that, the cross-correlation
coefficient is 0.4232.
Therefore, we can say, the two dimensional objects can be converted to 1 dimen-
sional sequence and then the correlation measure can infer about the respective
object shape.
The complete program [3] is given using the user given input by keyboard and
mouse in http://extras.springer.com .

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Fig. B.9 (continued)