Computer Vision Analysis of a Melting Interface Problem with Natural Convection - Visual Computing: Scientific Visualization and Imaging Systems - page 221

Fig. 12.13 Convolution

procedure

curve width is measured considering the number of standard deviations.The
Gaussian curve equation is given by:

g r ð x Þ ¼ 1

e x 2

p

2pr

ð 12 : 15 Þ

2r 2

To use this equation in image processing, it is necessary to generalize the
Gaussian curve into a two-dimensional space.

þ y 2
2r y

x 2
2r x

1
2pr x r y e

G ð x ; y Þ ¼ ð 12 : 16 Þ

where r is the standard deviation and the points (x, y) correspond to the distance
between the coordinates and the mask center. For the application of this chapter,
we used a 7 9 7 dimension mask with a standard deviation equal to r = 1, 4.

2
4

3
5

24542
49 294
5 2 5 25
49 294
24542

1
115

ð 12 : 17 Þ

The second step of the algorithm consists in determining the edge magnitude
from the gradient of the image. It can be found using a Sobel operator. This