What is sobel algorithm in digital image processing?

Answer 1

Most edge detection methods work on the assumption that the edge occurs where there is a

discontinuity in the intensity function or a very steep intensity gradient in the image. Using this

assumption, if one take the derivative of the intensity value across the image and find points

where the derivative is maximum, then the egde could be located. The gradient is a vector, whose

components measure how rapid pixel value are changing with distance in the

x and y direction.

Thus, the components of the gradient may be found using the following approximation:

( )

x

f x y

¶

¶

, = Dx = ( ) ( )

dx

f x

+ dx, y - f x, y

(3)

( ) ( ) ( )

dy

f x y dy f x y

y

x

f x

, y = D = , + - ,

¶

¶

(4)

where

dx anddy measure distance along the x and y directions respectively. In discrete images,

one can consider

dx and dy in terms of numbers of pixel between two points. dx = dy = 1

(

pixel spacing) is the point at which pixel coordinates are(i, j ) thus,

D

x = f (i +1, j )- f(i, j ) (5)

D

y = f (i, j +1)- f (i, j) (6)

In order to detect the presence of a gradient discontinuity, one could calculate the change in the

gradient at

(i, j ) .This can be done by finding the following magnitude measure

M

= Dx 2 + D2 y (7)

and the gradient direction

q is given by









D

D

=

-

x

1

y q tan