Feature Extraction and Image Processing

Low-level feature extraction (including edge detection) 129

As such, a more plausible model of the edge is a ramp rather than a step. For a ramp

function given by:

ux

ex

ex

ax

ax

() =

1 – 0.5 0

0.5 < 0

–

#

∃

%

(4.28)

where a is a positive constant depending on the image acquisition system’s characteristics.

A suggested range for a is between 0.5 and 3.0. The derived filter (which is optimal for

these ramp edges) is:

fr

e K Ar K Ar e K Ar K Ar K K e

wr

fr rw

ar –ar sr

() =

( sin( ) + cos( )) + ( sin( ) + cos( )) + +

– 0

– (– ) 0 <

12 34

5

6

#

∃

&

%

&

(4.29)

where w is the size of the filtering operator. Optimal values for the constants K

1

, K

2

, K

3

, K

4

,

K

5

, K

6

, A and w were determined, leading to templates which can be used to detect ramp

edges. In application, ...