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# Improved Digital Gradient Function for Image Edge Detection

IP.com Disclosure Number: IPCOM000107269D
Original Publication Date: 1992-Feb-01
Included in the Prior Art Database: 2005-Mar-21
Document File: 2 page(s) / 40K

IBM

## Related People

Winarski, DJ: AUTHOR

## Abstract

By use of rectilinear and diagonal digital gradient functions, an accurate yet simple means for the detection of the edges of digital images is described.

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Improved Digital Gradient Function for Image Edge Detection

By use of rectilinear and diagonal digital gradient
functions, an accurate yet simple means for the detection of the
edges of digital images is described.

In order to detect the edges of digital images, the gradient of
the digital can be defined in two different ways.  The first way is
rectilinearly, along the x (Eq. 1) and y (Eq. 2) axes of the pixels.
The function f(x,y) denotes the intensity at each pixel (x,y) of the
digital image.
Gx= f(x+1,y) - f(x,y) (1)
Gy= f(x,y+1) - f(x,y) (2)

The second way is diagonally, at 45 degrees from the x and y
axes of the pixels (Eq. 3).
Gxy= f(x+1,y+1) - f(x,y) (3)

edges of digital images can be detected via comparing the values of
the rectilinear digital gradient functions (Eqs. 1 and 2), and the
diagonal digital gradient function (Eq. 3).
G(f(x,y)) = m  FOR       Gxy -< -m/2 AND          (Gx+Gy) < -m/2
(4)
OR -m/2 <Gxy < m/2   AND -3m/2<(Gx+Gy) < -m/2
OTHERWISE, G(f(x,y)) equals zero.
G(f(x+1,y)) = m for       Gxy  > m/2  AND      Gx> m/2
G(f(x,y+1)) = m for       Gxy -> m/2  AND      Gy> m/2
G(f(x+1,y+1)) = m for     Gxy > m/2  AND Gx>m/2  AND Gy>m/2

In Eq. 4, m is a use...