# edge detection in matlab

**Topics:**Differential operator, Operator, Edge detection

**Pages:**4 (2388 words)

**Published:**April 28, 2014

(1975)

SHORT NOTE

Mixtures of Derivative Operators as Edge Detectors

R . B. EBERLEIN AND J. S. W E S Z K A

Computer Science Center, University of Maryland,

College Park, Maryland 20742

Communicated by A. Roset!feld

Received October 23, 1974

Derivative operators such as the gradient and Laplacian have been used for many years to detect edges in pictures. This note points out a possible advantage of using combinations of such operators for edge detection.

Isotropic derivative operators such as the gradient and Laplacian are commonly used [1 ] to detect edges in pictures. For digital pictures, these operators are approximated by finite differences; for example, if the neighborhood of point e is

abe,

def,

ghi,

then the magnitude

of the gradient can be approximated

by [2]

Fla. 1. (a) Four windows from an ERTS-I Band 7 picture (1(102-18134) of the Monterey, California, area. A histogram flattening transformation was used to enhance the contrast of these pictures. (b) Results of applying a gradient operator to (a). (c) Results of applying a Laplacian operator to (a). (The Laplaeian values have been multiplied by 2 to improve their visibility.) (d) Results of subtracting the Laplacian from the gradient. 180

Copyright ~) 1975 by Academic Press, Inc.

All rights of reproductio~ in ar[y form reserved,

MIXED

DERIVATIVE

EDGE

maxEla + b + c - g - h - i[,

I3ETECTORS

18 1

la + d + g - c - f -

i1],

and the magnitude of the Laplacian by

a+b+e+d+e+f+g+h+i9

e.

Since the Laplacian is a second-order derivative operator, it is not a good detector for step edges. Given an edge with a ramplike cross section, the Laplacian will h a v e high magnitude on the shoulders at the top and bottom of the ramp but it will have low or zero magnitude in the central part of the ramp. The gradient, on the other hand, will have high magnitude along the whole ramp. The...

References: 1. L. S. G. Kovasznay and H. M. Joseph, Image Processing, Proc. IRE 43, 560-570, 1955.

2. J. M. S. Prewitt, Object enhancement and extraction, in Picture Processing and Psychopictorics

(B. S. Lipkin and A. Rosenfeld, Eds.), pp. 75-149, Academic Press, New York, 1970.

3. E. B. Troy, E. S. Deutsch, and A. Rosenfeld, Gray-level manipulation experiments for texture

analysis, IEEE Trans. SMC-3, 91-98, 1973.

4. R. Eberlein, G. J. VanderBrug, A. Rosenfeld, and L. S. Davis, Edge and line detection in ERTS

imagery: A comparative study, Tech. Rept. 312, Computer Science Center, University of

Maryland, June 1974.

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