edge detection in matlab
COMPUTER GRAPHICS AND IMAGE PROCESSING 4, 1 8 0 - 1 8 3
(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.
(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.
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.