EDGE DETECTION

Prof. B.A.Khivsara

What is Edge Detection?• Identifying points/Edges in a digital image at which the image brightness changes sharply or has discontinuities.

• - Edges are significant local changes of intensity in an image.• - Edges typically occur on the boundary between two different regions in an

image.

Goal of edge detection

Edge detection is extensively used in image segmentation when we want to divide the image into areas corresponding to different objects.

If we need to extract different object from an image, we need Edge Detection.

Using Edge Detection, we can- recognition, Image comparizon, Unaccepted object can be remove.

TYPES OF EDGES

Variation of Intensity / Gray Level• Step Edge• Ramp Edge• Line Edge• Roof Edge

Process of Edge Detection

There are three steps to perform edge

detection:

Noise reduction

Edge enhancement

Detection – Identify edges

Process of Edge Detection - Noise reduction•  where we try to suppress as much noise as possible,

without smoothing away the meaningful edges.

Original Image After Nois Reduction

Process of Edge Detection - Edge enhancement• where we apply some kind of filter that responds strongly at

edges and weakly elsewhere.

METHODS OF EDGE DETECTION

First Order Derivative / Gradient Methods• Roberts Operator• Sobel Operator• Prewitt Operator

Second Order Derivative• Laplacian• Laplacian of Gaussian

Optimal Edge Detection• Canny Edge Detection

First Order Derivative

At the point of greatest slope, the first derivative has maximum value

• E.g. For a Continuous 1-dimensional function f(t)

Gradient • For a continuous two dimensional function Gradient is defined as

yfxf

GyGx

yxfG )],([

GyGxGyGxG 22

GxGy1tan

Gradient Methods – Roberts Operator

Convolution Mask

Gx =

Gy=

1 00 -1

0 -11 0

Roberts Operator - Example

The output image has been scaled by a factor of 5

Spurious dots indicate that the operator is susceptible to noise

Gradient Methods – Sobel Operator

The 3X3 convolution mask smoothes the image by some amount , hence it is less susceptible to noise. But it produces thicker edges. So edge localization is poor

Convolution Mask

-1 0 1-2 0 2-1 0 1

1 2 10 0 0-1 -2 -1

Gx= Gy=

Sobel Operator - Example

Compare the output of the Sobel Operator with Roberts• The spurious edges are

still present but they are relatively less intense

• Roberts operator has missed a few edges

• Sobel operator detects thicker edges

Outputs of Sobel (top) and Roberts operator

Second Order Derivative Methods

Zero crossing of the second derivative of a function indicates the presence of a maxima

Second Order Derivative Methods - Laplacian

• Defined as

• Mask

• Very susceptible to noise, filtering required, use Laplacian of Gaussian

0 1 01 -4 10 1 0

Second Order Derivative Methods - Laplacian of Gaussian

Steps• Smooth the image using Gaussian filter• Enhance the edges using Laplacian operator

• Zero crossings denote the edge location• Use linear interpolation to determine the sub-pixel location of the edge