EDGE DETECTIONPresented by: Vaddi Manikanta B212053 ETC

INTRODUCTIONEdges are significant local

changes of intensity in an image.

Edge Detection is the process of identifying and locating sharp discontinuities in an image.

Abrupt change in pixel intensity characterize boundary of an object and usually edges occur on the boundary of two regions.

Tulips image

Edges of the Tulips image

Tulips Image Part of the image Edge of the part of the image

Matrix generated by the part of the image

CAUSES OF INTENSITY CHANGEGeometric eventsDiscontinuity in depth and surface colour and textureNon-geometric eventsReflection of lightIlluminationshadows

Edge formation due to discontinuity of surface

Reflectance Illumination Shadow

APPLICATIONS

Enhancement of noisy images like satellite images, x-rays, medical images like cat scans.Text detection.Traffic management.Mapping of roads.Video surveillance.

DIFFERENT TYPES OF EDGES OR INTENSITY CHANGES

Step edge: The image intensity abruptly changes from one value on one side of the discontinuity to a different value on the opposite side.

Ramp edge: A step edge where the intensity change is not instantaneous but occur over a finite distance.

Ridge edge: The image intensity abruptly changes value but then returns to the starting value within some short distance (i.e., usually generated by lines).

Roof edge: A ridge edge where the intensity change is not instantaneous but occur over a finite distance (i.e., usually generated by the intersection of two surfaces).

MAIN STEPS IN EDGE DETECTION

Smoothing: Suppress as much noise as possible, without destroying true edges.

Enhancement: Apply differentiation to enhance the quality of edges (i.e., sharpening).

Thresholding: Determine which edge pixels should be discarded as noise and which should be retained (i.e., threshold edge magnitude).

Localization: Determine the exact edge location. Edge thinning and linking are usually required in this step.

EDGE DETECTION USING DERIVATIVE (GRADIENT)

The first derivate of an image can be computed using the gradient

(or)f

GRADIENT REPRESENTATIONThe gradient is a vector which has magnitude and

direction.

or

Magnitude: indicates edge strength.Direction: indicates edge direction.

| | | |f fx y

(approximation)

EDGE DETECTION STEPS USING GRADIENT

(i.e., sqrt is costly!)

GENERAL APPROXIMATIONConsider the arrangement of pixels about the pixel [i, j]:

The partial derivatives , can be computed by:

The constant c implies the emphasis given to pixels closer to the centre of the mask.

3 x 3 neighborhood:

SOBEL OPERATOR

3×3 convolution mask.Setting c = 2, we get the Sobel operator:

EDGE DETECTOR USING SOBEL OPERATOR IN C LANGUAGE #include <stdio.h>#include <stdlib.h>#include <float.h>#include "mypgm.h"

void sobel_filtering( ) /* Spatial filtering of image data */ /* Sobel filter (horizontal differentiation */ /* Input: image1[y][x] ---- Outout: image2[y][x] */{ /* Definition of Sobel filter in horizontal direction */ int weight[3][3] = { { -1, 0, 1 },

{ -2, 0, 2 }, { -1, 0, 1 } };

double pixel_value; double min, max; int x, y, i, j; /* Loop variable */

/* Maximum values calculation after filtering*/ printf("Now, filtering of input image is performed\n\n"); min = DBL_MAX; max = -DBL_MAX; for (y = 1; y < y_size1 - 1; y++) { for (x = 1; x < x_size1 - 1; x++) { pixel_value = 0.0; for (j = -1; j <= 1; j++) {

for (i = -1; i <= 1; i++) { pixel_value += weight[j + 1][i + 1] * image1[y + j][x + i]; }

} if (pixel_value < min) min = pixel_value; if (pixel_value > max) max = pixel_value; } }

if ((int)(max - min) == 0) { printf("Nothing exists!!!\n\n"); exit(1); }

/* Initialization of image2[y][x] */ x_size2 = x_size1; y_size2 = y_size1; for (y = 0; y < y_size2; y++) { for (x = 0; x < x_size2; x++) { image2[y][x] = 0; } }

/* Generation of image2 after linear transformtion */ for (y = 1; y < y_size1 - 1; y++) { for (x = 1; x < x_size1 - 1; x++) { pixel_value = 0.0; for (j = -1; j <= 1; j++) {

for (i = -1; i <= 1; i++) { pixel_value += weight[j + 1][i + 1] * image1[y + j][x + i]; }

} pixel_value = MAX_BRIGHTNESS * (pixel_value - min) / (max - min); image2[y][x] = (unsigned char)pixel_value; } }}

main( ){ load_image_data( ); /* Input of image1 */ sobel_filtering( ); /* Sobel filter is applied to image1 */ save_image_data( ); /* Output of image2 */ return 0;}

SOBEL EDGE DETECTOR

PREWITT OPERATOR3×3 convolution mask.Setting c = 1, we get the Prewitt operator:

PREWITT EDGE DETECTOR

GENERAL EXAMPLE

Idxd

IdydI

22d dI Idx dy

100Threshold

I

PRACTICAL ISSUESChoice of threshold

Gradient Magnitude

Low Threshold High Threshold

Edge thinning and linking.

CONCLUSIONReduces unnecessary information in the image while

preserving the structure of the image.Extract important features of an image like corners, lines

and curves.Recognize objects, boundaries, segmentation.Part of computer vision and recognition.Sobel and prewitt operators are similar.

REFERENCESMachine Vision – Ramesh Jain, Rangachar Kasturi, Brian

G Schunck, McGraw-Hill, 1995A Computational Approach to Edge Detection – John

Canny, IEEE, 1986CS485/685 Computer Vision – Dr. George Bebis

THANK YOU!