The gradient of the image is calculated for each pixel position in the image.

A=imread('peppers.png');

B=rgb2gray(A);

C=double(B);

for i=1:size(C,1)-2

for j=1:size(C,2)-2

%Sobel mask for x-direction:

Gx=((2*C(i+2,j+1)+C(i+2,j)+C(i+2,j+2))-(2*C(i,j+1)+C(i,j)+C(i,j+2)));

%Sobel mask for y-direction:

Gy=((2*C(i+1,j+2)+C(i,j+2)+C(i+2,j+2))-(2*C(i+1,j)+C(i,j)+C(i+2,j)));

%The gradient of the image

%B(i,j)=abs(Gx)+abs(Gy);

B(i,j)=sqrt(Gx.^2+Gy.^2);

end

end

figure,imshow(B); title('Sobel gradient');

%Define a threshold value

Thresh=100;

B=max(B,Thresh);

B(B==round(Thresh))=0;

B=uint8(B);

figure,imshow(~B);title('Edge detected Image');

The edge detected image can be obtained from the sobel gradient by

using a threshold value.

**The procedure and the MATLAB code for sobel edge detection without using MATLAB built-in function**:**MATLAB CODE:**A=imread('peppers.png');

B=rgb2gray(A);

C=double(B);

for i=1:size(C,1)-2

for j=1:size(C,2)-2

%Sobel mask for x-direction:

Gx=((2*C(i+2,j+1)+C(i+2,j)+C(i+2,j+2))-(2*C(i,j+1)+C(i,j)+C(i,j+2)));

%Sobel mask for y-direction:

Gy=((2*C(i+1,j+2)+C(i,j+2)+C(i+2,j+2))-(2*C(i+1,j)+C(i,j)+C(i+2,j)));

%The gradient of the image

%B(i,j)=abs(Gx)+abs(Gy);

B(i,j)=sqrt(Gx.^2+Gy.^2);

end

end

figure,imshow(B); title('Sobel gradient');

Sobel Gradient |

%Define a threshold value

Thresh=100;

B=max(B,Thresh);

B(B==round(Thresh))=0;

B=uint8(B);

figure,imshow(~B);title('Edge detected Image');

Edge detected Image |

Edge detected Image(Threshold value:35) |

using a threshold value.

- If the sobel gradient values are lesser than the threshold value then replace it with the threshold value.

if f < threshold value then

f = threshold value.

To avoid complex computation, the gradient can also be
computed using the formula:

The Image obtained from computing X-direction derivative:

The Image obtained from computing Y-direction derivative:

Also Check Sobel Edge Detection - Part 2 |

## 31 comments:

why did you substract 2 in the loops

for i=1:size(C,1)-2

for j=1:size(C,2)-2

????

@Mukesh Mann

From every (i,j)th position a 3x3 window is formed. On subtracting 2, the index out of bounds is avoided.

Hello, why are the results smaller than the original images? I tried to find it out but I couldn't. Or is it because of the sobel procedure itself? But I couldn't find any reference for this.

Can you help me write point processing functions in matlab without using built-in functions???

How can i design a highpass filter for reducing noise from an image in Matlab without using image processing toolbox?

can anybody help?

Shahnewz- depends on what type of noise u wanna remove... if u wanna get rid of high freq noise then u gotta apply fourier transform and remove high frequency components.

for i=1:size(C,1)-2

for j=1:size(C,2)-2

%Sobel mask for x-direction:

Gx=((2*C(i+2,j+1)+C(i+2,j)+C(i+2,j+2))-(2*C(i,j+1)+C(i,j)+C(i,j+2)));

%Sobel mask for y-direction:

Gy=((2*C(i+1,j+2)+C(i,j+2)+C(i+2,j+2))-(2*C(i+1,j)+C(i,j)+C(i+2,j)));

sir i'm not able to understand dis part.can u explain it with example?

suppose C is 3x3 size array then what could be value of j.

@vishal

Contact me through mail. Will try to explain it with an example.

please explain to all us

Thats really awesome code you have!!! But I have a question, so i am trying to manipulate or modify an image using the sobel filter along a slider in GUI. So, can you maybe explain a little bit about how you can link the sobel filter to the slider?

Very good article. Thank you!

aaron:

Gx=((2*C(i+2,j+1)+C(i+2,j)+C(i+2,j+2))-(2*C(i,j+1)+C(i,j)+C(i,j+2)));

i m not really understand this part. would you please explain with example?

thank you

@Sheldon Cooper

That line is the convolution between Sobel 3x3 horizontal mask and the image matrix. Let's say we consider the element C(i,j) from the original image matrix. To calculate the coresponding element in Gx matrix, Gx(i,j), we take the 8 neighbours surrounding the element C(i,j) and C(i,j), we multiply each of them with the coresponding element of the Sobel mask, and we sum these multiplications: Gx(i,j)=C(i-1,j-1)*S(1,1)+C(i-1,j)*S(1,2)*C(i-1,j+1)*S(1,3)+... (9 multiplications).

Can you tell me why you had to use double precision of the intensity image?

can we use the Edge detected Image as an input for occupancy sensing? I want to know details of it

Hello! Very good article. I have a question for you. Do you know how to create a subpixel sobel edge detector? I'm trying to do that.

anyone have first derivative example matlab coding? can share? thank you

@Kesava Vijayan

check this post http://angeljohnsy.blogspot.com/2013/07/edge-detection-fundamentals.html

This may help you.

any one have block diagram of Sobel edge detection

can anyone have block diagram of Sobel edge detection ??

sir

please tell me that , how should i will decide which filter is useful for my image. please tell me the parameter on which its depend.

thank you in advance.

This piece of code works like magic.

how to identyfy the color in matlab

how to find sobel gradient direction by using gx & gy values

for i=1:size(C,1)-2

for j=1:size(C,2)-2

%Sobel mask for x-direction:

Gx=((2*C(i+2,j+1)+C(i+2,j)+C(i+2,j+2))-(2*C(i,j+1)+C(i,j)+C(i,j+2)));

%Sobel mask for y-direction:

Gy=((2*C(i+1,j+2)+C(i,j+2)+C(i+2,j+2))-(2*C(i+1,j)+C(i,j)+C(i+2,j)));

sir i'm not able to understand dis part.can u explain it?

how to find sub pixesl value...please tell me

fantastic ,kudos

in this part B(i,j)=sqrt(Gx.^2+Gy.^2); why it isnt B(i+1,j+1)=sqrt(Gx.^2+Gy.^2); is there any problem at this point?

@Gabriela

before the multiplication between the sobel mask and image is done, is the sobel mask not supposed to be flipped vertically and horizontally because I think that's what convolution entails

It looks like you have mixed up the derivatives in the x- and y-directions.

I found in a journal that use sobel approximation with a threshold value of 0.02 for obtain edge map. How to get that threshold ?

because as I know, I only can use threshold with range 0 - 255 (based on maximum gray value) from sobel detection.

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