Write a program in "C" to perform Sobel edge detection, test it on pgm image (256x256), and then use the image with edges and added noise in it so that you can measure how good /or bad the Sobel is. For that you should go throw the following steps

1. Write a routing to perform Sobel edge detection.

2. Apply the Sobel edge detector to the noise-free image, to obtain the edge-image.

3. Select a threshold to determine the binary image of the edge-image, that we refer to as Binary edge-image.

4. Add noise( a random number within some pre-specified range) and use the function rand() to generate a random noise at each pixel in the original image( a different random noise value to be added to each different pixel). In your write-up make sure you specify the noise level you used.

5. Apply the Sobel edge detector to the noise image to obtain the noise-edge-image

6. Select an optimal threshold, and obtain the Binary noisy-edge-image

7. Determine the accuracy of the binary noise-edge-image with respect to the binary edge-image( what percentage of pixel were correct, what percentage of pixel were incorrect)

8. Give the plot, showing the level(magnitude) of the noise levels used in the x-axis, and in the y-axis showing the respective accuracy values obtained and corresponding to each of the noise values used. You may select three separate values of noise in your experiment.

9. Examine the effect of noise after image smoothing; that is use your convolution routing(developed in part 1) to apply a 3x3 mask averaging filter to the noisy image and prior to step 5, and repeat steps 5 to 8 above.

10. Based on your result explain the effect of noise and on Sobel-based edge detection algorithm, with noise filtering and without noise filtering.

In your write-up make sure you specify how you took care of the boundary conditions in your convolution, how you select an optimal threshold, and the accuracy of your edge detector on your simulated image(as well as the noise level)