Calculating the Magnitude of Edges for 11x11 Pixel Image

[Pandey1997]

Hello guys, if I have an image with 11x11 pixels and in the center of the image is a square of 5x5 pixels, with the gray level of the background 0 and the gray level of the square is 50. How can I compute the result of the magnitude of edges(intensity of the contour) given by the compass operator for this image taking into account that the image is not noisy? I need to apply simple derivation because the image it's not noisy. This needs to be done on paper using math.

 

[jvicens]

Hello,

Thank you for your question. To compute the magnitude of edges using the compass operator, we will first need to understand the concept of edge detection.

Edge detection is a fundamental technique in image processing and is used to identify boundaries between different regions in an image. The compass operator is a type of edge detection algorithm that uses a predefined set of directional kernels to detect edges in an image.

In your case, the image has a size of 11x11 pixels and a square of 5x5 pixels in the center. The background has a gray level of 0 and the square has a gray level of 50. To compute the magnitude of edges, we will follow the following steps:

Step 1: Convert the image to grayscale

Since the image is not noisy, we can simply convert it to grayscale by taking the average of the red, green, and blue values for each pixel. This will result in an 11x11 matrix with values ranging from 0 to 50.

Step 2: Define the directional kernels

The compass operator uses a set of directional kernels to detect edges in different directions. In this case, we will use four kernels: north, south, east, and west. The north kernel has a value of -1 on the top row, 0 in the middle row, and 1 on the bottom row. Similarly, the south kernel has a value of 1 on the top row, 0 in the middle row, and -1 on the bottom row. The east kernel has a value of -1 on the left column, 0 in the middle column, and 1 on the right column. The west kernel has a value of 1 on the left column, 0 in the middle column, and -1 on the right column.

Step 3: Convolve the image with the directional kernels

To detect edges, we will convolve the image with each of the directional kernels. This means we will slide the kernel over the image and multiply the values in the kernel with the corresponding values in the image. The result of this multiplication is then summed up to give a single value for each pixel. This process is repeated for each pixel in the image, resulting in a new matrix with the same size as the original image.

Step 4: Compute the magnitude of edges

To compute the magnitude of edges, we will take the square root of the sum of squares of the values obtained from convolving the image with