1. ------ | 1 | -------------- ------ | 1 | -2 | 1 | + | -2 | -------------- ------ | 1 | ------ The image has to be padded by 2 rows of zeros. The result of the correlation follows: ------------- | 0 | 1 | 0 | ------------- | 1 |-4 | 1 | ------------- | 0 | 1 | 0 | ------------- The resulting filter is the Laplacian filter. 2. The Prewitt edge detector for vertical edges follows: ------------- |-1 | 0 | 1 | ------------- |-1 | 0 | 1 | ------------- |-1 | 0 | 1 | ------------- The image of the exercise follows with 1 specifying white and 0 black. ------------------------- | 0 | 0 | 0 | 1 | 1 | 1 | ------------------------- | 0 | 0 | 0 | 1 | 1 | 1 | ------------------------- | 0 | 0 | 0 | 1 | 1 | 1 | ------------------------- | 0 | 0 | 0 | 1 | 1 | 1 | ------------------------- | 0 | 0 | 0 | 1 | 1 | 1 | ------------------------- | 0 | 0 | 0 | 1 | 1 | 1 | ------------------------- The image has to be padded with 1 row and column of zeros to have a same size result image. After that the convolution is applied. The padded image follows: --------------------------------- | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | --------------------------------- | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | --------------------------------- | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | --------------------------------- | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | --------------------------------- | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | --------------------------------- | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | --------------------------------- | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | --------------------------------- | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | --------------------------------- The result of the convolution follows (without scalar product): --------------------------- | 0 | 0 | -2 | -2 | 0 | 2 | --------------------------- | 0 | 0 | -3 | -3 | 0 | 3 | --------------------------- | 0 | 0 | -3 | -3 | 0 | 3 | --------------------------- | 0 | 0 | -3 | -3 | 0 | 3 | --------------------------- | 0 | 0 | -3 | -3 | 0 | 3 | --------------------------- | 0 | 0 | -2 | -2 | 0 | 2 | --------------------------- When the non zero values are replaced by ones, this is the result: ------------------------- | 0 | 0 | 1 | 1 | 0 | 1 | ------------------------- | 0 | 0 | 1 | 1 | 0 | 1 | ------------------------- | 0 | 0 | 1 | 1 | 0 | 1 | ------------------------- | 0 | 0 | 1 | 1 | 0 | 1 | ------------------------- | 0 | 0 | 1 | 1 | 0 | 1 | ------------------------- | 0 | 0 | 1 | 1 | 0 | 1 | ------------------------- 3. ----- | 1 | ----- -------------- | 2 | * | -1 | 0 | 1 | ----- -------------- | 1 | ----- To accurately process this convolution the image has to be padded by 2 columns of zeros. The result of the convolution follows: -------------- | -1 | 0 | 1 | -------------- | -2 | 0 | 2 | -------------- | -1 | 0 | 1 | -------------- This resulting filter is called Sobel edge detector for horizontal edges.