To detect horizontal edges we first convolve with a Gaussian and then differentiate the resultant image in the direction. But this is the same as convolving the image with the Derivative Of the Gaussian (DOG) in the y-direction, that is
Then, one marks the peaks in the resultant image that are above a prescribed threshold as edges (the threshold is chosen so as to minimize the effects of noise). The effects of doing this on the image of 1 are shown in 5.
Figure 5: Showing the horizontal edges of the original noiseless image