Baby Steps towards Convolution Nets - V

In earlier posts, we saw how convolution layer cross correlates the input and kernels then adds a scalar bias to produce outputs. In this post, we will apply it to perform a simple task of detecting the edge of an object. We do so by identifying the location of the pixel change.

Let’s assume that our image is made up of 6x8 pixels. This image is only made up of two colors Black (0) and White (1).

array([[1., 1., 0., 0., 0., 0., 1., 1.],
       [1., 1., 0., 0., 0., 0., 1., 1.],
       [1., 1., 0., 0., 0., 0., 1., 1.],
       [1., 1., 0., 0., 0., 0., 1., 1.],
       [1., 1., 0., 0., 0., 0., 1., 1.],
       [1., 1., 0., 0., 0., 0., 1., 1.]])

Next if we construct a kernel with a height of 1 and width of 2. When we perform the cross-correlation operation with the input, if the horizontally adjacent elements are the same then the output is 0 else it is non-zero.

K = [[1, -1]]

If we apply this kernel over the above shown input then we can detect a change along a column from one value (in this case, color) to another.

Y = crosscorr2d(X, K);

If we pass the kernel over our input then we can see that we will detect 1 for an edge from white to black and -1 for edge from black to white.

array([[ 0.,  1.,  0.,  0.,  0., -1.,  0.],
       [ 0.,  1.,  0.,  0.,  0., -1.,  0.],
       [ 0.,  1.,  0.,  0.,  0., -1.,  0.],
       [ 0.,  1.,  0.,  0.,  0., -1.,  0.],
       [ 0.,  1.,  0.,  0.,  0., -1.,  0.],
       [ 0.,  1.,  0.,  0.,  0., -1.,  0.]])

That’s our “Poor Man’s Edge Detector``.