Understanding of Convolutional Neural Networks • /r/MachineLearning

I am somewhat new to this deep learning thing. I fell under the spell when I realized that a computation of a layer of a multilayer perceptron ("vanilla neural network") is simply a composition of a linear map and the the vectorized activation function. Now, convolutional neural networks are seemingly something more complex. But then I realized, aren't convolutional neural networks just a special case of this "vanilla neural network"? In convolutional neural networks, each new feature is computed out of just some strict subset of features from the previous layer. Only some features are "selected" to the weighted sum.