We apply classical machine vision and machine deep learning methods to prototype signal classifiers for the search for extraterrestrial intelligence. Our novel approach uses two-dimensional spectrograms of measured and simulated radio signals bearing the imprint of a technological origin. The studies are performed using archived narrow-band signal data captured from real-time SETI observations with the Allen Telescope Array and a set of digitally simulated signals designed to mimic real observed signals. By treating the 2D spectrogram as an image, we show that high quality parametric and non-parametric classifiers based on automated visual analysis can achieve high levels of discrimination and accuracy, as well as low false-positive rates. The (real) archived data were subjected to numerous feature-extraction algorithms based on the vertical and horizontal image moments and Huff transforms to simulate feature rotation. The most successful algorithm used a two-step process where the image was first filtered with a rotation, scale and shift-invariant affine transform followed by a simple correlation with a previously defined set of labeled prototype examples. The real data often contained multiple signals and signal ghosts, so we performed our non-parametric evaluation using a simpler and more controlled dataset produced by simulation of complex-valued voltage data with properties similar to the observed prototypes. The most successful non-parametric classifier employed a wide residual (convolutional) neural network based on pre-existing classifiers in current use for object detection in ordinary photographs. These results are relevant to a wide variety of research domains that already employ spectrogram analysis from time-domain astronomy to observations of earthquakes to animal vocalization analysis.