In illustrative implementations of this invention, light sources illuminate a surface with multi-spectral, multi-directional illumination that varies in direction, wavelength, coherence and collimation. One or more cameras capture images of the surface while the surface is illuminated under different lighting conditions. One or more computers take, as input, data indicative of or derived from the images, and determine a classification of the surface. Based on the computed classification, the computers output signals to control an I/O device, such that content displayed by the I/O device depends, at least in part, on the computed classification. In illustrative implementations, this invention accurately classifies a wide range of surfaces, including transparent surfaces, specular surfaces, and surfaces with few features.