At this point, the most obvious omission in comparison to Chapter 4 is the acoustic equivalent of lenses. As stated above, refraction occurs for sound. Why is it that human ears do not focus sounds onto a spatial image in the same way as the eyes? One problem is the long wavelengths in comparison to light. Recall from Section 5.1 that the photoreceptor density in the fovea is close to the wavelength of visible light. It is likely that an ``ear fovea'' would have to be several meters across or more, which would makes our heads too large. Another problem is that low-frequency sound waves interact with objects in the world in a more complicated way. Thus, rather than forming an image, our ears instead work by performing Fourier analysis to sift out the structure of sound waves in terms of sinusoids of various frequencies, amplitudes, and phases. Each ear is more like a single-pixel camera operating at tens of thousands of ``frames per second'', rather than capturing a large image at a slower frame rate. The emphasis for hearing is the distribution over time, whereas the emphasis is mainly on space for vision. Nevertheless, both time and space are important for both hearing and vision.
Steven M LaValle 2016-12-31