Computational vision is at the heart of robotics and biomedicine but is still quite primitive when compared with our own visual sense. We effortlessly demonstrate enormous flexibility and generality, which hides its staggering complexity: more than one-third of the primate brain processes visual information. How do we characterize the function of billions of neurons in algorithmic terms? Steven Zucker is putting the requirements of vision systems together with insights from neurophysiology to develop an abstract theory of computational vision. Based on differential geometry, it leads to methods of curve detection, shading and texture analyses, and generic shape description. The key to studying and modeling vision is an interdisciplinary perspective, integrating computation, neuroscience, and mathematics.