Abhranil Das

Perspective: the Maths of Seeing Abhranil Das

Why do railway tracks appear to meet at the horizon? Why do circles appear flattened when seen at an angle? What is a 'straight line'? Do we really see it as straight? How do we perceive depth? These are questions that relate to what we do all the time: see things. The sense of vision is fundamental to our perception of the world, yet most of us go through our lives without wondering much about how it works. This book deals with the nature of distortions like the above that occur in the process of seeing. It starts with a single simple axiom, and builds from it to mathematical results that attempt to answer such questions. The discussion follows and compares different mathematical scales that can capture the process of vision. The ideas gathered are then used to understand the nature of binocular vision and how it enables the perception of depth, and ways in which we can exploit this capability to simulate a 3D experience. The arguments and derivations in the book require only a knowledge of high school mathematics.