A real-time variable sampling technique: DIEM

We describe a sampling technique particularly suitable for active vision: Dimensionally-Independent Exponential Mapping (DIEM), in which each dimension of the original data is sampled in an exponentially increasing or decreasing series of steps, with bilateral symmetry about the data mid-point. Multidimensional data sampling is achieved by combining single dimension sampling coordinates. DIEM is simple, fast, flexible and very useful for active vision, but may also have applications in other domains, possibly of higher dimensionality. Its most unusual feature, invertibility, is also one of its most useful. The many advantages of DIEM (computational simplicity, preserved linearity, real-time adjustability, learnability, human motion suitability, expandability, invertibility, frame grabber compatibility, and affordability) are each described. We also describe the functional characteristics of DIEM, provide formulae for DIEM specification and verification, and refer to how DIEM may best be exploited, giving our own work in visual robotics as an example.