Intrinsic Dimension - Applications and History

Applications and History

The case of a two-variable signal which is i1D appears frequently in computer vision and image processing and captures the idea of local image regions which contain lines or edges. The analysis of such regions has a long history, but it was not until a more formal and theoretical treatment of such operations began that the concept of intrinsic dimension was established, even though the name has varied.

For example, the concept which here is referred to as a image neighborhood of intrinsic dimension 1 or i1D neighborhood is called 1-dimensional by Knutsson (1982), linear symmetric by Bigün & Granlund (1987) and simple neighborhood in Granlund & Knutsson (1995).

The term intrinsic dimension was coined by Bennett (1965).