Representations Based on Zero-Crossings in Scale-Space.
Abstract
Using the Heat Equation to formulate the notion of scale-space filtering, we show that the evolution property of level-crossings in scale-space is equivalent to the maximum principle. We briefly discuss filtering over bounded domains. We then consider the completeness of the representation of data by zero-crossings, and observe that for polynomial data, the issue is solved by standard results in algebraic geometry. For more general data, we argue that gradient information along the zero-crossings is needed, and that although such information more than suffices, the representation is still not stable. We give a simple linear procedure for reconstruction of data from zero-crossings and gradient data along zero-crossings in both continuous and discrete scale-space domains. Keywords: Signal and image data; Convolution.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1986
- Accession Number
- ADA178961
Entities
People
- Robert A. Hummel
Organizations
- New York University