Excerpt from Representations Based on Zero-Crossings in Scale-Space 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 max imum principle. We briefly discuss filtering over bounded domains. We then con sider 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 ...
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Excerpt from Representations Based on Zero-Crossings in Scale-Space 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 max imum principle. We briefly discuss filtering over bounded domains. We then con sider 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 reconstruc tion of data from zero-crossings and gradient data along zero-crossings in both con timucus and discrete scale-space domains. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at ... This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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