1,721,110 research outputs found
A Note on Local Morse Theory in Scale Space and Gaussian Deformations
No full textIn this note we study the local behavior of singularities occurring in scale space under Gaussian blurring. Based on ideas from singularity theory for vector fields this is done by considering deformations or unfoldings. To deal with the special nature of the problem the concept of Gaussian deformation is introduced. Using singularity theory the stability of these deformations is considered. New concepts of one-sided stability and one-sided equivalence are introduced. This way a classification of stable singularities is obtained which agrees with those known in literature
Deep Structure from a Geometric Point of View
No full textThe geometry of empty scale space is investigated. Byvirtue of the proposed geometric axioms the generating PDE, the linearisotropic heat equation, can be presented in covariant, or geometricalform. The postulate of a metric for scale space cannot be upheld, asit is incompatible with the generating equation. Two familiar instancesof scale spaces consistent with the geometric axioms are considered byway of example, viz. classical, homogeneous scale space, and foveal scalespace
Using Top-Points as Interest Points for Image Matching
Get PDFWe consider the use of so-called top-points for object retrieval. These points are based on scale-space and catastrophe theory, and are invariant under gray value scaling and offset as well as scale-Euclidean transformations. The differential properties and noise characteristics of these points are mathematically well understood. It is possible to retrieve the exact location of a top-point from any coarse estimation through a closed-form vector equation which only depends on local derivatives in the estimated point. All these properties make top-points highly suitable as anchor points for invariant matching schemes. In a set of examples we show the excellent performance of top-points in an object retrievaltask
Coarse-to-fine partitioning of signals
No full textAn empirically acquired signal can be analyzed in a multi-scale framework. Its multi-scale structure induces a hierarchical partitioning of the signal domain into topologically meaningful segments. A method is proposed to operationalize this using elementary results from singularity theory for certain generic solutions of the one-dimensional heat equatio
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