Tschirsich, Martin ; Kuijper, Arjan (2013)
Discrete Deep Structure.
Scale Space and Variational Methods in Computer Vision.
doi: 10.1007/978-3-642-38267-3_29
Konferenzveröffentlichung, Bibliographie
Kurzbeschreibung (Abstract)
The discrete scale space representation L of f is continuous in scale t. A computational investigation of L however must rely on a finite number of sampled scales. There are multiple approaches to sampling L differing in accuracy, runtime complexity and memory usage. One apparent approach is given by the definition of L via discrete convolution with a scale space kernel. The scale space kernel is of infinite domain and must be truncated in order to compute an individual scale, thus introducing truncation errors. A periodic boundary condition for f further complicates the computation. In this case, circular convolution with a Laplacian kernel provides for an elegant but still computationally complex solution. Applied in its eigenspace however, the circular convolution operator reduces to a simple and much less complex scaling transformation. This paper details how to efficiently decompose a scale of L and its derivative Qt L into a sum of eigenimages of the Laplacian circular convolution operator and provides a simple solution of the discretized diffusion equation, enabling for fast and accurate sampling of L.
Typ des Eintrags: | Konferenzveröffentlichung |
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Erschienen: | 2013 |
Autor(en): | Tschirsich, Martin ; Kuijper, Arjan |
Art des Eintrags: | Bibliographie |
Titel: | Discrete Deep Structure |
Sprache: | Englisch |
Publikationsjahr: | 2013 |
Verlag: | Springer, Berlin, Heidelberg, New York |
Reihe: | Lecture Notes in Computer Science (LNCS); 7893 |
Veranstaltungstitel: | Scale Space and Variational Methods in Computer Vision |
DOI: | 10.1007/978-3-642-38267-3_29 |
Kurzbeschreibung (Abstract): | The discrete scale space representation L of f is continuous in scale t. A computational investigation of L however must rely on a finite number of sampled scales. There are multiple approaches to sampling L differing in accuracy, runtime complexity and memory usage. One apparent approach is given by the definition of L via discrete convolution with a scale space kernel. The scale space kernel is of infinite domain and must be truncated in order to compute an individual scale, thus introducing truncation errors. A periodic boundary condition for f further complicates the computation. In this case, circular convolution with a Laplacian kernel provides for an elegant but still computationally complex solution. Applied in its eigenspace however, the circular convolution operator reduces to a simple and much less complex scaling transformation. This paper details how to efficiently decompose a scale of L and its derivative Qt L into a sum of eigenimages of the Laplacian circular convolution operator and provides a simple solution of the discretized diffusion equation, enabling for fast and accurate sampling of L. |
Freie Schlagworte: | Business Field: Digital society, Research Area: Generalized digital documents, Discrete images, Partial differential equations, Digital image processing, Mathematics |
Fachbereich(e)/-gebiet(e): | 20 Fachbereich Informatik 20 Fachbereich Informatik > Graphisch-Interaktive Systeme |
Hinterlegungsdatum: | 12 Nov 2018 11:16 |
Letzte Änderung: | 12 Nov 2018 11:16 |
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