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- W2000399535 abstract "In order to achieve a mutiscale representation and texture extraction for textured image, a hierarchical<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mrow><mml:mrow><mml:mo stretchy=false>(</mml:mo><mml:mrow><mml:mi>B</mml:mi><mml:mi>V</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msup><mml:mi>L</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mo stretchy=false>)</mml:mo></mml:mrow></mml:mrow></mml:math>decomposition model is proposed in this paper. We firstly introduce the proposed model which is obtained by replacing the fixed scale parameter of the original<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mrow><mml:mrow><mml:mo stretchy=false>(</mml:mo><mml:mrow><mml:mi>B</mml:mi><mml:mi>V</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msup><mml:mi>L</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mo stretchy=false>)</mml:mo></mml:mrow></mml:mrow></mml:math>decomposition with a varying sequence. And then, the existence and convergence of the hierarchical decomposition are proved. Furthermore, we show the nontrivial property of this hierarchical decomposition. Finally, we introduce a simple numerical method for the hierarchical decomposition, which utilizes gradient decent for energy minimization and finite difference for the associated gradient flow equations. Numerical results show that the proposed hierarchical<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mrow><mml:mrow><mml:mo stretchy=false>(</mml:mo><mml:mrow><mml:mi>B</mml:mi><mml:mi>V</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msup><mml:mi>L</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mo stretchy=false>)</mml:mo></mml:mrow></mml:mrow></mml:math>decomposition is very appropriate for multiscale representation and texture extraction of textured image." @default.
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- W2000399535 date "2013-01-01" @default.
- W2000399535 modified "2023-09-23" @default.
- W2000399535 title "Multiscale Image Representation and Texture Extraction Using Hierarchical Variational Decomposition" @default.
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- W2000399535 doi "https://doi.org/10.1155/2013/107120" @default.
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