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Next: Unsupervised segmentation of textures Up: Indexing and segmentation Previous: Estimation of the model

Distance measure for textures

In this work we have chosen the Kullback distance between two Gaussian models of textures :

 \begin{displaymath}
\begin{array}{r}
D(P_{1},P{2})=\frac{1}{2}(\mu_{2}-\mu_{1})...
...\sum_{1}^{-1}\sum_{2}+\sum_{1}\sum_{2}^{-1}-2I)\\
\end{array}\end{displaymath}

Clearly, one is interested in being able to define a distance measure, which is invariant to translation and rotation.To achieve the desired invariance, we have implemented the following procedure:


  
Figure: Textures ordered using the Kullback distance. The test texture is structured, dominantly harmonic.
\includegraphics{../../FIGURES/texture7.eps}
Test Texture
\includegraphics{../../FIGURES/texture7_90.eps} \includegraphics{../../FIGURES/texture7_30.eps} \includegraphics{../../FIGURES/texture7_60.eps} \includegraphics{../../FIGURES/texture8_30.eps} \includegraphics{../../FIGURES/texture4_30.eps} \includegraphics{../../FIGURES/texture1_60.eps}
\includegraphics{../../FIGURES/texture1_30.eps} \includegraphics{../../FIGURES/texture6_30.eps} \includegraphics{../../FIGURES/texture1_90.eps} \includegraphics{../../FIGURES/texture6.eps} \includegraphics{../../FIGURES/texture1.eps} \includegraphics{../../FIGURES/texture6_90.eps}
\includegraphics{../../FIGURES/texture4.eps} \includegraphics{../../FIGURES/texture8_60.eps} \includegraphics{../../FIGURES/texture4_60.eps} \includegraphics{../../FIGURES/texture8_90.eps} \includegraphics{../../FIGURES/texture4_90.eps} \includegraphics{../../FIGURES/texture8.eps}

The Kullback distance is computationally expensive. Therefore we derived a hierarchical approach :


  
Figure: Textures ordered using the hierarchical distance. The test texture is structured, dominantly harmonic.
\includegraphics{../../FIGURES/texture7.eps}
Test Texture
\includegraphics{../../FIGURES/texture7_30.eps} \includegraphics{../../FIGURES/texture7_60.eps} \includegraphics{../../FIGURES/texture7_90.eps} \includegraphics{../../FIGURES/texture4.eps} \includegraphics{../../FIGURES/texture4_60.eps} \includegraphics{../../FIGURES/texture4_90.eps}
\includegraphics{../../FIGURES/texture1.eps} \includegraphics{../../FIGURES/texture1_60.eps} \includegraphics{../../FIGURES/texture1_30.eps} \includegraphics{../../FIGURES/texture1_90.eps} \includegraphics{../../FIGURES/texture6_90.eps} \includegraphics{../../FIGURES/texture6_30.eps}
\includegraphics{../../FIGURES/texture6_60.eps} \includegraphics{../../FIGURES/texture6.eps} \includegraphics{../../FIGURES/texture8_30.eps} \includegraphics{../../FIGURES/texture8_60.eps} \includegraphics{../../FIGURES/texture8_90.eps} \includegraphics{../../FIGURES/texture8.eps}


next up previous
Next: Unsupervised segmentation of textures Up: Indexing and segmentation of Previous: Estimation of the model
Radu Stoica
1999-05-21