Urban Texture analysis (2/3)

2D MODEL

We analyze the texture in the eight following directions:

In each direction we define a 2D Gaussian model. The local conditional probability is a normal law defined as follows:

So for each site s we estimate eight texture parameters in a window centered at s. These parameters are the eight local conditional variances estimated (empirical estimator) with the "comet tails" method:

We have to normalize the parameters with respect to the different directions. Let the step of the lattice be the unity distance. Thus, if one considers the direction (E/W), s is at a distance one form each of its neighbours. On the other hand, if one considers the direction (NWw/SEe), s is at a distance sqrt(5) from each of its neighbours. These different distances introduce a bias. That is why we normalize the considered parameters in order to correct the anisotropy of the lattice.

Image of the estimate of the considered texture parameter: (a)direction N, (b)direction NWw, (c) 2D isotropic model

The greenhouse which is oriented in the direction NWw appears as urban areas on the images (a) and (c). Indeed image (a) is the estimate of the texture parameter in the direction N. This value is high for the greenhouse. Image (b) is the estimate of the texture parameter in the direction NWw. This value is low for the greenhouse because it is oriented in this direction. . Image (c) is the estimate of the texture parameter of the isotropic model. These examples show why we have to consider different directions.

Last modified: Wed Feb 18 17:00:18 MET 2004