Back Propagation Algorithm for DEM Generation based on Quad tree Structure


2.2 Neural Network interpolation
The potential of neural networks in multidimensional interpolation explore using a multilayer perceptron for fitting surfaces to a synthetic topographic dataset [1]. For data interpolating, the network uses two input units, corresponding to the spatial Cartesian coordinates (x,y), and a single output unit representing the computed height of grid points. The network is trained using the irregular dataset. The trained network is subsequently used to compute the height of any node location (x,y) [3,4].

During our dataset is very large, we used quad tree structure for partitioning data into smaller dataset. This is performing twice that in first every region consists of maximum 2000 points and another dataset which consist of maximum 1000 points in any region. In figure 3. Results of applying this structure on our dataset are illustrated. Each region that does not have any point is not contributed in DEM generation process and those are shown as background in output results.



Fig. 3- Quad tree structure applied on all of data


For training of network we used multilayer perceptron (MLP) with one hidden layer that numbers of neuron in hidden layer is changed from 1 to 30. During as illustrated in figure 4, the optimum number of neuron is 19 but we select 10 neurons for decrease processing calculation.



Fig.4 - optimum neuron extraction


Every one of above parts is trained by following parameter:
  • The number of neuron in hidden layer=10;
  • Number of epoch=2000(in most cases, the network convergences in about 90 epoch.)
  • The value of goal function=1e-006;
  • The time of training=INF.

Figure 5 shows all of DEM generated based on neural network.



(a)




(b)
Fig.5- DEM reconstructed with neural network:
a. max data of any region are 2000 points and
b. max data of any region are 1000 points


2.3 DEM accuracy
The accuracy of DEM data depends on the source and resolution of the data samples. DEM data accuracy is derived by comparing linear interpolation elevations in the DEM with corresponding map location elevations and computing the statistical standard deviation or root mean-square error (RMSE). The RMSE is used to describe the DEM accuracy. RMSE results of 20 check point's witch interpolated with conventional and MLP approaches have been shown in table 2 and table 3.

Table 2. RMSE results of all method in DEM generation



Table 3. RMSE results of DEM generation based on neural network



3. CONCLUSIONS
An advantage of DEM over the TIN is that it is easier to find the height at a given location. Only a simple calculation is required to locate the nearest grid points and interpolate between them.

Compared with the conventional approaches, the neural network approach was found to better represent the nonlinearity in the synthetic dataset.

ACKNOWLEDJMENTS
The authors would like to thanks from University of Tehran for support this project and national cartographic center (NCC) for the IKONOS image and 1:2000 digital maps.

REFERENCES
  1. Atkinson, P.M., and Tatnal, A.R.L., 1997, "Introduction Neural Networks in Remote Sensing", International Journal of Remote Sensing, 18, pp 699-709.
  2. Caruso, C.; Quarta, F., "Interpolation Methods Comparison", Computers Math. Applic. 35(12):109-126, 1998.
  3. Menhaj M.B. and Hagan M., 1994, "Training Feed forward Networks with the Marquardt Algorithm", IEEE Transactions on Neural Networks, Vol. 5, No. 6, November 1994, pp. 989-993.
  4. Sarzeaud, O. and Stephan, Y., 2000, "Fast Interpolation Using Kohonen Self-Organizing Neural Networks", IFIP TCS 2000, Sendai, Japan, pp.126-139.
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