Building simplification using backpropagation neural networks: a combination of cartographers' expertise and raster-based local perception

Figures & data

Figure 1. A square detector with 24 × 24 or 576 cells.

Figure 2. A simplification boundary plotted via cartographers' expertise. Dark grey represents the building to be simplified. The dotted line depicts the expected boundaries after simplification. A 24 × 24 detector is situated on the left side of the building.

Figure 3. Basic (a) and extended (b) left turns.

Figure 4. Basic (a) and extended (b) right turns.

Figure 5. Basic (a) and extended (b) forward moves.

Table 1. Parameter settings in training

Parameter	Value
Input layer
No. of neurons	576
Transfer function	Linear function
Hidden layer
No. of neurons	4
Transfer funtion	Log-sigmoid function
Output layer
No. of neurons	3
Transfer function	Log-sigmoid function
Others
Learning rule	BP algorithm
Learning rate	0.015
Acceptable mean squared error	0.00001
Maximum number of epochs	10000
Termination condition	Based on minimum mean square error, or maximum number of epochs allowed
Initial weights	Small random numbers in the range of (–1, 1)

Figure 6. A BPNN simplification model.

Figure 7. Buildings within a small part of the study area. (a) Before and (b) after the simplification.

Figure 8. Two buildings extracted from Figure 7. The buildings before the simplification were in dark gray. The dotted lines outlined the buildings after the simplification.

Table 2. Descriptive statistics of the degrees in similarity

	Mean	Standard Deviation
SM(shape)	0.9697	0.0521
SM(area)	0.9696	0.1211
SM(orient)	0.9992	0.0003
SM(comp)	0.9796	0.0237

Figure 9. Comparison of two detectors with 12 × 12 cells (a) and 24 × 24 cells (b).

Figure 10. Comparison of simplification results generated by ESRI/ArcGIS^® (a) and BPNN model (b).