Area estimation in images is useful in the determination of an approximate area even for an irregular shaped image. Using the simple ratio and proportion used in Activity 1, the pixel area can be converted into a physical area quantity. Figure 1 shows an image of a circle of radius 0.7.
Figure 1: 500 x 500 pixel image of a circle of radius 0.7
The pixel positions of the edges of the white circle are determined and the area was calculated using Green's theorem given by equation 1.
Green's theorem for area calculation
The calculated pixel are for the image is 95228.5 square pixels. Since the image spans along x and y from -1 to 1, then the dimension per sq pixel is (2/500)^2 = 1.6e-5 square units per square pixel. The area calculated using this factor is 1.523656 square units wherein the exact are is pi*(0.7)^2 = 1.53938040 square units. The error reported using this approach is 1.0214 % from the theoretical value. Figures 2 and 3 shows two more images where Green's theorem was used in determining the area of the polygon.
Figure 2: 500 x 500 pixel rectangle(1.4 x 1.5)
Pixel Area: 132259.5
Unit Area per Pixel Area: 1.6e-5
Calculated Area : 2.116152
Theoretical Area: 2.100
Error: 0.76%
Figure 3: 500x500 Square with sides 1.4
Pixel Area: 121589
Unit Area per Pixel Area: 1.6e-5
Calculated Area : 1945424
Theoretical Area: 1.9600
Error: 0.7436%
The results from Figures 2 and 3 show that the accuracy of the approximation depends on the regularity of the shape of the object errors show a decreasing trend as the regularity of the polygon or the number of sides for the polygon is decreased which may be directly attributed to the grid-like structuring of the pixels in the image.
Figure 5: Araneta Center Dome Satellite Image
Figure 5 shows a google earth satellite image of the Araneta Center Dome. The image includes the scale to be used and in order for us to approximate the Dome's area we need to process the image to satisfy the conditions for the algorithm to proceed with validity. First we need to determine the edges of the dome and this can be done using Scilab's edge detection capabilities. Figure 6 shows the processed Image after edge detection. After edge detection, the inner area must be filled white for the result of the algorithm to be unambiguous.
Figure 6: Image After Edge Detection
Figure 7: Processed Image after Edge Detection
Pixel Area: 34910
Unit Area per Pixel Area: 0.354308
Calculated Area : 12368.9059 sq meters
Theoretical Area: 11060 sq meters
Error: 11.83%
Self Evaluation: 8. Results are complete but posting is late although i incorporated some edge detection techniques
References:
[1] M. Soriano, Activity 4: Area Estimation, June 2010
[2] Araneta Colliseum Map, www.googleearth.com, June 2010
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