A4 - Area Estimation for Images with Defined Edges

In this activity, the area of images with defined edges were obtained using two techniques: the Green's Theorem and morphological operations. Two types of shapes were considered. The first being a regular shape such as a circle or square whose area can be computed analytically, and the second, an arbitrary real shape such as the shape of the Dinagat Island found in Surigao del Norte obtained from Google Maps.

For the square, the area obtained using the Green's Theorem is 62001 pixels with 0.8 % error compared to the result using analytic and morphological operations which is 62500 pixels. For the circle, the area obtained using the Green's Theorem is 95319 pixels with 0.51 % error compared to the result using morphological operations which is 95812 pixels. The analytic area of the circle, 96211.275 pixels, varies from the actual area of the image (given by the result of morphological operations) because of the finite nature of the pixels.

For the shape of the Dinagat Island, the area obtained using the Green's Theorem is 32836 pixels with 2.49 % error compared to the result using morphological operations which is 33674 pixels. From the pixel to physical value conversion using the absolute scale of Google Maps and the value obtained using morphological operations, we compute the area to be 773.05 square kilometers with 3.62 % error compared to the recorded value of 802.12 square kilometers.

We find that the area obtained using the Green's Theorem exhibited less than 1 % error for the circle and square which are regular shapes and only 2.49 % error for an irregular shape such as an island compared to the actual area in the image obtained using morphological operations. Estimation of land area using these image processing methods as shown in the second example, gave 3.62 % error which could be attributed to the error in making the map, the difference in exposed land area due to tides, and the inclusion/exclusion of small islands surrounding the main island in the measurement of the recorded area.

For this activity, I give myself a grade of 11 for exploring two regular shapes which were the circle and the square, and for choosing a truly irregular shape such as an island to test the methods explored in this activity.