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2. Algorithms
Area calculations based on specific mathematical representations have been explored by some researchers [1]-[8]. The two techniques which we propose are: (i) the line-scanning method, and (ii) the contour-gyration method. They are more general than the existing methods. Furthermore, it is very easy to implement and apply the methods. As long as an image can be displayed on a computer screen, the area of any specific region can be calculated.

2.1 Line-scanning algorithm
The basic idea is to scan the area in range line by line, and count all the valid points (pixels).

2.2 Contour-gyration algorithm
The basic idea is to traverse the entire region of interest from an interior point which acts as the starting point, under a specified rule. If there is no path, retreat a step to find a new one until eventually retreating to the starting point. All points traversed are counted to make up the area.

3. Implementations

3.1 Line-scanning algorithm
There are three methods to implement the line-scanning algorithm.

1. Full-template method: All points in a template must be scanned one by one. Although this method is inefficient for dealing with a single large area, it is relatively effective if a graph is diffused all around the screen
2. Single-limit method: The method is to limit the scanning range in either the horizontal or the vertical orientation. For example, if the horizontal limits are set, vertical scan should be employed. On the other hand, horizontal scan is applied under the vertical limits. In vertical scan, firstly, it selects an arbitrary column across the graph as the starting line to be scanned. It then performs vertical scan, column by column towards both the left and right directions until blank columns (without any valid point in a whole column) are met in the two directions.
3. Double-limit method: It is in fact, a both-orientation-limit method.

3.2 Contour-gyration algorithm
There are also three methods to implement the contour-gyration algorithm.

1. Recursive method: It calculates the area from a point, and then performs recursion on all its eight adjacent points.
2. Stack method: A stack is used to record the information of accessed points in order to identify the retreated route.
3. Color method: To reduce the memory expense in a two-dimension array and a huge stack, some hardware attributes of points can be used to record the information instead. Colors are adequate to record the information such as accessed flags and retreating path.