Another idea about how to decide the boundaries of topics

After finishing the curve segmentation of original points for the pages, I should decide the boundaries of different topics according to the series of lines we got in the prior step. Some cases need considering. See figure in the following:

1. In the case (a), the line composed of p1 and p2 is a 'dominant' pattern segment whereas that of p2 and p3 is a 'drifting' pattern segment. The boundary between the two consecutive segments should be 'p2' which is located in the middle. But 'p2' represents a page whose value is similar to p1 instead of p3, so that p2 should belong to the segment starting at p1. Thus, the boundary should be p3. The same principle is used to the case (b), where the boundary should be p4 instead of p3.
2. As far as the case (c) and (d) are concerned, both of them are composed of drifting segments. The point in the middle (or in the peak) looks a good candidate for the boundary of topic patterns. But be carefully here, we have to reconsider the definition of topic segments!

Before, I didn't carefully tell the difference between topic segments and curve segments. Now it's just time. Curve segments are simple to define. They are just lines, more accurately, they are components composing into a curve. Each pair of consecutive lines shares the same connection point. Topic segments are a bit complex. A topic segment should be a page or a series of pages in A line. That is, a topic segment is a point, a line or some consecutive lines, but a line may not necessarily be a topic segment. So when deciding the boundaries of topics, we need consider more than shared points among lines.