Reading 16 : Combining Corner Detectors

Citation:

Wolin, Aaron, Martin Field, and Tracy Hammond. "Combining corners from multiple segmenters." Proceedings of the Eighth Eurographics Symposium on Sketch-Based Interfaces and Modeling. ACM, 2011.

Publication Link 

Summary:
This paper aims to consolidate all the previous attempts in the domain of corner-detection, and integrate all these algorithms to build a powerful corner detector. The accuracy of this detector was proven to surpass that of any individual detector. However, running this corner finding algorithm on the entire set of points proved to fail drastically, as there are sharp spikes in the error metric which prevent effective thresholding.

Discussion:

The first step is to run each of the 5 corner detectors individually, (Sezgin, Yu and Cai, ShortStraw, Douglas-Pecker, and Kim and Kim), and the union of all the obtained corners is taken, with duplicates removed.

Next, the a Sequential Backward Floating Selecion(SBFS) technique is used to remove corners one by one from this combined set. At every iteration, a removed corner can be added back if its found that the error decreases. The corner to be removed is determined as the one that causes the least error upon removal.

The error metric used in this case is Mean Squared Error, which is the mean distance between every point and the vertically closest point on the polyline formed by the remaining corners. 

The corner removing stops when there a sharp spike in M.S.E (an elbow in the curve), whose slope exceeds that of a threshold. The remianing set of corners are returned as the final output.

To determine the threshold, we use a training set where the corners are already labeled. Next, the we take the medians of the slope before the elbow, and the slope after the elbow for these shapes, and construct the Gaussian distribution for the 2 sets. The points where the probability of these two models are the same, is taken as the confusion point, i.e the threshold.