4 Conclusions

We have described various methods for measuring corner properties. In order to compare them they have been extensively tested on synthetic data. This paper presents their average performance. A more detailed analysis is presented in Rosin [ 15 ] which helps demonstrate their strengths and weaknesses, and shows under what conditions each method is suitable. It concludes that some methods work very well all the time; for instance the thresholding followed by median and the moments methods consistently measure contrast better than the multi-scale intensity histogram or thresholding followed by averaging methods. Other methods perform better than others only over a restricted range of conditions. For example, in the range of subtended angles the multi-scale orientation histogram method for measuring subtended angle outperforms the other methods, but outside this range it breaks down. Another example is when applying the multi-scale orientation histogram method to measure corner orientation. Again it outperforms all the other methods, but breaks down when the SNR drops below 10.

Overall, the average orientation, thresholding, intensity centroid and all the symmetry methods are all good choices for measuring orientation. Although it breaks down for very narrow or wide corners the multi-scale orientation histogram method is probably the best choice for measuring subtended angle. The thresholding followed by median and the moments methods are best for measuring contrast. The moments method being more robust under severe noise or when a small measurement window is used.

A more limited set of tests have been applied to the methods for measuring bluntness and cusp boundary curvature. For measuring bluntness the kurtosis and hyperbola fitting methods do better than the circle fitting method when the corner is substantially rounded. Finally, the method for measuring boundary shape of cusps appears to work reliably.