Acknowledgements
This contribution is a part of the KTH-Ballast project at KTH, supported by the Swedish Sand, Gravel and Crushed Rock Association together with the Swedish Board for Technical Development (NUTEK) and the Development Fund of the Swedish
Construction Industry (SBUF). Valuable discussions with Dr. Fredrik Bergholm are gratefully acknowledged. The author also thanks Professor Ove
Stephansson for his encouragement in this study.
Appendix A. Some thresholding situations
Four typical, or possible objects in the second thresholding round4 are shown in Fig. 11. The numbers are mean gray values m in each particle, or in Fig. 11d, the local background. The gray-level range Df (de®ned earlier) is m + 15 ÿ (m ÿ 15) for a single particle and max(m) + 15 ÿ (min(m) ÿ 15) for a cluster5.
All the objects have an area A $ (1225, 6400) pixels.
In cases A and D, the algorithm will, by the shape rule S>2.8, lead to a correct thresholding result, in case C in Fig. 11C will lead to an oversegmentation problem, and in case B in Fig. 11Bb, there is not any further thresholding required on the object. In our data, cases A and D are fairly frequent and cases B and C less frequent and clusters with more than 4±5 particles rare.
An object that includes background area often has a ragged or irregular shape.