References for Fractal Dimension:

Adler, J and Allen, M,  "Obtaining Fractal Dimensions and Examining Boundaries by Coordinate Averaging", Particle and Particle Systems Characterization 11:418-425 (1994a).

Allen, M. et. Al., "Measurement of boundary fractal dimensions:  review of current techniques", Powder Technology 84:1-14 (1995).95

Dubuc, B. "Evaluating the fractal dimension of profiles"  Phys. Rev. A 39(3):1500-1512 (1989). [Theoretical justification of variation method.]

Kaye, B.H., A Random Walk Through Fractal Dimensions, VCH, NY, 1989.

Pentland, Alex P., 1986, Artificial Intelligence 29:147-170, "Shading into Texture"

Pentland, Alex P., 1984, IEEE Trans. PAMI-6(6):661-674, "Fractal-Based Description of Natural Scenes".

Russ, J.C., THE IMAGE PROCESSING HANDBOOK, 2nd Ed, CRC Press, 1995.  p 525.

Russ, J. C., FRACTAL SURFACES, Plenum Press, NY, 1994.

G. W. Stachowiak, 'Numerical Characterization of Wear Particles Morphology and Angulatiry of Particles and Surfaces', .Tribology International 31(1-3) (1998) pp. 139-157. [One dimensional variation of a profile - average of absolute value of changes for given interval size.]