Forma, Vol. 14 (No. 3), pp. 249-263, 1999
Original Paper

Correlation of Measured Fractal Dimensions with Lacunarities in Computer-Generated Three-Dimensional Images of Cantor Sets and Those of Fractional Brownian Motion

Masaharu Domon and Eiichi Honda

Department of Dental Radiology and Radiation Research, Tokyo Medical and Dental University, 1-5-45 Yushima, Bunkyo-ku, Tokyo 113-8549, Japan

(Received August 5, 1999; Accepted October 25, 1999)

Abstract. Three-dimensional images constructed by CT and MRI has been recently taken as routine diagnosis in medicine and so measures such as fractal dimensions. Lacunarities for 3-dimensional networks or textures are expected to be used as diagnostic parameters. The method of moments and the box counting method to estimate the fractal dimensions of images were examined for their reliability, using images with theoretical fractal-dimensions, which computationally implemented from 3-dimensional triadic Cantor sets and 3-dimensional fractional Brownian motion. In addition, correlation between the deviations of the measured dimensions from the theoretical ones and lacunarities was analyzed. The lacunarity, L-dila was defined using a morphological filter of 3-dimensional dilation of an image. It was found that the measured fractal-dimensions by the method of moments were well fit to the theoretical ones for those images with less L-dila's, however, significantly deviated for those images with larger L-dila's. Thus, the method of moments is expected to estimate sufficiently accurate fractal dimensions of textures in 3-dimensional medical images with less L-dila's.

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