Imaging Sci Dent.  2011 Jun;41(2):71-78. 10.5624/isd.2011.41.2.71.

Fractal analysis of mandibular trabecular bone: optimal tile sizes for the tile counting method

• Huh KH
• Baik JS
• Yi WJ
• Heo MS
• Lee SS
• Choi SC
• Lee SB
• Lee SP

• KMID: 1449938
• DOI: http://doi.org/10.5624/isd.2011.41.2.71

Abstract

PURPOSE
This study was performed to determine the optimal tile size for the fractal dimension of the mandibular trabecular bone using a tile counting method.
MATERIALS AND METHODS
Digital intraoral radiographic images were obtained at the mandibular angle, molar, premolar, and incisor regions of 29 human dry mandibles. After preprocessing, the parameters representing morphometric characteristics of the trabecular bone were calculated. The fractal dimensions of the processed images were analyzed in various tile sizes by the tile counting method.
RESULTS
The optimal range of tile size was 0.132 mm to 0.396 mm for the fractal dimension using the tile counting method. The sizes were closely related to the morphometric parameters.
CONCLUSION
The fractal dimension of mandibular trabecular bone, as calculated with the tile counting method, can be best characterized with a range of tile sizes from 0.132 to 0.396 mm.

Keyword

Fractals; Dental Digital Radiograph; Trabecular Meshwork

MeSH Terms

Bicuspid
Fractals
Humans
Incisor
Mandible
Molar
Trabecular Meshwork

Figure

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  Fig. 1 Locations of region of interest (ROI) selected in the angle, the molar, the premolar and incisor regions.

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  Fig. 2 The images of ROI show the trabecular bone structure. A. Mandibular angle region, B. Mandibular molar region, C. Mandibular premolar region, D. Mandibular incisor region.

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  Fig. 3 Image processing procedures. A. Raw image before processing, B. Binary image, C. Outline image, D. Skeletonized image after preprocessing, E. Composition image of raw and outline images, F. Composition image of raw and skeletonized images.

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  Fig. 4 Mean number of tiles containing any part of the outline against the edge length of the tile or scale from 1 to 49 pixels in 4 anatomical regions. A. A range of scales with local slope of two, B. A range of scales considered for analysis, C. A determined range of scales significant for the fractal dimension.

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  Fig. 5 Box plots show the distribution of local slopes in ranges of scales. A. 1 to 3 pixels, B. 3 to 5 pixels, C. 5 to 7 pixels, D. 7 to 9 pixels, E. 9 to 11 pixels, F. 11 to 13 pixels. No significant differences among the regions in slopes of 1-3, 9-11, and 11-13. There are significant differences among the regions in slopes of 3-5, 5-7, and 7-9 (p<0.05).

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