Research Article| Volume 135, ISSUE 5, P669-677, May 2023

Download started.


Fractal analysis of dental periapical radiographs: A revised image processing method

Published:December 01, 2022DOI:


      To assess trabecular bone structure as calculated with fractal analysis by 2 binarization processes: White and Rudolph's original method (WR.o) and a revised version (WR.r). Fractal dimension (FD) values calculated with WR.r (FD.r) and a gray-scale-based method (FD.f) were also compared. FD, histogram parameters, and lacunarity were compared by dentate status, jaw location, and sex.

      Study Design

      Regions of interest from digital periapical radiographs were defined below the teeth roots and in the edentulous sites of 37 patients. Histograms were assessed for pixel values. Binarization was performed with WR.o and then with WR.r, in which the outliers were removed. FD was assessed using WR.r (FD.r) and (FD.f). Histograms were assessed to obtain pixel values. Lacunarity was calculated.


      WR.r revealed fewer trabeculae, branches, and junctions than WR.o (P < .0001). The majority of the mean differences between FD.r and FD.f were within the 95% CI. Dentate areas had greater mean gray levels than partially edentulous areas (P = .0027). FD.f was higher in the mandible (P = .01), but gray-level SD (P < .0001) and lacunarity (P = .02) were greater in the maxilla. FD.f and lacunarity were higher (P = .0005) and lower (P = .0014) in males, respectively.


      WR.r was effective in revealing skeletonized bone trabeculae by removing non-trabecular noise. FD.r and FD.f revealed good agreement. FD.f, histogram parameters, and lacunarity differed based on dentate status, jaw location, and sex.
      To read this article in full you will need to make a payment

      Purchase one-time access:

      Academic & Personal: 24 hour online accessCorporate R&D Professionals: 24 hour online access
      One-time access price info
      • For academic or personal research use, select 'Academic and Personal'
      • For corporate R&D use, select 'Corporate R&D Professionals'


        • Kato CN
        • Barra SG
        • Tavares NP
        • et al.
        Use of fractal analysis in dental images: a systematic review.
        Dentomaxillofac Radiol. 2020; 4920180457
        • Geraets WG
        • Van Der Stelt PF.
        Fractal properties of bone.
        Dentomaxillofac Radiol. 2000; 29: 144-153
        • Irie MS
        • Rabelo GD
        • Spin-Neto R
        • Dechichi P
        • Borges JS
        • Soares PBF.
        Use of micro-computed tomography for bone evaluation in dentistry.
        Braz Dent J. 2018; 29: 227-238
        • Rabelo GD
        • Roux JP
        • Portero-Muzy N
        • Gineyts E
        • Chapurlat R
        • Chavassieux P.
        Cortical fractal analysis and collagen crosslinks content in femoral neck after osteoporotic fracture in postmenopausal women: comparison with osteoarthritis.
        Calcif Tissue Int. 2018; 102: 644-650
        • Sindeaux R
        • Figueiredo PTDS
        • de Melo NS
        • et al.
        Fractal dimension and mandibular cortical width in normal and osteoporotic men and women.
        Maturitas. 2014; 77: 142-148
        • Gaeta-Araujo H
        • Oliveira-Santos N
        • Brasil DM
        • et al.
        Effect of micro-computed tomography reconstruction protocols on bone fractal dimension analysis.
        Dentomaxillofac Radiol. 2019; 4820190235
        • Leite AF
        • de Souza Figueiredo PT
        • Caracas H
        • et al.
        Systematic review with hierarchical clustering analysis for the fractal dimension in assessment of skeletal bone mineral density using dental radiographs.
        Oral Radiol. 2015; 31: 1-13
        • Lopes R
        • Betrouni N.
        Fractal and multifractal analysis: a review.
        Med Image Anal. 2009; 13: 634-649
        • White SC
        • Rudolph DJ.
        Alterations of the trabecular pattern of the jaws in patients with osteoporosis.
        Oral Surg Oral Med Oral Pathol Oral Radiol Endod. 1999; 88: 628-635
        • Franciotti R
        • Moharrami M
        • Quaranta A
        • et al.
        Use of fractal analysis in dental images for osteoporosis detection: a systematic review and meta-analysis.
        Osteoporos Int. 2021; 32: 1041-1052
      1. “FracLac for ImageJ.” Available at: Accessed February 9, 2022.

        • Dong P.
        Lacunarity for spatial heterogeneity measurement in GIS.
        Geogr Inf Sci. 2000; 6: 20-26
        • Doube M
        • Klosowski MM
        • Arganda-Carreras I
        • et al.
        BoneJ: free and extensible bone image analysis in ImageJ.
        Bone. 2010; 47: 1076-1079
        • Koo TK
        • Li MY.
        A guideline of selecting and reporting intraclass correlation coefficients for reliability research.
        J Chiropr Med. 2016; 15 (Erratum in: J Chiropr Med. 2017;16:346): 155-163
        • Leclezio L
        • Jansen A
        • Whittemore VH
        • de Vries PJ.
        Pilot validation of the tuberous sclerosis-associated neuropsychiatric disorders (TAND) checklist.
        Pediatr Neurol. 2015; 52: 16-24
        • Yaşar F
        • Akgünlü F.
        Fractal dimension and lacunarity analysis of dental radiographs.
        Dentomaxillofacial Radiol. 2005; 34: 261-267
        • Lindhe J
        • Lang NP
        • Karring T.
        Clinical periodontology and implant dentistry, 2 Volumes.
        5th ed. Wiley-Blackwell, Hoboken, NJUK, 2021
        • Kavitha MS
        • Park SY
        • Heo MS
        • Chien SI
        Distributional variations in the quantitative cortical and trabecular bone radiographic measurements of mandible, between male and female populations of korea, and its utilization.
        PLoS One. 2016; 11E0167992
        • Gaalaas L
        • Henn L
        • Gaillard PR
        • Ahmad M
        • Islam MS.
        Analysis of trabecular bone using site-specific fractal values calculated from cone beam CT images.
        Oral Radiol. 2014; 30: 179-185
        • Parsa A
        • Ibrahim N
        • Hassan B
        • Van Der Stelt P
        • Wismeijer D.
        Bone quality evaluation at dental implant site using multislice CT, micro-CT, and cone beam CT.
        Clin Oral Implants Res. 2015; 26: e1-e7
        • Miyaura K
        • Morita M
        • Matsuka Y
        • Yamashita A
        • Watanabe T.
        Rehabilitation of biting abilities in patients with different types of dental prostheses.
        J Oral Rehabil. 2000; 27: 1073-1076
        • Gonçalves TMSV
        • Campos CH
        • Gonçalves GM
        • de Moraes M
        Rodrigues Garcia RCM. Mastication improvement after partial implant-supported prosthesis use.
        J Dent Res. 2013; 92: 189S-194S
        • Fanghänel J
        • Gedrange T
        • Proff P.
        Bone quality, quantity and metabolism in terms of dental implantation.
        Biomed Tech. 2008; 53: 215-219
        • Ulm C
        • Tepper G
        • Blahout R
        • Rausch-Fan X
        • Hienz S
        • Matejka M.
        Characteristic features of trabecular bone in edentulous mandibles.
        Clin Oral Implants Res. 2009; 20: 594-600
        • Dougherty G
        • Henebry GM.
        Lacunarity analysis of spatial pattern in CT images of vertebral trabecular bone for assessing osteoporosis.
        Med Eng Phys. 2002; 24: 129-138