This retrospective study was conducted in the dental clinic of Oral and Maxillofacial Radiology department and was approved by the local ethics committee (2013/203). The participants had approached the Prosthodontics Clinic between 2012 and 2019 for partial or complete tooth complaints. Among the data of 116 patients reviewed, panoramic radiographs of 67 patients were examined and included in this study. The panoramic radiographs were selected according to the following inclusion criteria: (1) no apparent observations of excessive imaging artifact; (2) patients who had all five panoramic radiographs—before implantation, immediately after prosthodontic loading (2 ± 2 weeks), at 2 months ± 2 weeks after implantation, at 6 months ± 2 weeks after loading, and at 12 months or more after loading (Fig. 1.); and (3) panoramic radiographs of patients without bone metabolism disease. Informed consent was obtained from all patients before their enrollment in the study. Information about the medical status of the patients was obtained from their anamnesis records.

Sixty-seven dental panoramic radiographs (DPRs) were evaluated. All DPRs were obtained with the same radiography device (OP200 D; Instrumentarium Dental, Tuusula, Finland; radiography parameters, 66–85 kVp, 10–16 mA, 14.1 s exposure time). Patients were positioned for radiography according to the manufacturer’s recommendations; the Frankfort horizontal plane was parallel to the floor and the sagittal plane was aligned with the vertical line of the device. The region of interest (ROI) was arbitrarily selected on each radiograph (Fig. 2).

Fractal analysis was performed using the box counting method developed by White and Rudolph [22] and Geraets et al. [23]. The DPRs were analyzed with the ImageJ version 1.38x software (National Institute of Health, Bethesda, MD, USA) on a Dell Precision T5400 workstation (Dell, TX, USA) with a 32-inch Dell liquid crystal display screen with a resolution of 1280 × 1024 pixels in a darkroom. After selection of ROI, the image was duplicated (Fig. 3a). The image was then blurred with a Gaussian filter. Overlapping soft tissues or ghost images of the anatomical structures were removed with the density correction step of the Gaussian filter with large-scale alterations in image brightness caused by varying thickness of the object. Only large differences in density were retained (Fig. 3b). The generated blurred images were subtracted from the original image (Fig. 3c). A gray value of 128 was added to each pixel location, which resulted in an image with individual alterations that reflect certain properties with different brightness, such as the trabeculae and bone marrow (Fig. 3d). A binary image was generated by thresholding with a brightness value of 128. In this process, the image was segmented into regions that represented the bone marrow and trabeculae (Fig. 3e). Thereafter, the image was inverted, and the segments that represented the trabeculae were set to black color, and the bone marrow was set to white color (Fig. 3f). The resulting eroded and dilated image had reduced noise (Fig. 3 g, h). Lastly, with the skeletonization process, the image was further eroded until only the central line of pixels remained (Fig. 3i). The box counting algorithm provided by the software was used for fractal analysis of the reduced images. The image was divided into squares of pixels of size 2, 3, 4, 6, 8, 12, 16, 32, and 64. The squares that included the segments of trabeculae and the total number of squares were calculated for each pixel size. A logarithmic scale graph of the obtained values was plotted. The dimensional value was obtained from the slope of the line that was drawn according to the plotted points on the logarithmic graph.