Introduction

Computer-aided image analysis is extraction of meaningful information from digital images by means of digital image processing techniques. Fractal dimension (FD) calculation has become a popular analysis method to characterize image textures. It has been used on periapical and panoramic radiographs as a descriptor of the complex architecture of cancellous bone surrounding teeth [1, 2]. With introduction of digital dental systems, it has become even more feasible as digitalization of film is no longer needed. In dentistry, FD calculation has been performed on non-standardized radiographs for assessment of dental implant sites [3], evaluation of root canal therapy [4], and detection of many systemic pathological conditions such as osteoporosis [5] and sickle cell anemia [6]. According to the results of early studies, FD calculations were considered to be insensitive to variations in film exposure, alignment, and region of interest (ROI) placement [2, 7]. Later, two consecutive studies by the same group of researchers reported that FD is affected by the size, shape, and location of ROI [8, 9]. In recent studies, the information available with regard to the robustness of this technique was rare and inconsistent. Chen and Chen demonstrated significant change in fractal dimension with projection geometry [10], while Pornprasertsuk et al. and Bollen et al. showed that different types of image receptors significantly affect estimates of FD [11, 12]. In contrast, a recent study proved that variations in radiographic settings including tube potential, impulse, and cone angulation have a minimal impact on the fractal dimension [13].

Contemporary digital dental systems have wide range of technical specifications [14] and many of them provide options to acquire images at different resolutions. For storage phosphor systems (SPP), the resolution is determined by the scan speed of the scanner. The slower the scan speed, the higher the spatial resolution. It was clearly established that the higher the spatial resolution, the smaller the radiographic details that can be observed [15]. Although there were many studies that have tested the problems that hinder an effective texture analysis in medical images [16–18] no studies were done to test the effect of image resolution and exposure of intraoral digital images on FD calculation.

The aim of this study was to evaluate the effect of exposure time and image resolution on FD calculation of periapical bone on images obtained using a SPP system.

Materials and methods

Radiographic technique

Dry human mandibles, containing premolars and molars with no restorations or previous root canal therapy were selected to ensure absence of periapical pathology. Ten mandible posterior segments were used in the study. An optical bench was used to standardize projection geometry. Specimens were radiographed with size 2 (31 × 41 mm) blue storage phosphor plates (SPPs) of Digora® Optime (Soredex Corporation, Helsinki, Finland) system. A Gendex Oralix DC (Gendex Dental Systems, Milan, Italy) dental X-ray unit was operating at 60 kVp, 7 mA, and 1.5 mm Al equivalent filtration, a focus-receptor distance was 25 cm. Image plates were exposed with three exposure times (0.05, 0.12, and 0.30 s) corresponding consecutively to underexposed, exposure baseline, and overexposed for SPPs. Plates were scanned immediately after exposure using a Digora® Optime scanner with “super” and “high” (names will be used without quotations in the following text) resolution with 651 and 397 dpi, respectively. Automatic grayscale adjustment implemented in scanner software, was used during image acquisition. In total, 60 images were obtained and saved in uncompressed TIF format with Digora for Windows software (Soredex Corporation, Helsinki, Finland).

Fractal dimension calculation

On each image, two non-overlapping rectangular ROIs were selected in periapical trabecular bone not including roots or periodontal space. Positions and sizes of ROIs were determined according to the size and shape of the periapical region resulting in sizes ranging between 3.8 and 118.2 mm2 (Fig. 1). Wide range of ROI sizes was included to make the result independent of area size. Position and size of each ROI in corresponding images with different resolution and exposure was identical. A total of 120 FD calculations were done on 60 images. FD of all ROIs was calculated with public domain Image J software (http://rsbweb.nih.gov/ij/) and FracLac plug-in (http://rsbweb.nih.gov/ij/plugins/fraclac/FLHelp/Introduction.htm), which is implementing a differential box-counting method [19], developed for analysis of grayscale images. Maximum box size was 45% of each ROI and ranged from 5 to 57 pixels, depending on the ROI size; minimum box size was always two, and box series was linear. These parameters were independent from resolution and exposure. For each of the four calculations, a different part of ROI was used and it represented 45% of the ROI, as explained above. FD of each ROI was determined as the mean of the four calculations inside the ROI.

Fig. 1
figure 1

Two images demonstrating the amount of available bone on the periapical area and descriptive sizes of the smallest (a) and the biggest (b) regions of interest (ROIs) used for fractal dimension calculations

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Statistical analysis

Fractal dimensions of ROIs from images with different exposure times and scan resolutions were compared using two-way ANOVA test (p = 0.05). Post-hoc pairwise comparisons between FDs from different images were made with Tukey–Kramer multiple comparison tests (p = 0.05).

Results

FDs from images obtained from super-resolution images were significantly higher compared to FDs obtained from high-resolution images (p < 0.0001). Images obtained with super-resolution scanning gave significantly higher FD than high-resolution images for all exposures (p < 0.05) (Fig. 2). FD of different exposure times were significantly different as for both resolutions as well (p < 0.0001). Tukey–Kramer multiple comparisons test revealed that FD values of images obtained with 0.05 s exposure were significantly higher than images obtained with 0.12 s (p < 0.05) and 0.3 s (p < 0.001) exposures. However, no difference was found in FD of images exposed with 0.12 and 0.3 s at both resolutions (p > 0.05).

Fig. 2
figure 2

Mean and standard deviation of periapical bone fractal dimension of images, obtained with three different exposure times (0.05, 0.12, 0.3 s) and two different scan resolutions (super and high)

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Discussion

In Digora Optime scanner, the image resolution is determined by a scanning speed of SPP. The slower the scan speed (longer the scan time), the higher the resolution. The device provides two resolutions, namely “super” and “high” resolution. Higher FD was found for super resolution and this was true for all exposure times used in the present study. This is in accordance with results of mathematical simulation study [17], predicting that FD increases with an increasing resolution, as more details are depicted. Similar results were obtained in a study comparing the difference in FD using periapical and panoramic radiographs [11].

Digital images contain image noise of various levels which might arise from fluctuations in X-ray photons, low radiation doses, instability or deficiencies in the detectors’ electronics. It was demonstrated that noise reduces the discriminative performance of texture analysis in radiographs which in turn may reduce the diagnostic accuracy, and hence have a negative impact on the overall prognosis [17]. This study was performed using three different levels of exposure times (low to high) with two interchangeable spatial resolutions. It is well-known that the higher spatial resolution, the smaller the radiographic details that can be observed [15]. However; the spatial resolution is typically limited by the noise level.While increased resolution enables observing smaller details [20], increasing spatial resolution or lowering the exposure time results in higher level of noise in the resultant images [21, 22]. In the present study, SPPs scanned with super (higher) resolution results in images with smaller pixel size but higher noise level. In mathematical simulation [17], increase of image noise was predicted to increase FD; therefore, increase of FD of super-resolution images obtained in the present study can be partially attributed to the higher noise level However, it is not possible to compare this result since this is the first study demonstrating the effect of resolution and accordingly the noise on FD calculations using intraoral SPP images

As already mentioned above, increase in noise also results from reduction of exposure time. Optimal exposure times recommended for Digora SPPs were reported to vary between 0.02 and 0.13 s [23]. It was demonstrated that noise increases with decrease of exposure time in SPP systems [24] and according to the results obtained, FD increases as the exposure time decreases for both resolutions. If the two parameters, i.e., exposure time and resolution, tested in this study were evaluated with regard to noise, it is possible to conclude that findings supplemented each other. As exposure time decreases and resolution increases, signal-to-noise ratio decreases and FD gets higher in noisy images. As already mentioned above, this result is in accordance with results of studies that calculated FD using medical images [17], but somehow, contrary to the results of two studies in dental literature that evaluated the effect of exposure time on FD calculation and both reported no change in FD with changing exposure time [2, 13]. Shrout et al. reported that exposure time had minimal but insignificant effect on FD and found that FD of 1.0 s exposure was higher than 0.2 and 0.6 s [2]. It can be seen that they used almost double amount of exposure time than the baseline (0.12 s) and overexposure (0.3 s) times used in our study. Similarly, we could not be able to demonstrate any difference in FDs of SPP images exposed for 0.12 and 0.3 s since the noise do not decrease linearly with increasing exposure time [14]. In both studies, digitalization of the conventional films was utilized which may also have an impact on the image noise and accordingly FD calculations. In addition, both studies [2, 13] used different methods for FD calculation other than the box-counting method.

Originally, a box-counting method for FD calculation was developed for analysis of binary images. As radiographs are grayscale images, they must be converted to binary images before fractal analysis was performed. The process, precisely described by White et al. has several steps [5]. To facilitate the fractal analysis in various application fields employing grayscale images, a modification of box-counting method, namely differential box-counting method was proposed [19]. It was proved that the differential box-counting method has more precise estimated value of fractal dimension [25]. In biomedicine, it has been used in ultrasonography for characterization of salivary gland tumors [26].

In conclusion, FD analysis seems not so robust method as it was believed previously. It shows significant changes with image resolution and exposure time. Both factors have influence on image noise as it increases with increase of resolution and decrease of exposure time. Therefore, exposure time and scanning resolution of SPPs should be carefully chosen when evaluating the change in FD of alveolar bone for various bone disorders.