Single-click automated fractal analysis for dental radiographs: a comparative evaluation with classic ImageJ method

Abstract

Objectives

This study aimed to develop a single-click automated fractal analysis module for dental radiographs and compare its efficiency and accuracy with the classic ImageJ method. The study hypothesized that the new module would reduce analysis time and minimize errors.

Materials and methods

A prospective study was conducted using 10 orthopantomographic images from an open-access dataset on Kaggle. Fractal analysis was performed on 100 regions using both the classic ImageJ method and the newly developed automated module. The results were analyzed for accuracy, time efficiency, and error rate.

Results

The average difference in fractal dimension values between the two methods was minimal (0.057106 ± 0.0764495; p < 0.001). However, the new method significantly reduced the time required for analysis, averaging 31.3 s per radiograph compared to 717.6 s with the classic method. The automated method also minimized errors, with only one error recorded compared to 29 errors with the classic method.

Conclusions

The single-click automated fractal analysis module significantly improves the efficiency and accuracy of fractal analysis in dental radiographs, reducing both time and error rates. This new module has the potential to become a standard tool in dental research, facilitating large-scale studies and enhancing the reliability of fractal analysis in dentistry.

Clinical trial number

Not applicable.

Introduction

The fractal analysis method, popularized by Benoît B. Mandelbrot in the 1970s, was initially used to describe and model nature using mathematical and geometrical calculations [1]. This method, which examines the complexity of a structure and the intricate patterns it contains using specific mathematical techniques, is employed when traditional measurement methods fall short in evaluating geometric complexity [2–4]. Since its inception, the fractal analysis method has been discovered to be applicable in various fields, including mathematics, physics, economics, biology, and medicine, with its areas of application continuously expanding [2, 5–7]. Despite its wide-ranging applications, challenges persist in its practical implementation, particularly in disciplines requiring high precision and efficiency, such as dentistry.

In dentistry, the fractal analysis method was first utilized for analyzing supragingival dental calculus [8]. Over time, with advancements in imaging and software systems, it has become possible to evaluate radiographic images using this method [5, 9, 10]. Fractal analysis applied to radiographic images provides benefits in several areas, such as examining bone loss patterns, measuring bone quality, and analyzing bone trabecular structure [11–13]. The method developed by White and Rudolph in 1999 marked a significant milestone in fractal analysis studies within dentistry, and subsequent research frequently employed this methodology [14]. However, the classical fractal analysis approach, particularly when using ImageJ software, involves a lengthy and intricate sequence of steps that can lead to significant challenges in practical application.

In the classic fractal analysis methodology, the ImageJ software is used, requiring at least 13 steps for the fractal analysis of a point on a dental radiograph. These steps include uploading the image to the system, selecting the region of interest (ROI), cropping the ROI, duplicating it, applying Gaussian blur, subtracting the original image from the filtered image, adding 128 to the result at each pixel location, and sequentially binarizing, eroding, dilating, inverting, and skeletonizing the image before finally counting the fractal box numbers [14]. The multi-step nature of this method introduces two primary issues: time inefficiency and susceptibility to human error. The manual execution of each step significantly extends the duration of analysis, making it impractical for large-scale studies or routine clinical use. Additionally, the complexity of the process increases the likelihood of errors, particularly in steps involving manual image processing, such as region selection, filtering, and binarization. Even minor inconsistencies in these steps can lead to variations in the final fractal dimension calculation, reducing the reliability and reproducibility of results.

Recent studies have aimed to address these limitations by automating the fractal analysis process. For instance, Unal Erzurumlu et al. developed an automated system for fractal analysis of mandibular structures in bruxers using ImageJ software, reducing manual intervention and improving efficiency [15]. While these studies mark an important advancement, there is still room for further refinement to enhance their applicability across diverse clinical settings and expand their usability for broader dental imaging applications.

Given these limitations, an automated approach to fractal analysis is necessary to enhance both efficiency and accuracy. The automation of these steps not only minimizes human intervention, thereby reducing errors, but also significantly decreases the time required for analysis, making fractal analysis a more feasible tool for clinical and research applications in dentistry. Furthermore, this method has the potential to improve diagnostic accuracy in various dental conditions, including bone density assessment, periodontal disease diagnosis, and osteoporosis analysis. By facilitating faster and more reliable evaluations, automated fractal analysis could support early detection and monitoring of these conditions, ultimately improving patient outcomes.

The aim of this study is to develop a module that performs automated fractal analysis with a single click for dental radiographs. Additionally, the specific goal of the study was to compare the results and the time dedicated to fractal analysis between the classic ImageJ fractal analysis method and the newly developed single-click automated fractal analysis method. By addressing the inefficiencies and error-prone nature of the classical method, this study aims to bridge a critical gap in the practical application of fractal analysis in dentistry. The authors hypothesize that the new module will save time and reduce the margin of error during the process. Moreover, by enhancing the efficiency and precision of fractal analysis, this method may contribute to improved clinical decision-making in dentistry, particularly in evaluating bone health and disease progression.

Materials and methods

In this prospective study, orthopantomography images, one of the most commonly used radiography types in dentistry, were obtained from Kaggle, a machine learning platform, for fractal analysis. Since the data sets used were publicly available on Kaggle, ethical approval was not required, and the study was conducted in accordance with the Helsinki Declaration.

Data sets used and power analysis

The dataset published by Abdi et al. was used for panoramic radiographs (https://www.kaggle.com/datasets/volodymyrpivoshenko/panoramic-dental-x-rays-with-segmented-mandibles) [16]. The panoramic radiographs in the dataset used were at least 1000 pixels in both horizontal and vertical dimensions, with a resolution of at least 265 dpi. A power analysis was conducted to determine the appropriate sample size for the study. A pilot study was performed using five panoramic radiographs. In this study, fractal analysis calculations were carried out on 10 selected points per radiograph using both a single-click fractal analysis module and the conventional ImageJ fractal analysis method. The mean fractal dimension difference between the developed module and the conventional ImageJ method was found to be 0.0506 ± 0.0356. Using G*Power 3.1 software, the effect size was determined to be 1.421348. With an alpha error probability (α) of 0.05 and power (1-β) of 0.95, it was calculated that at least eight panoramic radiographs were required. Considering potential data loss, the sample size was increased by 25%, leading to the selection of 10 panoramic radiographs for analysis.

A total of 10 panoramic radiographs were selected from a dataset containing 116 radiographs. To ensure randomness in image selection, a randomization application (https://www.randomizer.org/) was used to generate 10 numbers from a range of 1 to 116. The selected images were not filtered based on any specific anatomical or radiographic criteria but were purely chosen through this randomization process. Within these images, 10 regions were selected for fractal analysis, and these measurements were repeated for each radiograph (Fig. 1). A total of 200 fractal analysis results were obtained from 100 different points. This included 100 automated fractal analyses and 100 conventional ImageJ fractal analyses.

Fig. 1.

Selected regions in orthopantomography. Each ROI is 50 × 50 pixels in size

Classic ImageJ fractal analysis method

In this method, ImageJ software was used for fractal analysis. After the images were uploaded to the software, a 50 × 50 pixel ROI was selected, cropped, and then duplicated. A Gaussian Blur filter with a sigma value of 35.0 was applied to the duplicated version. The filtered image was subtracted from the original image. To the result at each pixel location, 128 was added. The image was then sequentially binarized, eroded, dilated, inverted, and skeletonized. The fractal dimension was calculated using the Fractal Box Count function in ImageJ.

Single-click automated fractal analysis module

To develop this module, Python software, along with the cv2, time, numpy, and skimage libraries, was used. In the first stage of the module, the user is asked to define the ROI value and provide the file path of the image to be analyzed. By clicking on the region of interest in the opened image file, the fractal dimension is automatically calculated. Along with the fractal dimension, the coordinates of the top left corner of the selected ROI and the processing time are also provided as output (Fig. 2). The GitHub link for the module used: https://github.com/semruktech/fractal-box-counter.

Fig. 2.

Image of the developed module

Fractal dimension evaluation

Before starting the fractal analyses, the regions to be analyzed and their coordinates were determined by researcher YB. Subsequently, fractal analyses were independently performed by researchers YB and KS using both the classic ImageJ method and the new single-click automated fractal dimension calculation method, and the fractal values were recorded in an Excel spreadsheet. The workflow diagram for both analysis methods is shown in Fig. 3. After completing the fractal analyses, the results were compared, and any inconsistent fractal analysis results were jointly reviewed to calculate the final fractal dimension. Additionally, the time taken for fractal analysis for each image was recorded in seconds (the total evaluation time for 10 regions per panoramic radiograph), and errors that occurred during fractal analyses were recorded in numbers.

Fig. 3.

Workflow diagram used for both methods

Statistical analysis

For statistical analysis, SPSS v26 software was used. Continuous data were presented as mean ± standard deviation. Spearman’s rank correlation coefficient was calculated to assess the concordance between the fractal analysis results obtained by the two researchers. The normality of data distribution was checked using the Shapiro-Wilk test, and it was found to be normally distributed. The agreement between the fractal analysis results obtained by the two observers was evaluated by calculating the Intraclass Correlation Coefficient (ICC). The Paired Samples T-test was used to compare continuous data measurements obtained from the two analysis methods. P-values less than 0.05 were considered statistically significant.

Results

In this study, the fractal dimension of 200 different regions from 100 different points on 10 panoramic radiographs was calculated using two different measurement methods. There was excellent agreement between the classical method fractal measurements of the two observers (ICC: 0.98; 95% CI 0.971 to 0.987; p < 0.001), while there was perfect agreement between the new single-click automated fractal analysis measurements (ICC: 1; 95% CI 1 to 1). In the classic method, 6 out of 100 measurements (6%) differed between the two observers. The mean fractal dimension values obtained from the two different fractal analysis methods are shown in Table 1.

Table 1.

Mean fractal dimension values obtained from two different measurement methods

	N	Mean	SD	Minimum	Maximum
New Method	100	1.364545	0.0765852	1.1960	1.5268
Classical Method	100	1.307439	0.0576213	1.1682	1.4196

There was a statistically significant difference between the two different fractal analysis methods (Table 2). The fractal dimension calculated using the classic method was 0.057106 ± 0.0764495 (95% CI 0.0419368 to 0.0722752; p < 0.001) higher than that obtained using the new method. Although this difference was statistically significant, the clinical value was relatively low. In 16 regions, the new fractal analysis method produced higher fractal values compared to the classic method, while in 84 regions, the classic method produced higher fractal dimensions than the new method.

Table 2.

Evaluation of the difference in fractal dimension values between two measurement methods using paired samples T-Test

Compare	Mean	SD	95% Confidence Interval of the Difference		t	df	p
			Lower	Upper
Classical-New	0.057106	0.0764495	0.0419368	0.0722752	7.470	99	< 0.001

The evaluation and comparison of fractal analysis times are shown in Table 3. Considering the fractal analysis times of both observers, the time taken to calculate the fractal values of 10 different regions on one radiograph, starting from the ROI selection in the classic model, was 717.6 ± 21.49 s. In the new automatic fractal analysis model, this time was 31.3 ± 2.79 s. The fractal analysis of 10 different regions on one radiograph took 686.3 ± 22.61 (95% CI 675.71 to 696.88; p < 0.001) seconds longer in the classic model than in the new automatic model.

Table 3.

Mean duration in seconds of the application times for two different fractal analysis methods and evaluation of the difference in application times using paired samples T-Test

Fractal Analysis Method	Descriptive Statistics			Paired Samples Test
	N	Mean (sn)	SD (sn)	Mean (sn)	SD (sn)	95% Confidence Interval of the Difference		p
						Lower	Upper
Classical	20	717.6	21.49761	686.3	22.61	675.71	696.88	< 0.001
New	20	31.3	2.79285

During the fractal analyses, a total of 29 errors (14.5%) were made by the two researchers in the classic method. Of these errors, 23 were due to skipping some of the steps in the fractal analysis, while the cause of 6 errors was unknown, resulting in a difference in fractal values between the two researchers. In the new automatic fractal analysis method, a total of 1 error was made by the two researchers. This error was due to an issue that occurred while loading the image into the model.

Discussion

The fractal analysis method is quite popular in dentistry because it provides an accessible, repeatable, and free means of measuring the trabecular structure, quality, and bone loss patterns of the bone [17–20]. Its use is becoming increasingly widespread. However, the multi-step nature of the fractal analysis method introduces potential risks of error between steps. Additionally, this methodology, which involves complex step-by-step algorithms, negatively impacts the time available to clinicians and researchers. With the advancement of coding and software, automation has become possible in many systems [21, 22]. In this study, the authors aimed to develop a single-click automated fractal analysis module and compare it with the classic method.

According to the results of our study, there was a statistically significant difference in fractal dimension measurement between our single-click fractal analysis model and the classic model. However, this difference was as low as 0.05 ± 0.07. The primary reason for this difference was the disparity between the Gaussian Filter used by ImageJ and the one used in our model. The main purpose of this filter is to eliminate large-scale variations in brightness in the images. In the Gaussian Filter applied by White and Rudolph, a sigma value of 35 and a kernel size of 33 × 33 pixels were selected [14]. While ImageJ allows the sigma value to be manually set, it does not allow the kernel size to be manually set, instead using its own algorithms for this calculation.

When examining ImageJ’s open-source code (Access link: https://github.com/imagej/ImageJ), it is observed that the Gaussian kernel is calculated using a Gaussian function with a specific standard deviation (sigma). The basic steps used to determine the kernel size in ImageJ are as follows: The sigma value is the standard deviation of the Gaussian distribution, which determines how much the blur will spread. The accuracy parameter is used to determine the kernel size, where a lower accuracy value results in a more accurate kernel, but this increases the kernel size and processing time. The kRadius is calculated based on the sigma and accuracy values:

Here, the expression Math.sqrt(-2 * Math.log(accuracy)) represents the width of the Gaussian function at a certain accuracy level. By multiplying it by the sigma, the number of pixels over which this width will spread is determined. As a result, kRadius is obtained as the kernel radius.

The kernel size may be limited depending on the image size in some cases. In the code, this limitation is implemented using the maxRadius variable. After determining the kernel size, the Gaussian function is applied to each position to calculate the kernel weights. This formula shows how the weights decrease proportionally with the position:

The calculated kernel weights are normalized to sum to 1, ensuring the kernel is effectively applied to the image. After these steps, the kernel size and the corresponding weights for the Gaussian filter are calculated for a specific sigma value. The kernel size is calculated as 2 * kRadius + 1 since kRadius represents the radius, thus the total length is taken as twice the radius plus one central point.

Because the kernel size of 33 × 33 specified in the Gaussian Filter by White and Rudolph cannot be manually set in ImageJ software, it was decided to create the new code on a platform other than ImageJ [14]. The main purpose of the Gaussian filters used in both ImageJ and our model was to remove large-scale variations in brightness, and this did not significantly affect the final fractal dimension calculation result [9, 14, 23].

The newly developed method offers several advantages over the classical fractal analysis approach. The most significant advantage is that the newly designed module significantly reduces the time required for fractal analysis and simplifies the process. This improvement enables clinicians to incorporate fractal analysis into their routine clinical evaluations. Moreover, the benefits of the model extend beyond just speed; there are also methodological enhancements. In the Gaussian Filter applied by White and Rudolph [14], a sigma value of 35 and a kernel size of 33 × 33 pixels were used. However, while ImageJ allows manual adjustment of the sigma value, it does not permit manual modification of the kernel size. This limitation introduces a slight methodological uncertainty when using ImageJ for fractal analysis compared to the approach by White and Rudolph [14]. In our Python-based study, both of these values can be adjusted directly through the code, ensuring more methodologically consistent and reliable results.

The automation of fractal analysis has introduced significant advancements in efficiency and accuracy, as demonstrated in our study. While the study by Unal Erzurumlu et al. [15] also introduced an automated fractal analysis approach within the ImageJ environment, their method still required a sequence of semi-automated preprocessing steps, such as region selection and filtering. In contrast, current study developed a Python-based single-click module that integrates all necessary processes into a unified workflow, significantly reducing the total analysis time and minimizing user-dependent variability. Conversely, our automated module streamlined the process, eliminating unnecessary steps and minimizing the likelihood of errors. The fractal analysis of 10 different points in a panoramic radiograph took an average of 31.3 s in our automated fractal analysis model, while it took an average of 717.6 s in the classic method. The longest step in the automatic fractal analysis module was the ROI selection and loading the image into the module, which took an average of 15 s, whereas the fractal dimension calculation itself was completed in less than a millisecond after region selection. This significant time reduction suggests that automated fractal analysis may facilitate larger-scale studies and enhance its potential clinical applicability. Additionally, the absence of steps that could cause errors in the classic methodology may contribute to improved consistency and reliability of the analysis outcomes. By streamlining and standardizing fractal analysis, the proposed method may encourage broader adoption and support future research utilizing fractal dimension measurements.

This study has some limitations. First, the sample size was limited to 10 panoramic radiographs, which may restrict the generalizability of the findings. Future studies should test the automated fractal analysis module on larger datasets and diverse patient populations to ensure its robustness across different clinical conditions. Additionally, the radiographs used in this study were obtained from a single publicly available dataset. Variations in imaging parameters, patient demographics, and device-specific factors may influence the accuracy and reliability of fractal dimension calculations. Further validation using images from different imaging devices and clinical settings is recommended to assess the model’s performance under varied conditions. Another limitation is that the developed module is Python-based, which may pose accessibility and usability challenges for researchers and clinicians unfamiliar with programming. However, the module is designed to be user-friendly, requiring only a single click to perform fractal analysis. To further enhance accessibility, a graphical user interface is planned for future versions of the software, making it more intuitive for non-technical users. Moreover, the module’s performance may be affected by variations in image quality, contrast, and the presence of artifacts. While ImageJ was used to standardize image dimensions, it does not provide sufficient overall quality enhancement. Addressing these issues may require additional preprocessing steps or specialized software to optimize image quality before analysis. Future developments will focus on integrating advanced image processing techniques to enhance the module’s robustness against such variations. Despite these limitations, the automated fractal analysis module has demonstrated high accuracy, significantly reduced analysis time, and minimized errors compared to the classical method. Given its advantages, the module is ready for research applications and has the potential to be implemented in clinical workflows. Future improvements will focus on refining the algorithm, expanding its applicability to different dental imaging modalities, and integrating it into clinical software for seamless use in practice.

Conclusion

In conclusion, this study demonstrates that automation of the fractal analysis method used in dentistry is feasible and that this automation provides significant benefits in terms of both time savings and accuracy. The adoption of the developed module by researchers and clinicians will allow for faster and more reliable fractal analyses in dentistry. The developed module has the potential to establish a new standard for fractal analysis studies in dentistry. With its high accuracy, low error rate, and speed advantages, it may contribute to an increase in studies conducted on large datasets. However, further studies are required to validate its performance across diverse datasets and clinical conditions. In particular, future research should focus on increasing dataset diversity by testing the module on a broader range of dental radiographs acquired from different imaging devices and patient populations. Expanding the dataset will help assess the model’s robustness and ensure its generalizability to different clinical conditions. Another important aspect of future work is the development of a more user-friendly clinical interface. Since the current Python-based implementation may present accessibility challenges for clinicians unfamiliar with programming, a graphical user interface (GUI) is planned to facilitate ease of use. This will allow users to perform fractal analysis seamlessly without requiring technical expertise, making the module more suitable for routine clinical applications. By addressing these key areas, the automated fractal analysis module can evolve into a more versatile tool for both research and clinical practice, contributing to improved diagnostic precision and efficiency in dental imaging.

Abbreviations

ROI

Region of Interest

ICC

Intraclass Correlation Coefficient

CI

Confidence Interval

GUI

Graphical User Interface

Author contributions

YB: Conceptualization, Software, Formal analysis, Supervision, Validation, Investigation, Visualization, Methodology, Writing – original draft, Project administration KS: Methodology, Software, Investigation, Writing– Review and Editing.

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Data availability

The data and materials used in the study can be obtained by contacting the corresponding author.

Declarations

Ethics approval and consent to participate

In this prospective study, orthopantomography images were obtained from Kaggle, a machine learning platform, for fractal analysis. Since the data sets used were publicly available on Kaggle, ethical approval was not required. Since the publicly available data obtained were anonymous, we did not obtain consent from the individuals from whom the orthopantomograms were obtained. The study adhered to the Declaration of Helsinki.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.