Variational Autoencoder-based Estimation of Chronological Age and Changes in Morphological Features of Teeth

doi:10.21203/rs.3.rs-1750283/v1

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Variational Autoencoder-based Estimation of Chronological Age and Changes in Morphological Features of Teeth

https://doi.org/10.21203/rs.3.rs-1750283/v1

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published 13 Jan, 2023

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The present study developed a variational autoencoder (VAE) capable of estimating the chronological age of subjects using feature values extracted from their teeth, and further determine how given teeth images affected the accuracy of estimation. The developed VAE was trained with first molar and canine teeth images, and a parallel-VAE structure was further constructed to extract common features shared by the two types of teeth in a more effective manner. The encoder of the VAE was designed to be combined with a regression model to estimate age. In an attempt to determine which parts of tooth images were more or less important when estimating age, a method of visualizing the obtained regression coefficient using the decoder of the VAE was developed. The developed age estimation model was trained with data obtained from a total of 910 individuals aged 10–79 years. This model showed a median absolute error (MAE) of 6.99 years, demonstrating its ability to estimate age accurately. Further, this method of visualizing the influence of particular parts of tooth images on the accuracy of age estimation using a decoder is expected to provide novel insights for future research on explainable AI.

Morphological changes of teeth over time provide substantial evidence when estimating the age of unidentified individuals, and thus approaches using such data have been widely used in various applications, such as forensic dentistry and age estimation for immigrants¹. Various methods based on forensic dentistry using teeth for age estimation have been proposed. Among them, statistical approaches, in which the morphological features of teeth are quantified and statistically analyzed, have been accepted as conventional^2,3. This approach makes it possible to estimate age based on tooth data obtained from unidentified individuals with no age information, and based on these statistical data, the age of subjects can be estimated. However, this method of quantifying the morphological features of teeth of subjects using auxiliary indexes through manual work and estimating their age based on the obtained dimensional information generally takes quite a long time and may lead to different outcomes depending on the proficiency of operators who analyze teeth radiographic images^4,5,6.

To overcome these problems, various studies have been performed to develop Artificial Intelligence (AI) models that can automatically extract the features of teeth via deep learning using orthopantomograms (OPGs) and estimate age based on the obtained feature values^5,7,8,9. Among various machine learning-based methods for extracting feature values from medical images, a deep learning analytical method based on the convolutional neural network (CNN) has proved highly effective in diagnosing symptoms of subjects based on medical images or estimating the age of bones¹⁰. These AI models developed based on OPG and CNN are not only less affected by the proficiency of their users but also are capable of estimating the age of subjects based on a large amount of data in a relatively short time^11,12. CNN-based algorithms, however, are known to lack interpretability, because when using age prediction models based on these algorithms, users often find it difficult to determine which part of a given tooth image has affected the age estimation result or what causal relationship there may be between aging and morphological changes in teeth^1,5,13.

Vila-Blanco et al.⁵ and Kim et al.¹ developed CNN algorithms capable of estimating the age of subjects using OPGs and further employed a Grad-CAM technique to identify the regions of teeth that significantly affect the results of age estimation models. When estimating the age of teeth the Grad-CAM technique indicates the degree of importance of each part of the input dental radiographs as a heatmap, thus allowing users to easily spot the parts of given images of all or individual teeth that are important to age estimation. Milošević et al.¹³ developed age prediction models based on the existing CNN structure, which had already proved highly effective. In the study, various prediction models, such as individual tooth-based models and models with teeth removed, were developed to determine which region of given OPG images contained useful age indicators, and the age estimation accuracy of each model was compared and analyzed. In an attempt to enhance the interpretability of deep learning algorithms, Zhang et al.¹⁴ and Zhao et al. ¹⁵ developed an autoencoder-based model capable of both age estimation and result interpretation and further verified the performance of the developed model using face and brain images.

The present study proposes a method for extracting feature values from teeth images using AI algorithms and then estimates the age of subjects based on the extracted feature values, while also determining which regions of the teeth were more important than others for age prediction based on dental radiographs. A variational autoencoder (VAE) specially designed for the extraction of feature values from images was used to develop the feature value-based prediction models, and methods for data interpretation. The VAE was trained with first molar and canine teeth images obtained from previous studies. In addition, a method for quantitatively determining and analyzing the correlation between age and morphological changes in teeth is proposed. To be more specific, the age estimated by the VAE was compared with the amount of morphological variation between consecutive teeth images over time, i.e., with advancing age.

Dataset

OPG data obtained from a total of 910 Korean outpatients who were treated at the Jeonbuk National University Dental Hospital were used as research data. Informed consent was obtained from all participants and all methods were performed in accordance with the relevant guidelines and regulations. This study was duly approved by the Institutional Review Board of the Jeonbuk National University Hospital (CUH 2021-03-021). The age of subjects was determined based on the date of radiography. Their age range is presented in Table 1. With reference to a previous study in which mandibular first molar and canine teeth were used for age estimation, in the present study each image was cropped into a total of four sub-images of two types of teeth on the left and right^1,13,16. More specifically, the images were manually segmented under the guidance of skilled dentists into a total of four sub-images, of left and right mandibular first molar teeth, and left and right mandibular canine teeth. The obtained images were then resized into 256 x 256 pixels to contain the maximum pixel information. From a total of 910 dental radiographs, 1,216 images of first molar teeth and 1,634 images of canine teeth were obtained. In the present study, when these tooth images were used to train the developed model, all of the left-side images were mirrored before use to ensure that the learning process was not affected by whether a given tooth was located on the left or right side^17,18.

Table 1

Age and gender distribution of dental x-ray datasets.
Age group	Gender		Total
Age group	Male	Female	Total
10–19	30	54	84
20–29	79	116	195
30–39	23	66	89
40–49	57	97	154
50–59	53	111	164
60–69	74	73	147
70–79	33	44	77
Total	349	561	910

Variational Autoencoder-linear Regression Model

Single VAE with linear regression

Convolutional neural networks (CNN) are one of the powerful deep learning tools that can automatically extract feature values from input image data to establish a nonlinear relationship model between label data and the corresponding feature values¹⁹. Meanwhile, convolutional VAE is a probabilistic graphical model capable of extracting features of input image data as a continuous probability distribution function using two symmetrical CNNs²⁰. When the dental radiograph $x$ is entered into ${q}_{\varnothing }\left(z\right|x)$, which is the VAE's encoder model, the probability distribution of all latent z variables, which correspond to all characteristic values that the input data can result in, is then returned as output. The decoder ${p}_{\theta }\left(x\right|z)$, also known as the generative model, in turn, returns virtual image data, $\stackrel{-}{x}$, which has been reconstructed from the input latent z variables.

To train this VAE model, the Kullback-Leibler divergence that minimizes the distribution of latent z variables between $q\left(z\right|x)$ and $p\left(z\right)$ is first calculated, as shown in Eq. (1). Next, a reconstruction error is calculated, as shown in Eq. (2), in an attempt to minimize the difference between $x$, the dental radiograph that has been entered into the encoder and $\stackrel{-}{x}$, the resultant image obtained from the decoder. The total loss of the VAE model ${\mathcal{L}}_{VAE}$ is used to train the model with hyperparameters in a way that minimizes both the KL divergence loss ${\mathcal{L}}_{KL}$ and image reconstruction loss ${\mathcal{L}}_{rec}$, as shown in Eq. (3). In order to optimize the learning process of the developed model, each loss term was weighted by the factor γ.

$${\mathcal{L}}_{KL}= {D}_{KL}\left(q\right(z\left|x\right)\left|\right|p\left(z\right))$$

$${\mathcal{L}}_{rec}= -{\mathbb{E}}_{q\left(z|x\right)}\left[\text{log}p\left(x\right|z)\right]$$

$${\mathcal{L}}_{VAE}= {{\gamma }_{1}\mathcal{L}}_{KL}+ {\gamma }_{2}{\mathcal{L}}_{rec}$$

In the present study, a VAE composed of five convolutional layers was developed, and grayscale images of 256 x 256 pixels were used as input for the model, as shown in Fig. 1 (a). From the input images, the encoder model returns 512×8×8 distribution variables $\mu$ and $\sigma$. The latent z variables are then calculated from the obtained distribution variables. The decoder model receives the latent z variables as input and then generates virtual images of 256 x 256 pixels as output. A linear regression equation was developed to estimate the age of teeth by using the latent z variables obtained from the encoder, as shown in Fig. 1 (b). The VAE model was built using Python's TensorFlow Library and trained in an unsupervised learning manner, while the linear regression equation was developed using Python's Scikit-learn Library and trained in a supervised manner.

Parallel VAE with linear regression

Accuracy and precision are among the most critical factors that determine the performance of dental age estimation methods for adults, especially from the perspective of forensic odontology. The accuracy of these methods may vary depending on what tooth is selected and examined or what estimation method is employed. Thus, it is important to select and apply at least two estimation methods in order to improve both accuracy and precision²¹. This is also the case for dental age estimation using AI techniques; multiple teeth need to be comprehensively examined. In this light, the present study developed a parallel VAE model capable of estimating the age of subjects by comprehensively analyzing the feature values obtained from at least two types of teeth images, generating a virtual image of the teeth^22,23.

Assuming that images of first molar and canine obtained from a single subject contained common latent variables that may help estimate the age of the subject, a parallel-VAE model that partly shared the same latent z variables were developed, as shown in Fig. 2 (a). Encoder 1 and Decoder 1 of the parallel VAE used datasets of first molar images as input and output data, while Encoder 2 and Decoder 2 used datasets of canine images as input and output data. Here, it was assumed that, among the $\mathcal{n}$ latent variables calculated from Encoder 1, ${z}_{1u}$, which corresponded to half the $\mathcal{n}$ latent variables ($\mathcal{k})$, included unique variables specific to first molar teeth, and the other half of the latent variables (${z}_{1c}$) included common variables shared by both first molar and canine teeth. Similarly, among the $\mathcal{n}$ latent variables obtained from Encoder 2, ${z}_{2u}$, which corresponded to half the $\mathcal{n}$ latent variables ($\mathcal{k})$, were assumed to include unique variables specific to canine teeth, and the other half (${z}_{2c}$) were assumed to have common variables shared by both the first molar and canine teeth. In order to ensure that the latent variables ${z}_{1u}$ and ${z}_{2u}$ would have respective feature values for each tooth type while allowing the latent variables ${z}_{1c}$ and ${z}_{2c}$ to include common information shared by both types of teeth, Eq. (4) was added to the VAE loss calculation term²².

The ${\mathcal{L}}_{separate}$ value, which is the separate loss, was obtained by dividing the difference between the common variables ${\mathcal{L}}_{common}$ for the two teeth types by the difference between the unique variables ${\mathcal{L}}_{unique}$. The mean square errors between two latent variable sets can be expressed as in Eq. (5) and Eq. (6). ${\mathcal{L}}_{{KL}_{m}}$ and ${\mathcal{L}}_{{rec}_{m}}$in Eq. (7) refer to the KL loss and image reconstruction loss of the VAE that receives first molar images as input, respectively. ${\mathcal{L}}_{{KL}_{c}}$ and ${\mathcal{L}}_{{rec}_{c}}$ are the KL loss and image reconstruction loss of the VAE that receives canine as input, respectively. If one trains the entire parallel-VAE model using the loss functions in Eq. (7) and gradient descent methods, the common latent variables for each teeth type, that is, ${z}_{1c}$ and ${z}_{2c}$, tend to converge toward the same value in a gradual manner to minimize the ${\mathcal{L}}_{common}$ value. However, at the same time, this learning process proceeds in a way that maximizes the ${\mathcal{L}}_{unique}$ value, allowing the values of the unique latent variables for each teeth type, i.e., ${z}_{1u}$ and ${z}_{2u}$, to be as different as possible from each other.

$${\mathcal{L}}_{separate}= \frac{{\mathcal{L}}_{common}}{{\mathcal{L}}_{unique}}$$

$${\mathcal{L}}_{common}=\frac{1}{\mathcal{k}}\sum _{i=1}^{k}{({z}_{{1c}_{i}}-{z}_{{2c}_{i}})}^{2}$$

$${\mathcal{L}}_{unique}=\frac{1}{\mathcal{k}}\sum _{i=1}^{k}{({z}_{{1u}_{i}}-{z}_{{2u}_{i}})}^{2}$$

$${\mathcal{L}}_{parallel-VAE}= {{\gamma }_{1}\mathcal{L}}_{K{L}_{m}}+ {{\gamma }_{2}\mathcal{L}}_{K{L}_{c}}+{{{{\gamma }_{3}\mathcal{L}}_{re{c}_{m}}+\gamma }_{4}\mathcal{L}}_{re{c}_{c}}+{{\gamma }_{5}\mathcal{L}}_{separate}$$

A linear regression model capable of age estimation using the latent variables obtained from the parallel VAE was developed, as illustrated in Fig. 2 (b). The configuration of this linear regression model was basically the same as that employed for the single VAE in that it received latent variables as input and returned the age of subjects as output. However, it differed in that this regression model was built using only 3/4 of all latent variables. This configurational difference is attributed to the fact that, once the parallel VAE is sufficiently trained, the common latent variables ${z}_{1c}$ and ${z}_{2c}$ become almost identical, and thus there is no need to use both of them to develop a regression model. Ultimately, the developed regression model contained a total of $\mathcal{n}+\mathcal{k}$ regression coefficients $\beta$, along with $\alpha$, a single intercept.

Generation Of Teeth Images That Reflect Age Changes

The present study developed a method for quantitatively determining and analyzing the correlation between age and the morphological changes in teeth by generating dental images that may vary continuously with age. This was accomplished using the coefficients of a regression model trained with age data, along with a decoder. Once fully trained, the regression model can be expressed as an equation, as shown in Eq. (8).

$${\beta }_{1}*{z}_{1}+{\beta }_{2}*{z}_{2}+{\beta }_{3}*{z}_{3}+\dots +{\beta }_{n}*{z}_{n}+\alpha ={y}_{age}$$

The regression coefficient ${\beta }_{k}$ may be used not only to estimate age but also to generate latent variables corresponding to teeth images when the subject is either younger or older compared to the reference image. The latent variables extracted from the encoder contain various information, including the brightness of the teeth images used, gender, and age. When a regression model is developed using age as a dependent value, coefficients for latent variables that have a strong correlation with age tend to be highly positive or negative. When the correlation with age is weak, the coefficients tend to be small. Based on this relationship between latent variables and their coefficients, it is possible to selectively control only the values of the latent variables that have a strong correlation with age. For example, when adding or subtracting the regression coefficient $\beta$ to or from the latent variables obtained from the reference image, the values of the latent variables that have a strong correlation with age tend to change greatly (Fig. 3). When the correlation is weak, the corresponding changes are also small. Accordingly, virtual images in which the subject is younger compared to the reference image can be generated by subtracting the regression coefficient $\beta$ from the extracted latent variables and then reconstructing them using the decoder. Similarly, virtual images in which the subject is older can be obtained by adding the regression coefficient $\beta$ to the latent variables and reconstructing them using the decoder.

Age estimation

In the present study, two models, i.e., single-VAE and parallel-VAE models, were developed to determine more effective methods of age estimation, especially when multiple types of teeth were comprehensively considered. The single-VAE model was designed to be trained with a combined dataset of first molar and canine teeth images. Thus, the latent variables of this model were trained to consider the feature values of both types of teeth. In contrast, the parallel-VAE model was designed to be trained with unique latent variables, which reflect the respective feature values of each type of tooth, and common latent variables, which reflect the feature values shared by both types of teeth. The ages of the subjects were estimated using the VAE, as follows. Using an encoder that had been fully trained, latent variables were extracted from given teeth images, and the extracted values were then entered into the regression model to estimate age.

Table 2

Prediction accuracy of each training model, MAE is the median absolute error.
	Parallel-VAE			Single VAE
Age range	MAE	mean	std	MAE	mean	std
10–19	10.02	9.90	5.67	12.53	13.62	7.36
20–29	6.73	8.02	5.83	10.38	11.07	7.20
30–39	5.32	5.96	3.80	5.53	6.72	5.07
40–49	5.64	6.07	4.81	5.95	7.18	5.64
50–59	7.25	7.94	5.46	8.07	9.37	6.46
60–69	10.43	11.48	7.89	14.21	14.07	8.18
70–79	12.84	13.31	8.27	22.31	20.51	7.50
All	6.99	8.24	6.10	9.50	10.62	7.49

All of the test subjects in the present study were divided according to age into seven groups with ten-year intervals, and the age estimation accuracy was analyzed by age group, as shown in Table 2. Overall, the parallel-VAE model was found to be more accurate than the single-VAE model for age estimation. The MAE was lowest, at 5.32, for the thirties age group. The estimation error of both models was found to decrease as the age range increased from teens to thirties but started to increase in the age groups of forties or above. This result was consistent with the result of a study by Milošević et al.¹³ that analyzed the accuracy of age estimation based on single tooth images by age group.

Here, the estimation error was measured to be ten years or more for subjects in their sixties or above, and this result was also consistent with that of the previous study. For children, the accuracy of age estimation based on eruption stages is relatively high, but the estimation is more difficult for adults because all their permanent teeth have fully erupted. Thus, the error in age estimation is generally rather higher for adult subjects¹⁸. In addition, adults’ eating habits and living environments increasingly affect their teeth in a cumulative manner over time. Thus, the older the subjects are, the larger the error and discrepancies in age estimation become²⁴.

Analysis Of Generated Images

The VAE decoder model is characterized by its ability to generate virtual images from the latent variables that represent the characteristics of target teeth. The coefficients of the regression model trained with both latent variables and chronological age data contain information regarding the correlation between age and the corresponding feature values. Accordingly, it is possible to selectively change only the latent variables that contain age information, by adding or subtracting the regression coefficient to or from the latent variables extracted from the reference teeth image. The corrected variables are then reconstructed using the decoder, and as a result, the correlation between the morphology of teeth and age can be visualized, as shown in Figs. 4 and 5.

Virtual dental images that reflected an increase or decrease in the age of subjects were generated and analyzed based on the latent variables obtained from the first molar teeth, as shown in Fig. 4. Among the images in the first row, the second is a reference tooth image, which was reconstructed from the original image. The first and third images were images of the same teeth when the subject was younger and older than the reference image, respectively. The images on the left were generated by subtracting the regression coefficient from the latent variables obtained from the reference teeth image and reconstructing them using the decoder. In contrast, the images on the right were generated by adding the regression coefficient to the latent variables obtained from the reference teeth image and reconstructing them using the decoder.

The images in the second row were generated by subtracting the pixel values of the reference image from those of the virtually generated images in an attempt to determine how the morphology of teeth changed with respect to the regression coefficient. Here, red refers to the case where the pixels are brighter in the virtually generated image than in the original image. Blue refers to the case where the pixels are darker in the virtually generated image than in the original image. In addition, when the intensity of the color is higher, this means that there is a larger difference in pixels in the corresponding region. The images in the third row were generated by overlaying the obtained color maps onto the corresponding teeth images to analyze the morphological change of teeth by region. The intensity of color in this color map indicates the amount of variation in image pixels by the regression coefficient. Thus, regions with higher color intensity are considered to more significantly affect the outcomes of the age estimation model.

The values of the latent variables that were highly correlated with age were selectively increased by adding the regression coefficient to the latent variables extracted from the reference image. The corrected variables were then reconstructed using the decoder. The results showed that the pulp cavity of first molar teeth appeared brighter, and the dental cervical region became darker with age. These analysis results based on virtually generated teeth images were consistent with clinical results demonstrating that with the advance of age, the pulp cavity became smaller and thus increasingly more radiopaque, and the cervical region became increasingly more radiolucent due to dental cervical abrasion and alveolar bone resorption^25,26. The same analysis procedures were applied to canine teeth images, and the results are shown in Fig. 5. For canine teeth, the pulp cavity appeared brighter, and the dental cervical region became darker as the subject grew older, similar to the results obtained from first molar teeth, even though morphological changes were not as pronounced as in the first molar teeth cases.

In the present study, the difference in pixels between the virtually generated images and the reference image was estimated and then expressed as different colors in the form of a color map. By using this color map, a method for determining the correlation between each part of the teeth and the estimated age was proposed. The difference in pixels between images indicate what parts of the teeth affected the age estimation process, and how significant the effects were. The method proposed in the present study was found to provide improve interpretability with higher resolution compared to existing grad-CAM methods used to interpret CNN results. The developed method is also capable of visualizing the correlation between the morphological changes in teeth and advancing age.

A number of studies have been conducted to find methods to estimate the age of subjects using dental radiographs and deep learning algorithms, as well as determine what part of the teeth was more significantly affected by age, which is important in age prediction. Most previous studies have employed convolutional neural networks (CNN)-based models to estimate the age of subjects using dental radiographs, and attempted to visualize the parts of teeth that affect the age estimation process via various techniques, such as Grad-CAM methods. In the present study, a variational autoencoder (VAE), which is highly effective for image generation, was combined with a regression model. It provided excellent interpretability in attempts to determine what parts of teeth images more significantly affected the estimated age in more detail, and establish a correlation between the morphological changes in teeth and advancing age.

Two types of age prediction models, which combined the VAE with linear regression models, were developed to determine the effect of learning methods on age prediction performance. For the single VAE-based model, a single VAE was trained with a combined dataset of mixed first molar and canine teeth images. In contrast, a parallel VAE-based model was composed of two VAEs to extract both the unique and common features of the two types of teeth in parallel.

The ages of subjects were then estimated based on their first molar and canine teeth images using the two types of estimation models developed in the present study. The median absolute error (MAE) of the single VAE-based model was 9.5, higher than that of the parallel VAE-based model at 6.99, indicating that the parallel-VAE model was more accurate. This confirmed that the parallel VAE-based model, in which two types of images were learned in parallel, was more effective than the single VAE-based model, in which a combined dataset of two types of images that were randomly mixed was learned, for extracting common latent variables relevant to age shared by both types of teeth²².

The present study also proposed a method for visualizing the correlation between the morphological changes in teeth that occurs with advancing age, by controlling the latent variables using regression coefficients. To be more specific, when adding or subtracting the regression coefficient to or from the original latent variables generated from the reference image, the values of the latent variables that have a strong correlation with age tend to change greatly. The morphological changes in teeth with age can then be visualized by reconstructing the affected variables using the decoder. Subsequently, the differences in pixels between the virtually generated images and the original image were estimated and expressed as different colors in the form of a color map. The obtained color maps indicated that the pulp cavity, cervical, and alveolar bone regions significantly affected age estimation.

In addition, additional images were obtained by overlaying the obtained color maps onto the generated teeth images, and these images confirmed that the pulp cavity appeared brighter as the subject grew older, indicating that the two factors have a positive correlation. In contrast, the cervical region became darker as the subject grew older, indicating a negative correlation. These analysis results were consistent with clinical results, and demonstrated that with advancing age, the pulp cavity became smaller due to pulp calcification, dental cervical abrasion increased, and loss of alveolar bone occurred^25,26. The chronological age estimation model using dental radiographs of first molar and canine teeth provided excellent prediction accuracy; however, further research to improve estimation accuracy, especially for children and elderly subjects, is required for this model to be applied to clinical applications in practice.

In the present study, methods were proposed for identifying the parts of teeth which more significantly affect the age estimation process, and to quantitively analyze the morphological changes in teeth with age. This was accomplished using color maps representing pixel differences between virtual images of teeth generated by increasing or decreasing the age of subjects. These methods of controlling latent variables using regression coefficients and visualizing the resultant changes are expected to be employed as a new approach to determine and analyze in detail regions of interest in images that are closely related to specific variables, especially in medical deep learning. In addition, because the amount of variation in a given image can be visualized with respect to changes in certain variables using this approach, the major findings of the present study are expected to contribute to the development of explainable AI going forward.

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Acknowledgements

The research was supported by the Research Program of the Korea Institute of Machinery and Materials (No. NK238D).

Author contributions statement

S.J. wrote the manuscript text and designed research, W.J. acquired, analyzed the data and interpretation of the results, S.E.O. supervised the project and the manuscript. All authors reviewed the manuscript.

Competing interests

The authors declare no competing interests.

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No competing interests reported.

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Variational Autoencoder-based Estimation of Chronological Age and Changes in Morphological Features of Teeth

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Journal Publication

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Abstract

Figures

Introduction

Experimental Methods And Procedures

Dataset

Variational Autoencoder-linear Regression Model

Single VAE with linear regression

Parallel VAE with linear regression

Generation Of Teeth Images That Reflect Age Changes

Result

Age estimation

Analysis Of Generated Images

Discussion

Declarations

References

Additional Declarations

Status:

Journal Publication

Version 1