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# Ozone Concentration Estimation from Infrared Images Using Extinction Coefficient

Alexandra Duminil, Jean-Philippe Tarel, Jean Dumoulin

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Alexandra Duminil, Jean-Philippe Tarel, Jean Dumoulin. Ozone Concentration Estimation from Infrared Images Using Extinction Coefficient. CAIP 2025 - 21st International Conference on Computer Analysis of Images and Patterns, Sep 2025, Las Palmas de Gran Canaria, Spain. pp.292-303, 10.1007/978-3-032-05060-1_25. hal-05425737

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# Ozone Concentration Estimation from Infrared Images using Extinction Coefficient

Alexandra Duminil¹[0000-0001-7180-4119], Jean-Philippe Tarel¹[0000-0002-9241-5347], and Jean Dumoulin²[0000-0003-0378-6136]

¹ University Gustave Eiffel, COSYS-PICS-L, F-77454 Marne-la-Vallée, France

² University Gustave Eiffel, Inria, COSYS-SII, I4S Team, F-44344 Bouguenais, France jean-philippe.tarel@univ-eiffel.fr

**Abstract.** Air quality assessment requires concentration measurement of various polluting gases, typically requiring multiple expensive sensors, each dedicated to a specific pollutant. Therefore, there is a need for cost-effective sensors capable of detecting one or more pollutants, with less reliability, such as camera-based sensors, but enabling denser sampling. In this paper, we investigate how the extinction coefficients estimated from an infrared camera may be useful for predicting ground-level ozone concentration. In addition to these coefficients, we show how weather and pollution measures collected from stations near the studied area are useful, with different machine learning methods, to better predict ozone concentration. The performance of the models is validated through a comprehensive evaluation using MAE, RMSE and R-Squared metrics. Parameter selection methods are also used to study the impact of different meteorological parameters and other pollutant concentrations on the prediction of ozone concentration.

**Keywords:** Pollution · Ozone prediction · Infrared images · Visibility

## 1 Introduction

Ambient ozone ($O_3$) is a naturally occurring gas in the atmosphere, formed through the chemical reaction of primary pollutants (nitrogen dioxide (NO2), volatile organic compounds (VOCs)) under ultraviolet radiation. However, it poses toxic risks to living organisms. Under persistent anticyclonic conditions, characterized by dry, sunny weather and low wind activity, it tends to gradually accumulate in the atmosphere [1]. As a result, implementing $O_3$ monitoring and prevention systems could significantly benefit public health. Monitoring air quality typically relies on measuring the concentration of various polluting gases, which is usually done using multiple expensive sensors, each dedicated to a specific pollutant. Therefore, there is a growing need for low-cost effective solutions, such as camera-based sensors, capable of detecting one or more pollutants, enabling more extensive and denser sampling. Several models have been proposed in the literature to estimate the concentration of pollutants and IQAs in particular, including statistical, deterministic, physically-based, and Machine
Learning (ML)-based models. According to Kumar et al. [9], ML models have been shown to be more efficient than statistical and deterministic models. In particular, SVR [18], Random Forest [2], K-means, multiple linear regression, and MLP models are widely used. Liang et al. [10] investigated the performance of six ML classifiers in predicting Taiwan’s IQA based on 11 years of data. The authors reported, in this study, that Adaptive Boosting (AdaBoost) and Stacking Ensemble were the most suitable, but prediction performance seems to vary between geographical regions. Several studies [12, 17] have shown that the performance of prediction models is improved by adding meteorological data such as temperature, humidity, wind speed and direction. In [8], the linear regression model, which is a simple model, is not effective in taking into account local variations. Juarez et al. [7] proposed a comparison analysis of O₃ prediction in Delhi, India, using eight different ML methods. The study, carried out both seasonally and annually, showed improvements in O₃ prediction, particularly during winter. Deep CNNs are not widely used for pollutant prediction but have been shown to be suitable for non-linear processes related to air quality [4].

Some studies proposed image processing-based methods, which focused on particulate matter concentration predictions [11, 16, 3, 14]. Part of them aimed to analyze images by focusing on sky regions and estimating visual features such as the dark channel prior [11, 16], or the color histogram [3]. Mohan et al. [14] proposed using pre-trained CNN methods to directly classify outdoor RGB images with different levels of pollution.

While previous studies have proposed image-based methods to predict particulate matter concentrations from RGB images, our work aims to go a step further by using infrared images to help estimate ozone concentrations in Champs-sur-Marne, a town around twenty kilometers east from Paris, France. Specifically, our work stands out by investigating the interest in using extinction coefficients *k* calculated from infrared camera images, a specific feature, jointly with other meteorological and pollution measures. To the best of our knowledge, this approach has not yet been investigated in the literature. We also studied the interest of different input measures with also their lagged values and the interest of using a parameter selection method such as SHAP. Different ML models are used to perform predictions including SVR, random forest, boosting, MLP and CNN.

# 2 Materials and methods

## 2.1 Data

The data are collected from our system located on the roof of the University, at Champs-sur-Marne in France. It is composed of two RGB cameras, an infrared camera and a visibilimeter, which allow us to obtain meteorological data such as temperature, background luminance, cumulative water sum (cws) and the visibility distance. Pollution data, which are used to obtain the ground truth, are collected from the Airparif database [1] until 2018. Currently, the dataset comprises a single scene, as obtaining data over a long period of time using a specific sensor system is challenging. However, even though the dataset only
contains a single scene, the system takes pictures continuously, enabling data to be obtained under different meteorological conditions.

The dataset used in this study consists of a data series of 18500 samples collected between 2018 and 2023. Data for 2020 were excluded due to a lower sample count compared to other years. To avoid imbalances, the number of samples for each remaining year is approximately equal. Then, missing and NaN values led to the removal of the data line.

## 2.2 Method

Air quality depends primarily on the intensity of pollutant emissions, which are influenced by various factors, particularly meteorological conditions. These conditions also determine the dispersion or accumulation of pollutants in the atmosphere. Wind and rain, for instance, promote the dispersion, mixing, and removal of pollutants. In contrast, persistent anticyclonic conditions, characterized by dry, sunny weather and the absence of wind at ground level, can lead to gradual accumulation of pollutants. Consequently, the summer season is characterized by hot and sunny days that favor the formation of ozone. Fig. 1, shows the $O_3$ concentration over several years. A low concentration of $O_3$ is noticeable in autumn and winter, while it increases in spring and summer.

<figure><img src="image_3.png" /><figcaption>Fig. 1. Lines plot describing the monthly trends in $O_3$ concentrations over several years.</figcaption></figure>

In addition to the meteorological data, we aim to exploit the infrared images provided by the camera. $O_3$ absorbs and emits in the infrared range and is strongly influenced by meteorological conditions, including sunshine and high temperatures. Fig. 2 presents cropped images from the infrared camera with associated $O_3$ concentration. The right image shows higher contrast, likely due to seasonal temperature differences. The dark area, where the horizon is barely
visible, may result from atmospheric absorption, where ozone would be involved. Infrared imagery can be used to visualize thermal variations in the atmosphere, leading indirectly to the location of ozone.

<figure><img src="image_4.png" /><figcaption>Fig. 2. Infrared camera images of areas of interest with associated $O_3$ concentration.</figcaption></figure>

**Extinction coefficients k** To achieve this, we rely on the use of extinction coefficients, which have been used in previous works to estimate the concentration of particulate matter in the atmosphere [11]. The visible veil, caused by high concentrations of particulate matter, is due to the interaction of light with the particles in the air, called light scattering, which causes an attenuation of transmitted light. The Koschmieder law [13] is a physically based model of the apparent luminance of objects on sky background near the horizon:

$$I = I_0 e^{-kd} + I_s (1 - e^{-kd}) \quad (1)$$

where I is the intensity of an object seen at distance d, $I_0$ is the clear intensity of this object, $I_s$ is the intensity of the sky and k is the atmospheric extinction coefficient to estimate. Eq. 1 assumes constant lighting conditions. In practice, the weather and the position of the Sun vary between the days and seasons. For this reason, assuming a cold sky, the hypothesis of neglecting the second term of I in Eq. 1 is explored, leading to a simpler model with only the first term:

$$I \approx I_0 e^{-kd} \quad (2)$$

<figure><img src="image_5.png" /><figcaption>Fig. 3. Infrared image with distances in meters and points of interest with marks used for coefficient calculations.</figcaption></figure>
<table><caption>**Table 1.** Label names of the estimated extinction coefficient *k* depending on the set of used point marks, with numbers as shown in Fig. 3.</caption><thead><tr><th>Estimated k</th><th>Target object</th><th>Set of point marks</th></tr></thead><tbody><tr><td>k<sub>optim</sub></td><td>vegetation</td><td>3,4,5</td></tr><tr><td>k<sub>1b</sub></td><td>buildings</td><td>1,2</td></tr><tr><td>k<sub>2v</sub></td><td>vegetation</td><td>3,4</td></tr><tr><td>k<sub>3v</sub></td><td>vegetation</td><td>3,5</td></tr><tr><td>k<sub>4v</sub></td><td>vegetation</td><td>3,6</td></tr><tr><td>k<sub>5v</sub></td><td>vegetation</td><td>4,6</td></tr></tbody></table>

Fig. 3 presents the different points of interest with a number mark and displays their approximate distances to the camera in meters (m). Table 1 shows the label names of the estimated extinction coefficient *k* depending on the used point marks shown in Fig. 3. Points of interest were chosen on buildings (1 and 2) and on vegetation (3 to 6). The purpose is to investigate the optimum choice of the point marks set. Buildings tend to get warmer compared to vegetation. Thus, it could be relevant to analyze the impact of these choices on the calculation of the extinction coefficient. When considering the simpler model of Eq. 2, the *k* can be computed using only two image points at different known distances to simplify the unknown $I_0$ [5]. Therefore, $k_n$ can be estimated as follows:

$$k_n = \frac{1}{(d_j - d_i)} \log\left(\frac{I_i}{I_j}\right) \quad (3)$$

where $I_i$ and $I_j$ are the average intensities of a 5×5 area around points *i* and *j*, $d_i$ and $d_j$ are the distances between camera and pointed objects *i* and *j* (see Fig. 3). The $k_n$ computations are independent of the global illumination conditions.

When considering the complete model of Eq. 1, the equation is with three unknowns: $k$, $I_s$ and $I_0$, and thus three points at three different distances are requested to estimate *k*. These unknowns' values are obtained by least squares minimization. The $k_{optim}$ can thus be computed from where the minimum of the following error is achieved:

$$ \begin{aligned} & (I_3 - (I_{03} e^{-kd_3} + I_s(1 - e^{-kd_3}))^2 + \\ & (I_4 - (I_{03} r_{34} e^{-kd_4} + I_s(1 - e^{-kd_4}))^2 + \\ & (I_5 - (I_{03} r_{35} e^{-kd_5} + I_s(1 - e^{-kd_5}))^2 \end{aligned} \quad (4) $$

where $r_{34}$ and $r_{35}$ are the ratios of the mean intensities between points 3 and 4 and points 3 and 5, respectively. By comparing these different estimates, this will allow us to determine what is the best estimate of the extinction coefficient of $O_3$ concentration.

**Data analysis** Studies have shown that pollutant concentrations over time *t* depend on previous values [6]. To analyze these temporal dependencies, the Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF)
are used. ACF captures the general correlation with past values, while PACF isolates the direct effect of each lag. The time increment in our case is one hour. As with pollutants, meteorological data and the *k* coefficients at a given time *t* are correlated with the two previous hours. These additional information are also used as input parameters. The suffixes *lag1* and *lag2* are used to differentiate time-shifted parameters in the rest of the paper.

<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Heatmap of the linear correlation matrix between $O_3$ and the different extinction coefficients.</figcaption></figure>

Fig. 4 presents the heatmap of the correlation matrix obtained from a set of data including the estimated *k* coefficients, and the Airparif data $O_3$. The values turn red as positive correlations increase and blue for negative correlations. The weakest correlations with $O_3$ are $k_{\text{optim}}$ and $k_{5v}$ followed by $k_{1b}$. A similar pattern was observed in the lagged versions, which tended to increase with lag. This suggests that these *k* values may not be optimal for estimating ozone concentration. For $k_{1b}$, the points of interest taken in the buildings may slightly distort the results due to their higher temperature. For $k_{5v}$, the distance between the two points is around 1705 m, corresponding to the shortest case. The best correlation values with $O_3$ are $k_{4v}$ and its lagged values. The points of interest were chosen in vegetation areas and at a greater distance than the other *k* values. To compare with the extinction coefficient obtained in the visible spectrum, the parameter $k_{4rgb}$ has been estimated similarly to $k_{4v}$ but on RGB
images and is added at the first line of the correlation matrix. Its correlation value with $O_3$ is lower than 0.1, showing the interest of using infrared images instead of RGB. However, the correlation matrix captures only linear correlations. Thus, in addition, the mutual information (MI) between $O_3$ and the different extinction coefficients is computed to measure a non-linear link between them. The MI is presented in Fig. 5. The results confirm previous statements about the correlations of $k_{\text{optim}}$, $k5_v$ and $k1_b$ and their lagged values. In general, the coefficients with the highest MI scores are $k3_v$ and $k4_v$ with their lags.

<figure><img src="image_7.png" /><figcaption>**Fig. 5.** Bar plot describing the mutual information between $O_3$ and the different extinction coefficients.</figcaption></figure>

**Meteorological data** The use of meteorological data has been shown to be essential to predict or monitor the concentration of pollutants. Many studies have used data such as absolute humidity, air temperature, absolute pressure, and wind direction. In our study, our objective is to use the available meteorological data. The meteorological sensor is located on the station with the cameras on our acquisition site. The data retrieved are air temperature, background luminance, cumulative water sum (cws) and visibility distance. The background luminance corresponds to the ambient light and the cws is the total accumulated precipitation. The visibility distance may depend on particles in the air, rain or fog. Ozone concentration peaks appear in cycles, as shown in Fig. 1. The peaks occur at a certain time of year, mainly in summer and generally in the afternoon. It thus seems relevant to add hours value, days value and seasons value as cyclical variables to the previous meteorological data vector. For example, the variable
$day$ is included as two variables: $sin_{day} = \frac{sin(2\pi \times day)}{7}$ and $cos_{day} = \frac{cos(2\pi \times day)}{7}$. The number 7 denotes the number of days in a week. This is performed similarly for hours and seasons.

The concentration of pollutant from Air-Quality stations close to Champs-Sur-Marne are also interesting to study. Fig. 6 presents the MI with the different parameters previously selected and the $O_3$ concentration. We observed a strong link between $NO_2$ and $O_3$. This can be due to the formation of $O_3$ by chemical reaction with primary pollutants, including $NO_2$. Temperature and $cws$ are also important features. The former is indeed essential for the formation of $O_3$, since its concentration increases with temperature. For the latter, precipitation favors the dispersion and leaching of pollutants. As a result, the $O_3$ concentration should decrease as $cws$ increases. The importance of particulate matter PM2.5 and PM10 can be noticed. In fact, there are involved in slowing the fall of radical aerosols, which are one of the precursors of $O_3$ [15]. Some parameters, such as luminance, have more information in the lag2 version. Cyclic parameters appear less important, and MI between $O_3$ and the other data varies across features. Since some parameters may be redundant, it is essential to select the most predictive ones.

<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Bar plot describing the mutual information between $O_3$ concentration and other selected parameters.</figcaption></figure>

# 3 Results

The collected data serves to train different ML models in order to predict $O_3$ concentration. Inspired by the state-of-the-art, classical ML models are selected:
Linear regression (LR), SVR, Random forest (RF), Xtreme gradient boosting (XB), as well as MLP and CNN. The CNN model consists of five layers of 1D convolution followed by two dense layers. The original data consists of a data series of approximately 18500 collected data from 2018 to 2023. The ML models are trained on data of size 11863 and 2966 for validation, including data from 2018 to 2023. The test sets t1 and t2 are based on data from 2022 and 2023, respectively. The data were split using odd months for training/validation and even months for testing, ensuring test independence while retaining data. Three performance metrics are used in this section: The Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and R-Squared (R²), to measure the prediction errors for O₃ concentration prediction. Lower MAE and RMSE values and higher R² value demonstrate better performance.

<table><caption>**Table 2.** Prediction errors on validation (v) and test data (t1 and t2). The best values are in bold.</caption><thead><tr><th rowspan="2">Methods</th><th colspan="6">Without k parameters + lags</th><th colspan="6">With k parameters + lags</th></tr><tr><th>LR</th><th>SVR</th><th>RF</th><th>XB</th><th>MLP</th><th>CNN</th><th>LR</th><th>SVR</th><th>RF</th><th>XB</th><th>MLP</th><th>CNN</th></tr></thead><tbody><tr><td>MAE v</td><td>0.436</td><td>0.250</td><td>0.276</td><td>0.280</td><td>0.278</td><td><strong>0.188</strong></td><td><strong>0.432</strong></td><td><strong>0.234</strong></td><td><strong>0.270</strong></td><td><strong>0.280</strong></td><td><strong>0.270</strong></td><td>0.190</td></tr><tr><td>RMSE v</td><td>0.554</td><td>0.336</td><td>0.364</td><td>0.381</td><td>0.367</td><td><strong>0.255</strong></td><td><strong>0.548</strong></td><td><strong>0.315</strong></td><td><strong>0.358</strong></td><td><strong>0.377</strong></td><td><strong>0.350</strong></td><td>0.257</td></tr><tr><td>R² v</td><td>0.707</td><td>0.892</td><td>0.873</td><td>0.862</td><td>0.871</td><td><strong>0.938</strong></td><td><strong>0.714</strong></td><td><strong>0.905</strong></td><td><strong>0.878</strong></td><td><strong>0.864</strong></td><td><strong>0.883</strong></td><td>0.937</td></tr><tr><td>MAE t1</td><td>0.503</td><td>0.450</td><td>0.396</td><td>0.436</td><td><strong>0.412</strong></td><td>0.423</td><td><strong>0.490</strong></td><td><strong>0.448</strong></td><td><strong>0.389</strong></td><td><strong>0.427</strong></td><td>0.433</td><td><strong>0.399</strong></td></tr><tr><td>RMSE t1</td><td>0.615</td><td><strong>0.577</strong></td><td>0.504</td><td>0.554</td><td><strong>0.529</strong></td><td>0.544</td><td><strong>0.599</strong></td><td>0.581</td><td><strong>0.496</strong></td><td><strong>0.545</strong></td><td>0.557</td><td><strong>0.510</strong></td></tr><tr><td>R² t1</td><td>0.637</td><td><strong>0.681</strong></td><td>0.756</td><td>0.706</td><td><strong>0.732</strong></td><td>0.716</td><td><strong>0.656</strong></td><td>0.676</td><td><strong>0.764</strong></td><td><strong>0.715</strong></td><td>0.702</td><td><strong>0.751</strong></td></tr><tr><td>MAE t2</td><td><strong>0.473</strong></td><td><strong>0.398</strong></td><td>0.349</td><td>0.376</td><td><strong>0.384</strong></td><td>0.395</td><td>0.479</td><td>0.409</td><td><strong>0.342</strong></td><td><strong>0.365</strong></td><td>0.400</td><td><strong>0.375</strong></td></tr><tr><td>RMSE t2</td><td><strong>0.590</strong></td><td><strong>0.514</strong></td><td>0.453</td><td>0.485</td><td><strong>0.498</strong></td><td>0.502</td><td>0.598</td><td>0.534</td><td><strong>0.448</strong></td><td><strong>0.472</strong></td><td>0.522</td><td><strong>0.492</strong></td></tr><tr><td>R² t2</td><td><strong>0.696</strong></td><td><strong>0.769</strong></td><td>0.821</td><td>0.795</td><td><strong>0.783</strong></td><td>0.780</td><td>0.688</td><td>0.751</td><td><strong>0.825</strong></td><td><strong>0.805</strong></td><td>0.762</td><td><strong>0.788</strong></td></tr></tbody></table>

Table 2 presents the prediction errors for validation and tests with and without k parameters for different ML models. The general results on validation v and on tests t1 and t2 demonstrate better performance with the k parameters, compared to without. Specifically, the CNN, RF and Boosting models produce the best results on t2 and t3, which include the k parameters. Above all, RF appears to be the most suitable model for this type of task.

Based on these results, a SHAP analysis is applied on the CNN model to display the importance of each parameter, using the SHAP summary plot in Fig. 7. As we saw in the previous section, NO₂ has a significant impact on O₃ concentration. More specifically, in terms of SHAP values, higher NO₂ values tend to reduce O₃ levels. This means that high NO₂ levels are not required to raise O₃, as they also correlates with meteorological factors such as temperature, especially at night and during the colder seasons. In addition, the plot shows that higher temperatures, luminance and k₄ values are linked to increased ozone concentrations, as indicated by their positive SHAP values. The visibility feature has negative values associated with a decrease in O₃ concentration. Finally, the others' values demonstrate their limited impact on O₃ concentration. In sum-
<figure><img src="image_9.png" /><figcaption>**Fig. 7.** Graph showing the importance of parameters using the SHAP method.</figcaption></figure>

In this work, we present the results of using the SHAP method to explain the importance of various parameters on the learned model. However, the SHAP method appears to be relatively sensitive, since the results differ significantly depending on the types of model, the size of the datasets, and the number of input parameters.

# 4 Conclusion

The purpose of this work was to study the interest in using extinction coefficients computed from infrared images independently of their acquisition time to help predict *O*₃ concentration. The experimental study is conducted in Champs-sur-Marne, France, from a dataset collected quite regularly each hour from 2018 to 2023 under various different weather and traffic conditions. The first experiments are based on data from a single scene acquired under different weather conditions and throughout the day over several years. The preliminary results showed a significant correlation between these extinction coefficients and the *O*₃ concentration, making the use of camera data interesting for *O*₃ prediction. We were also able to measure the impact of other meteorological conditions that are relatively rarely studied in the literature, such as visibility or sky luminance.
Then, we performed a comparison with several ML models and a CNN, which gave promising results on test sets. The perspective of collecting more data over the years to cover as many situations as possible and to improve the generalization properties of prediction models is important to consider. In future work, we also aim to extend the proposed method to more infrared scenes, improve the quantitative evaluation by adding advanced models, and to exploit the use of multi-spectral cameras.

## Acknowledgment

Thanks to BRIGHTER project for funding. BRIGHTER has received funding from the Chips Joint Undertaking (JU) under grant agreement No 101096985. The JU receives support from the European Union's Horizon Europe research and innovation program and from France, Belgium, Portugal, Spain and Turkey.

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