Object Recognition in Foggy and Hazy Conditions Using Dark Channel Prior-Based Fringe-Adjusted Joint Transform Correlator

Abstract

Extreme weather conditions like fog and haze present substantial challenges to object recognition systems. Reduced visibility and contrast degradation significantly affect the auto-correlation process, often leading to failure in object recognition. To address this critical issue and to make object recognition accurate and invincible, we propose a hybrid digital–optical correlator specifically designed to perform under adverse weather conditions. This approach integrates the dark channel prior (DCP) with the fringe-adjusted joint transform correlator (FJTC), promising significant potential to enhance the robustness of the object recognition process under challenging environmental conditions. The proposed scheme presents a unique and alternative approach for object recognition under bad weather conditions. The incoming input scenes are processed with the DCP, enabling the FJTC to perform optical correlation on the refined images. The effectiveness of the proposed method is evaluated using several performance metrics like the structural similarity index measure (SSIM), peak signal-to-noise ratio (PSNR), correlation peak intensity (CPI), processing time, and recognition accuracy. To validate the performance of the proposed study, numerical simulation along with hybrid digital–optical demonstrations have been conducted.

1. Introduction

Optical pattern recognition has attracted significant research interest owing to its benefits, including rapid processing and high accuracy [1,2,3,4,5,6,7,8,9,10]. An optical correlator performs object recognition by quantifying the similarity between two objects or patterns [1,2,3]. The joint transform correlator (JTC) is a widely preferred architecture due to its simpler experimental setup [2]. An alternative method, the VanderLugt correlator (VLC), is also utilized, but it necessitates pre-synthesized filter fabrication and precise alignment for accurate operation [3]. Over time, various approaches to JTCs have been reported, including binary JTCs, binary differential JTCs, non-linear JTCs, and fringe-adjusted JTCs [4,5,6,7,8,9,10,11,12,13]. These approaches offer a wide range of applications across different domains [14,15,16,17,18,19,20]. Among all the reported JTCs, the fringe-adjusted JTC (FJTC) is preferred due to its unique features, such as sharper auto-correlation peaks, greater discrimination capability, the extinction of dc from the correlation plane, and smaller sidelobes [11,12]. The advantages of the FJTC over other traditional techniques have established it as a popular method for object recognition [21,22,23,24,25,26]. Interestingly, it has demonstrated excellent performance in identifying objects with varying sizes and orientations within a scene, owing to its flexibility in handling scale and rotation adjustments [27]. Its capability to maintain a degree of invariance to illumination variations has shown enhanced results in real-world scenarios [28]. The FJTC has proven effective for near-real-time object detection [29].

Fog and haze present real-world noise that significantly degrades object recognition. Pre-processing becomes essential to refine the input scenes [30,31,32,33,34,35,36,37,38,39,40]. However, some reported methods face limitations in accurately estimating haze density, which is crucial for image de-hazing. The dark channel prior (DCP) emerges as a leading technique, which is distinguished as a fundamental method among the various architectures presently employed for scene enhancement [32,33]. By leveraging information from the dark channel, the DCP effectively removes atmospheric haze with greater accuracy and enhances visual quality compared to other approaches. Reduced processing time and lower computational demands make the DCP suitable for pre-processing in object recognition applications. Due to these unique features, the DCP is preferred over other image de-hazing techniques [39,40].

In the current technological landscape, optical correlators have earned significant popularity in object recognition [41]. However, their performance may be compromised when the input scene is captured under varying weather conditions, particularly in the presence of complex noise, which severely impacts the correlation process [42,43,44,45,46]. One of the primary challenges associated with an optical correlator is the clarity and visibility of the input scene. Pattern recognition is particularly hindered by adverse weather conditions such as fog, rain, and snow, which degrade the quality of input images. Identifying objects under such circumstances becomes significantly challenging. Attempts have been made to minimize various kinds of real-world noise from the input scene using machine learning and neural networks [47,48,49,50,51,52]. However, these approaches typically involve intensive computation, resulting in additional processing time for object detection. In our previous work, we utilized a wavelet-modulated logarithmic FJTC to perform under low to moderate levels of additive and multiplicative noise [53]. Optical pattern recognition has not yet been fully extended to this domain. Hence, there is substantial scope for advancing object recognition in real foggy or hazy environments using optical correlators.

To enhance the reliability and robustness of optical pattern recognition in real-world foggy and hazy conditions, this study combines the DCP with the FJTC. The DCP effectively mitigates fog/haze from the input scene, after which the processed scene is optically correlated with a pre-stored reference scene using the FJTC. This hybrid approach combines digital and optical techniques, presenting an innovative strategy in optical pattern recognition, addressing modern world challenges. To the best of our knowledge, no such study has used optical technology for object recognition in adverse weather conditions. Integrating digital and optical techniques can potentially address the limitations of each, leading to more robust and efficient object recognition solutions. This study introduces a unique approach that provides an alternate solution to the long-standing issue of object detection under haze/fog degradation in visual data by smoothly incorporating the DCP into the FJTC architecture. The proposed scheme significantly mitigates atmospheric obscurations. By thoroughly investigating the proposed method across various foggy conditions, including dense fog dataset, non-uniform fog dataset, and open haze dataset, we have explored the efficacy and practical utility of the proposed approach. This research would open up new possibilities for better, more reliable optical correlators that work well even in difficult weather conditions. Our approach leverages the potential of the DCP to improve image clarity and contrast and then feeds the refined images into the FJTC for accurate object identification. The proposed hybrid digital–optical correlator operates with great speed. This innovative fusion of techniques represents a significant advancement in object recognition using optical methods.

The proposed technique offers improved and precise visual information even in inclement weather conditions, potentially revolutionizing various applications such as autonomous navigation, surveillance, and environmental monitoring. To comprehensively assess the effectiveness of the suggested approach, we utilized several performance metrics, including the structural similarity index (SSIM), peak signal-to-noise ratio (PSNR), correlation peak intensity (CPI), processing time, and recognition accuracy. In this study, a deliberate effort was made to include real backgrounds with the input scenes to evaluate the FJTC’s performance under realistic conditions, ensuring our method’s practical applicability and robustness for the correlation process. Furthermore, we analyzed the processing time of the DCP to assess the efficiency of our approach, particularly its suitability for real-world applications.

2. Dark Channel Prior (DCP)

Fog and haze result from continuous scattering and absorption by tiny water droplets in the air. These conditions create a whitish region with reduced contrast, severely limiting visibility. The haze-added image can be expressed by the following equation [32,33]:

(1)$I(x)=J(x)t(x)+A\left\{1-t(x)\right\}$

Here, I(x) is the hazy/foggy image, J(x) is the haze-free image, and A is atmospheric light. t(x) denotes the transmission, which is a function of scene depth and is expressed as follows:

(2)$t(x)=e^{-\beta d(x)}$

where β is the attenuation coefficient, and d(x) is the scene depth. So, the first term of Eq. (1) is direct attenuation, whereas the second is air-light [32]. From Equation (1), the haze-free image J(x) can be restored as follows:

(3)$J(x)={\displaystyle \frac{I(x)-A}{t(x)}}+A$

For the restored image, atmospheric light (A) and transmission t(x) are needed to be calculated from I(x). Since the solution is non-trivial, some basic assumptions have been used as follows [32]:

(4)$A=\max \{I_{dark}(x)\}$

I_dark(x) is known as the dark channel, which is the minimum pixel intensity in at least one color channel out of r (red), g (green), and b (blue) in an input image. It has been observed with many datasets that these dark pixels are mostly present in outdoor images. The dark channel is calculated as follows:

(5)$J_{dark}(x)=\underset{y\in \mathrm{\Omega }(x)}{\min }\left(\underset{c\in \left\{r,g,b\right\}}{\min }{\displaystyle \frac{I^c(y)}{A^c}}\right)$

Here, I^c(y) is a color channel within the local patch around the pixel x, A^c is the normalized atmospheric light, and Ω(x) is a local window centered at x. The maximum intensity value of the dark channel is known as atmospheric light (A). From the dark channel, transmission is found as follows:

(6)$t(x)=1-w.J_{dark}(x)$

Here, w is a small constant whose value ranges from 0 to 1 [32]. Now, using Equation (3), the haze-free image J(x) can be restored using A and t(x).

3. Fringe-Adjusted JTC (FJTC)

For JTC operation, the input image and reference images are placed side by side onto a liquid crystal spatial light modulator (SLM) [11].

(7)$f\left(x,y\right)=t\left(x,y-b\right)+r\left(x,y+b\right)$

Here, t(x,y) is the input image, r(x,y) is the reference image, and f(x,y) expresses the joint image comprising both the reference and input images. The Fourier transform of the joint image is recorded on an intensity sensing device, a complementary metal–oxide semiconductor (CMOS) camera.

(8)${\left|F\left(u,v\right)\right|}^2=T^2\left(u,v\right)+R^2\left(u,v\right)+R\left(u,v\right)T^{\ast }\left(u,v\right)\exp \left(-i2ub\right)+R^{\ast }\left(u,v\right)T\left(u,v\right)\exp \left(i2vb\right)$

where F(u,v), T(u,v), and R(u,v) denote the absolute values of Fourier transforms of f(x,y), t(x,y), and r(x,y), respectively. The asterisk symbol used in the equation denotes complex conjugates. To remove the first two terms, collectively termed as the dc term, and to minimize the unwanted false alarms from the correlation output, the power spectrum subtraction method is used. The reference and target-only power spectra are subtracted from the recorded intensity [54].

(9)$G\left(u,v\right)={\left|F\left(u,v\right)\right|}^2-R^2\left(u,v\right)-T^2\left(u,v\right)$

R²(u,v) and T²(u,v) denote the power spectra corresponding to the reference scene and input scene, respectively. G(u,v) is the modified intensity. The fringe-adjusted filter (FAF) is applied to the modified intensity to make the auto-correlation outputs sharper. The FAF is defined as the inverse of the reference-only power spectrum.

(10)$FAF(u,v)={\displaystyle \frac{1}{{\left|R\left(u,v\right)\right|}^2}}$

(11)$I\left(u,v\right)=G\left(u,v\right)\times FAF(u,v)$

I(u,v) is the joint power spectrum (JPS) obtained after the multiplication of the FAF. I(u,v) undergoes inverse Fourier transformation to yield the auto-correlation peaks [11,24].

(12)$C_1\left(x,y+2b\right)=r\left(x,y\right)\otimes t^{\ast }\left(x,y\right)\otimes \delta \left(x,y+2b\right)$

(13)$C_2\left(x,y-2b\right)=r^{\ast }\left(x,y\right)\otimes t\left(x,y\right)\otimes \delta \left(x,y-2b\right)$

where $\otimes$ and * denote convolution and complex conjugates, respectively. C₁ and C₂ are the two auto-correlation peaks.

4. DCP-Based Object Recognition

Optical correlators are highly sensitive to noise. Fog and haze introduce significant noise into the input scenes, hindering the optical correlation process. A pre-processing technique can be applied to optical correlators to mitigate this issue. In this study, raw input scenes are pre-processed using the DCP method. The DCP restores haze-free images from hazy scenes using Equation (3). It involves three key factors: the dark channel, atmospheric light, and transmission. The dark channel is estimated from the input hazy scene, where dark pixels are present in any color channel within a small window or patch [32,33]. The global atmospheric light is calculated from the highest pixel intensity within that window. Transmission is determined from the dark channel using Equation (6). This information is then used to restore haze-free images from the degraded input scenes. Figure 1 illustrates a block diagram of the proposed method.

First, the input hazy/foggy image is pre-processed using the DCP method and then passed onto the SLM as the input scene, where it is placed alongside the reference image. The JPS is obtained from this joint image by taking the Fourier transform and then squaring the modulus. The JPS is then multiplied with a fringe-adjusted filter, which is simply the inverse of the reference-only power spectrum. To eliminate the zero-order dc term, the reference-only power spectrum and the input-only power spectrum are subtracted from the JPS. This Fourier plane subtraction suppresses the dc component and reduces false alarms from the correlation output. The modified JPS then undergoes an optical Fourier transform to yield the correlation output, resulting in two auto-correlation peaks for each matching.

Figure 2a presents a hazy image of a bike. Figure 2b,c show the dark channel and transmission map of Figure 2a. The global atmospheric light can be estimated by choosing a small window from the dark channel. Figure 2d presents the haze-free version of Figure 2a after applying the DCP. DCP processing restores good-quality images from degraded scenes corrupted by fog or haze. Thus, the auto-correlation process can be improved as noise is reduced, enhancing the degree of similarity. This will enhance the FJTC’s object recognition capability. Hence, DCP-based optical pattern recognition is a powerful tool that is suitable for bad weather conditions.

5. Results and Discussion

Computer simulation has been performed on the MATLAB R2022a platform. Input images with varying densities of fog and haze were processed using the DCP. These processed images were then used as inputs to the FJTC to generate correlation outputs. Both input and reference images with a size of 150 × 150 pixels were utilized to form a joint image with a size of 512 × 512 pixels. The joint image is zero-padded, as the same will be directly used onto the SLM. The Fourier plane subtraction method is employed to remove dc from the correlation output. A Fringe-adjusted filter is multiplied with the JPS before taking the inverse Fourier transformation.

The experimental set-up used to implement the FJTC with DCP processing is illustrated in Figure 3. The laser beam, emitted from a 630 nm diode laser source, is collimated by a 135 mm focal length lens. The collimated beam is guided onto a transmission-type liquid crystal SLM with dimensions of 800 × 600 pixels with a pixel size of 32 × 32 µm (Holoeye, LC-2002). After collimation, an optical Fourier transform is performed using a 135 mm Fourier transforming lens. For capturing the correlation outputs, a CMOS camera (GiGE DFK23GP031) with dimensions of 2592 × 1944 pixels with a pixel pitch of 2.2 µm is used. The hybrid digital–optical approach is used for carrying out the experiment as it has advantages like the combined effect of optical digital signal processing, faster processing, and compact size [55,56,57,58,59,60]. The conventional JTC method is a two-step process, where in the first step, the JPS is recorded, and in the second step, the recorded JPS is displayed onto the SLM to yield the final correlation output, which is recorded with a CMOS camera. The intermediate step can introduce a time delay. This delay can be minimized with the help of a hybrid digital–optical approach. A joint image is formed by taking the previously stored reference image and DCP-processed input. The JPS is obtained by taking the modulus square of the Fourier transform of the joint image. A fringe-adjusted filter is multiplied with the JPS to yield the modified JPS, which is displayed onto the SLM placed at the front focal plane of the lens. An optical inverse Fourier transform is recorded on a CMOS camera placed at the back focal length of the lens. Auto-correlation peaks with the central zero order dc are observed in the correlation plane.

The haze simulation in the study follows a physically inspired model based on atmospheric scattering and haze density, as discussed in Equation (1). Figure 4a shows the joint image of a car as a reference and an input scene with a fog density of 0.75 (the density range is on a scale from 0 to 1). Along with fog, a real background is also present in the input scene. Figure 4b shows the corresponding correlation output of Figure 4a, where auto-correlation peaks with negligible heights are observed. Figure 4c shows the joint image of the same input scene and reference image after DCP processing. Figure 4d presents the correlation output for the proposed method, which shows significant enhancement in the height of the auto-correlation peaks as compared to the result shown in Figure 4b. A slightly higher fog density of 0.85 has been added to the input scene of a bike with a complex background, as shown in Figure 4e. Figure 4f presents the correlation output where only noise and false peaks are observed. Figure 4g shows the joint image of the same bike with its input scene, which is processed with the DCP. Figure 4h presents the correlation output of Figure 4g. In Figure 5a–d, the experimental correlation outputs have been presented for images shown in Figure 4a,c,e,g, respectively.

The auto-correlation peaks for hazy inputs are so low in intensity that they are difficult to visualize, primarily due to the presence of fog in the input scene. However, with the proposed method, the intensities of the auto-correlation peaks are significantly enhanced, resulting in brighter and more visible peaks.

A haze density of 0.8 is added to the input scene of a vehicle shown in Figure 6a, and the corresponding correlation output is shown in Figure 6b. Correlation peaks with much lower heights are observed. Figure 6c shows the joint image of the same input scene with reference after DCP processing, and the correlation output is shown in Figure 6d. In Figure 6e, a car image in an input scene with a background has been added with a haze density of 0.7. Figure 6f presents the correlation output of Figure 6e. The auto-correlation peaks are observed to be very small in height. The DCP-processed input scene is presented in the joint image of Figure 6g, and the corresponding correlation output is shown in Figure 6h. The experimental correlation outputs corresponding to Figure 6a,c,e,g have been shown in Figure 7a–d, respectively. Significant enhancement in the auto-correlation peaks is observed by comparing the correlation outputs of the proposed method with the correlation outputs of conventional JTC under foggy or hazy conditions. In Figure 6a,e, both the reference and input scenes are shifted to the corners, and as a result, the auto-correlation peaks are also observed to be shifted to the corners in the correlation outputs. This implies that the amount of pixels shifted by the object in the input scene will linearly vary with the change in positions of the auto-correlation peaks. This characteristic ensures the possibility of target tracking ability under such foggy and hazy conditions using the proposed scheme.

5.1. Simulation Results with Dense Fog Images

The proposed scheme has been investigated using a dense fog dataset, where the target object is embedded with fog/haze of higher densities (may vary from 0.8 to 1 on a normalized scale) with a complex background, closely simulating real fog effects [61]. Professional haze machines have been used to produce real fog effects. These are all outdoor images designed to test the robustness of the object recognition algorithm. In Figure 8(a1–f1), joint images of different input scenes with higher fog effects have been shown. Figure 9(a1–f1) display the corresponding correlation outputs, where auto-correlation peaks are observed to be heavily suppressed. Figure 8(a2–f2) show the joint images with DCP-processed input scenes. The corresponding correlation outputs are shown in Figure 9(a2–f2), which confirm the capability of the proposed object detection scheme with enhanced auto-correlation peaks.

The experimental correlation outputs are shown in Figure 10, where Figure 10(a1–f1) show the correlation outputs of Figure 8(a1–f1) and Figure 10(a2–f2) present the correlation outputs of Figure 8(a2–f2).

5.2. Simulation Results with Non-Homogeneous Hazy Images

Object recognition under real foggy conditions is considered a challenging task. The presence of non-homogeneous fog/haze noise significantly affects the correlation process. Non-homogenous haze dataset has been used in this work to test the efficacy of the proposed method [62]. In Figure 11a–c, the joint images with non-homogeneous haze have been shown. The reference objects are located in the lower half of the joint images. Figure 12a–c show the corresponding numerical correlation outputs, where correlation peaks are very low in intensity, indicating the difficulty of object recognition under such conditions. The DCP-processed input scenes are shown in Figure 11d–f. Figure 12d–f present the corresponding correlation outputs. The experimental correlation outputs have been presented in Figure 13, where Figure 13a–c present the outputs correspond to Figure 11a–c, and Figure 13d–f show the outputs of Figure 11d–f, respectively.

The correlation outputs correspond to the DCP-processed joint images exhibit improved auto-correlation peaks compared to previous methods for non-homogeneous fog. Despite the challenges of a strong background and high noise density, the proposed scheme shows convincing correlation results.

5.3. Simulation Results with Open Haze Dataset

The proposed scheme has also been evaluated with the open haze dataset (O-haze) [63]. This database contains images captured under real haze conditions, created with professional haze machines. In Figure 14, input scenes with O-haze dataset are presented. In Figure 14a–f, the joint images of the hazy input scenes with the reference image are presented. Figure 15a–f represent the joint images after DCP processing. Figure 16(a1–f1) are the correlation outputs of the joint images of Figure 14. Figure 16(a2–f2) represent the correlation outputs corresponding to the joint images shown in Figure 15. From the simulation results, it is evident that the auto-correlation peaks are obscured by background noise, and several false alarms appear in the correlation output. This occurs because the height of the auto-correlation peaks decreases as the dissimilarity between the input and reference images increases. This dissimilarity is primarily caused by the presence of fog or haze in the input scene, which acts as noise and significantly impacts the correlation process.

The experimental correlation outputs for the open haze dataset have been shown in Figure 17. The FJTC outputs for the joint images affected by haze effects have been presented in Figure 17(a1–a6). Auto-correlation peaks with negligible intensities are observed. For a few of them, auto-correlation peaks are not visually observed in the correlation plane. This is due to the dissimilarity introduced into the correlation process by the presence of fog/haze in the input scene. The DCP-processed joint images can hugely enhance the auto-correlation peak intensity by improving the similarity between the input and the reference scenes. The experimental correlation outputs corresponding to the DCP-processed joint images have been shown in Figure 17(b1–b6). Very intense and sharp auto-correlation peaks are observed for the processed input images. Object recognition is severely challenged under such environmental conditions. However, by mitigating noise through the application of DCP on the input scene, similarity is enhanced, thereby increasing the intensity of auto-correlation peaks. The proposed scheme indicates a significant improvement in auto-correlation peak sharpness and intensity following DCP processing.

6. Performance Analysis

To quantify the efficiency of the proposed method, the findings have been analyzed using performance measure parameters like the SSIM, PSNR, and CPI [64,65]. The SSIM tells us about the similarity between two images, whereas the PSNR gives the relationship between the original image, which represents the maximum power of the signal and the noise power, which is determined by the difference between the original and processed images.

(14)$SSIM={\displaystyle \frac{(2{\mu }_x{\mu }_y+K_1)(2{\sigma }_{x,y}+K_2)}{({\mu }_x^2+{\mu }_y^2+K_1)({\sigma }_x^2+{\sigma }_y^2+K_2)}}$

where ${\mu }_x$ and ${\mu }_y$ are the pixel sample of x and y, ${\mu }_x^2$ and ${\mu }_y^2$ are the variance of x and y, and ‘${\mu }_{x,y}$’ is the covariance of x and y. K₁ and K₂ are two small constants.

(15)$PSNR=10\times {\log }_{10}\left[{\displaystyle \frac{Max I^2}{MSE}}\right]$

where ‘×’ denotes multiplication, Max(I) is the maximum pixel value of the original image, and MSE stands for mean square error. The CPI is the highest auto-correlation peak value in the correlation output.

(16)$CPI=\max \left(correlation\_plane\right)$

The calculated performance measure parameters are shown in Table 1 and Table 2. Table 1 contains both the SSIM and PSNR. The CPI values are shown in Table 2. The data presented in the respective tables show the strength of the DCP-based FJTC for noisy object recognition.

The measurement parameters have been calculated for all datasets used in this study, and the statistical distributions of the SSIM and PSNR are shown through box plots and histograms. Figure 18, Figure 19 and Figure 20 display the SSIM and PSNR using box plots, where noticeable improvements are observed in both metrics for the proposed method. Additionally, Figure 21 presents the average values of these metrics across all datasets. The SSIM increased by 0.23, 0.35, and 0.41 for dense fog, non-homogeneous haze, and open haze inputs, respectively. Similarly, the PSNR increased by 4.73 dB, 6.1 dB, and 7.95 dB for the corresponding datasets.

The CPI is a key figure of merit in optical pattern recognition, as it contains all the relevant information. The proposed scheme has been applied to all the dataset images, and the results are shown in Figure 22, Figure 23 and Figure 24. The blue curve represents CPI values for hazy/foggy inputs, while the red curve shows CPI values for DCP-processed inputs. Across all datasets, the proposed method demonstrates a significant improvement in CPI. A higher CPI indicates stronger correlation peaks, leading to more accurate object recognition, enhancing system performance, and improving overall recognition accuracy under adverse weather conditions.

Processing time is crucial for object recognition. In the proposed method, the DCP is a pre-processing step, necessitating fast execution for real-world applications. Processing time depends on various factors like image resolution, scene complexity, algorithm implementation, computing hardware, and optimization techniques. We have utilized datasets of different resolutions with different fog/haze intensities, ranging from low to high. The numerical simulation has been conducted using MATLAB R2022a with 16 GB of RAM and an Intel-core i5 CPU, resulting in a range of observed processing times. The maximum observed time is 0.35 s, while all others are within 0.30 s. Details are presented in Table 3. The average DCP processing times for all the datasets are shown in Figure 25. It is observed that dense fog dataset takes 0.29 s, non-homogeneous haze dataset takes 0.27 s, and open haze dataset takes 0.20 s, on average, for DCP processing.

In this research, the proposed scheme has been evaluated using three different datasets. A dense fog dataset has been employed to assess the method’s performance under extreme environmental conditions. Recognition accuracy has been presented in Table 4. A recognition accuracy of 96% has been achieved with the dense fog dataset. A non-homogeneous haze dataset has been used to evaluate the strength and robustness of the proposed method against real-life fog/haze effects. The proposed scheme has shown 94% accuracy for non-uniform foggy environments. Additionally, the scheme has been tested with an open haze dataset created using professional haze machines to mimic real-world haze effects. The proposed method has witnessed 98% recognition accuracy. Recognition accuracy can be further improved by addressing the influence of strong backgrounds in the input scene, which affects the correlation process. These results underscore the potential of integrating the DCP with the FJTC to enhance the reliability and accuracy of optical correlators in real-world applications.

Optical pattern recognition and digital object recognition methods, such as machine learning, convolutional neural networks (CNNs), single-shot multi-box detectors (SSDs), and YOLO, operate on fundamentally different principles [1,66]. Both techniques are relevant in their respective domains. Digital methods rely on fully computational models trained on large datasets to learn and recognize features. In contrast, optical methods work on the principles of the Fourier transforming property of a lens and the convolution theorem. Although digital object recognition methods have many applications across various fields, they still suffer from processing speed regarding frames per second (FPS) and recognition accuracy with very small object detection in real-time applications [66]. Optical correlators are relaxed from such constraints as they use optical systems like SLMs, which can be operated in real time. The LC-2002 SLM has been used in this study offers 60Hz FPS, which is challenging for digital methods to match [66]. The FPS can be further enhanced in optical methods by using binary SLMs, which are commercially available.

7. Conclusions

In this study, we have introduced a new and effective object recognition model for foggy and hazy environments. We enhanced input scene clarity and quality by integrating the DCP in the pre-processing stage of optical correlation. The refined images are then processed using the FJTC. Both simulation and experiment validate the algorithm’s robust performance in adverse weather conditions. We evaluated the method using dense fog, non-uniform fog, open haze datasets, and scenarios with strong backgrounds to assess its detection capabilities. The proposed scheme has shown excellent performance under these adverse conditions. Significant enhancement of the performance metrics ensures the strong credibility of the proposed algorithm. This research can potentially be used in practical applications like object detection in mountains, autonomous vehicles, airplane lane detection, navigation, and video surveillance. Our future endeavor will be to develop optical correlators tailored for diverse applications.

Author Contributions

Conceptualization, N.K.N.; methodology, J.B.M.; validation, J.B.M., J.M. and N.K.N.; formal analysis, N.K.N. and J.M.; investigation, J.B.M.; resources, N.K.N.; data curation, J.B.M.; writing—original draft preparation, J.B.M.; writing—review and editing, N.K.N. and J.M.; visualization, J.B.M.; supervision, N.K.N.; project administration, N.K.N. and J.M.; All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Acknowledgments

The authors acknowledge the technical discussions held with Rahul Kumar and Akash Pal.

Conflicts of Interest

The authors declare no conflicts of interest related to this study.

Footnotes

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Figures and Tables

Figure 1. Block diagram of DCP-based object detection algorithm.

Figure 2. (a) Hazy image of a bike, (b) dark channel image of (a), (c) transmission map of (a), and (d) restored image after DCP.

Figure 3. Block diagram of experimental demonstration of DCP-based object recognition.

Figure 4. Joint images: (a) input image Car 1 with fog density 0.75 and reference image Car 1, (c) de-hazed scene of Figure 4a, (e) input scene (bike) with fog density 0.85 with bike as reference, and (g) de-hazed input after DCP for Figure 4e. Correlation outputs: (b) for Figure 4a, (d) for Figure 4c, (f) for Figure 4e, and (h) for Figure 4g.

Figure 5. Experimental results: (a–d) correlation outputs of Figure 4a,c,e,g, respectively.

Figure 6. Joint images: (a) vehicle as input with haze density 0.8 with reference vehicle, (c) de-hazed scene of Figure 6a, (e) input scene (Car 2) with haze density 0.7 with Car 2, and (g) de-hazed input after DCP. Correlation output: (b) of Figure 6a, (d) of Figure 6c, (f) of Figure 6e, and (h) of Figure 6g.

Figure 7. Experimental results: (a–d) correlation outputs of Figure 6a,c,e,g, respectively.

Figure 8. Joint images with dense fog inputs: (a1–f1). Joint images with DCP-processed inputs: (a2–f2).

Figure 9. Numerically simulated correlation outputs; (a1–f1) correspond to Figure 8(a1–f1), and (a2–f2) correspond to Figure 8(a2–f2).

Figure 10. Numerical correlation outputs: (a1–f1) for Figure 8(a1–f1), (a2–f2) for Figure 8(a2–f2).

Figure 11. Joint images with non-homogeneous hazy inputs: (a–c). Joint images with DCP-processed inputs: (d–f).

Figure 12. Numerical correlation outputs: (a–c). Numerical correlation outputs with DCP-processed inputs: (d–f).

Figure 13. Experimental results: (a–c) correlation outputs for non-homogeneous hazy inputs; (d–f) correlation outputs for DCP-processed images.

Figure 14. Joint images with open hazy inputs: (a–f).

Figure 15. Joint images after DCP-processed inputs: (a–f).

Figure 16. Numerical correlation outputs: (a1–f1) for open haze inputs; (a2–f2) for DCP-processed inputs.

Figure 17. Experimental results. First row (a1–a6): correlation outputs of Figure 14a–f; second row (b1–b6): correlation outputs of Figure 15a–f.

Figure 18. Boxplot distributions of (a) SSIM and (b) PSNR for dense fog inputs and de-hazed inputs.

Figure 19. Boxplot distributions of (a) SSIM and (b) PSNR for non-homogeneous hazy inputs and de-hazed inputs.

Figure 20. Boxplot distributions of (a) SSIM and (b) PSNR for open haze inputs and de-hazed inputs.

Figure 21. (a) Mean SSIM for all the datasets and (b) mean PSNR for all the datasets.

Figure 22. CPI plot for dense fog inputs and de-hazed inputs.

Figure 23. CPI plot for non-homogeneous hazy inputs and de-hazed inputs.

Figure 24. CPI plot for open haze inputs and de-hazed inputs.

Figure 25. Mean processing time of DCP for all datasets.

Table 1

Calculation of SSIM and PSNR for different joint images.

Joint Images	SSIMwith Fog	SSIMwith DCP	PSNRwith Fog	PSNRwith DCP
Input Car 1 vs. reference Car 1	0.55	0.76	7.03	12.36
Input Bike vs. reference Bike	0.58	0.80	7.70	18.69
Input Vehicle 1 vs. reference Vehicle 1	0.27	0.78	4.74	18.31
Input Car 2 vs. reference Car 2	0.20	0.82	4.82	15.73
Figure 8(a1,a2)	0.36	0.58	8.48	15.09
Figure 8(b1,b2)	0.34	0.59	7.20	16.35
Figure 8(c1,c2)	0.30	0.63	5.61	15.55
Figure 8(d1,d2)	0.22	0.52	8.36	12.86
Figure 8(e1,e2)	0.48	0.69	9.61	13.36
Figure 8(f1,f2)	0.31	0.58	7.44	11.91
Figure 11a–d	0.18	0.48	3.74	10.02
Figure 11b–e	0.34	0.59	6.32	11.97
Figure 11c–f	0.27	0.57	5.94	14.61
Figure 14a vs. Figure 15a	0.31	0.75	8.12	15.41
Figure 14b vs. Figure 15b	0.34	0.85	7.68	17.76
Figure 14c vs. Figure 15c	0.24	0.64	3.28	11.32
Figure 14d vs. Figure 15d	0.35	0.85	7.63	19.21
Figure 14e vs. Figure 15e	0.28	0.80	7.40	16.29
Figure 14f vs. Figure 15f	0.31	0.83	9.77	18.72

Table 2

Calculation of CPI for different joint images.

Joint Images	CPIwith Fog	CPIwith DCP
Input Car 1 vs. reference Car 1	0.15	0.40
Input Bike vs. reference Bike	0.27	0.51
Input Vehicle 1 vs. reference Vehicle 1	0.09	0.33
Input Car 2 vs. reference Car 2	0.08	0.50
Figure 8(a1,a2)	0.05	0.31
Figure 8(b1,b2)	0.18	0.51
Figure 8(c1,c2)	0.15	0.71
Figure 8(d1,d2)	0.14	0.38
Figure 8(e1,e2)	0.05	0.72
Figure 8(f1,f2)	0.25	0.68
Figure 11a–d	0.17	0.52
Figure 11b–e	0.19	0.59
Figure 11c–f	0.18	0.55
Figure 14a vs. Figure 15a	0.19	0.68
Figure 14b vs. Figure 15b	0.28	0.73
Figure 14c vs. Figure 15c	0.17	0.74
Figure 14d vs. Figure 15d	0.16	0.74
Figure 14e vs. Figure 15e	0.22	0.84
Figure 14f vs. Figure 15f	0.19	0.62

Table 3

DCP processing time.

Foggy Images	Processing Time
Car 1	0.20 s
Bike	0.21 s
Vehicle 1	0.21 s
Car 2	0.19 s
Figure 8(a1)	0.28 s
Figure 8(b1)	0.30 s
Figure 8(c1)	0.28 s
Figure 8(d1)	0.29 s
Figure 8(e1)	0.29 s
Figure 8(f1)	0.29 s
Figure 11(a)	0.19 s
Figure 11(b)	0.35 s
Figure 11(c)	0.19 s
Figure 14(a)	0.16 s
Figure 14(b)	0.13 s
Figure 14(c)	0.21 s
Figure 14(d)	0.15 s
Figure 14(e)	0.15 s
Figure 14(f)	0.19 s

Table 4

Recognition accuracy.

Datasets	Accuracy
Dense fog dataset	96.00%
Non-homogeneous dataset	94.50%
Open haze dataset	98.00%

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