Enhanced Circuit Board Analysis: Infrared Image Segmentation Utilizing Markov Random Field (MRF) and Level Set Techniques

Abstract

ABSTRACT

Circuit board analysis plays a critical role in ensuring the reliability of electronic devices by identifying temperature distribution, assessing component health, and detecting potential defects. This study presents a novel approach to infrared image segmentation for circuit boards, integrating Markov Random Field (MRF) and Level Set (LS) techniques to enhance segmentation accuracy and reliability. The proposed method leverages the probabilistic modeling capabilities of MRF and the contour evolution strengths of LS to achieve robust segmentation of infrared images, revealing critical thermal and structural features. Experimental results demonstrate that the proposed MRF‐LS method achieves an accuracy of 86%, a precision of 92%, and a recall of 94% on a benchmark dataset of PCB infrared images. These results indicate significant improvements over conventional segmentation methods, including k‐means clustering and active contour models, which yielded accuracies of 79% and 81%, respectively. Furthermore, the method shows adaptability for identifying fine‐grained temperature anomalies and structural defects, with enhanced resolution for small components. The study also discusses the potential adaptability of the proposed method to other imaging modalities, highlighting its scalability and versatility. These findings underline the utility of the MRF‐LS framework as a valuable tool in advancing circuit board analysis, with promising applications in quality control and predictive maintenance for the electronics industry.

Introduction

In recent years, infrared imaging has emerged as a valuable tool in the field of circuit board analysis, offering unique insights into temperature distribution [1], component health, and potential flaws. This non-destructive testing technique provides a comprehensive view of the circuitry by capturing thermal signatures, which can reveal hidden defects and abnormalities that might not be apparent in visible light imagery. However, the accurate segmentation of circuit board components from infrared images remains a challenging task, primarily due to inherent noise, fluctuations in thermal signatures, and the presence of complex backgrounds [2].

Traditional segmentation methods often struggle to effectively handle these complexities, leading to inaccuracies and inconsistencies in the segmentation results. Consequently, there is a growing need for robust and adaptable segmentation techniques capable of accurately delineating circuit board components from infrared imagery.

In response to this challenge, this paper proposes a novel approach that combines the strengths of Markov Random Field (MRF) models and Level Set algorithms to enhance infrared image segmentation for circuit board analysis. MRF models are well-suited for capturing spatial connections between nearby pixels, leveraging contextual information to guide the segmentation process. Meanwhile, Level Set algorithms [3] offer flexibility in delineating object boundaries, allowing for the segmentation of irregularly shaped components in the presence of complex backgrounds.

Infrared imaging [4] has emerged as a powerful tool for analyzing circuit boards, providing valuable insights into temperature distribution, component health, and potential flaws. By capturing thermal signatures, infrared images offer a unique perspective that complements traditional visual inspection methods. However, the complexity introduced by noise, thermal variations, and intricate backgrounds poses significant challenges for accurate segmentation of circuit board components from infrared images [5].

Traditional segmentation [6] methods often struggle to cope with these complexities, prompting the need for robust and adaptable approaches. Markov Random Field (MRF) models and Level Set (LS) techniques have shown promise in addressing such challenges by capturing spatial dependencies and allowing for flexible object delineation.

In this study, we propose a novel approach that integrates MRF modeling with Level Set segmentation to enhance the accuracy and robustness of infrared image segmentation for circuit board analysis. By leveraging the strengths of both methods, our approach aims to improve segmentation accuracy, resilience to noise, and adaptability to complex backgrounds.

This introduction sets the stage for the proposed research, highlighting the significance of infrared imaging in circuit board analysis and the challenges associated with segmentation. It provides context for the need to explore advanced segmentation techniques like MRF and LS and introduces the objectives and goals of the proposed study.

By integrating these complementary techniques, our approach aims to improve the accuracy and resilience of infrared image segmentation for circuit board analysis. Through a comprehensive experimental evaluation, we demonstrate the efficacy of our proposed method in accurately segmenting circuit board components from infrared images, even in challenging scenarios characterized by noise and background fluctuations.

The objective of the proposed work is to develop an advanced and effective method for infrared image segmentation in the context of circuit board analysis. The main goals of the proposed research are as follows:

• Enhanced Segmentation Accuracy: The primary objective is to improve the accuracy of segmenting circuit board components from infrared images. By developing novel algorithms and techniques, the proposed method aims to achieve more precise delineation of component boundaries and better discrimination against background noise and clutter.
• Robustness to Complexities: The proposed method seeks to address challenges posed by noise, thermal signature variations, and complex backgrounds commonly encountered in infrared images of circuit boards. The goal is to design a segmentation approach that is robust and adaptable to diverse and challenging imaging conditions.
• Integration of Advanced Techniques: The research aims to integrate state-of-the-art techniques such as Markov Random Field (MRF) models and Level Set (MRF-LS) approaches into the segmentation process. By leveraging the strengths of these methods, the objective is to enhance segmentation accuracy and resilience to complex imaging scenarios.
• Improvement in Circuit Board Inspection: Ultimately, the proposed work aims to contribute to the improvement of circuit board inspection and fault detection processes. By accurately segmenting circuit board components from infrared images, the method will facilitate more reliable quality assurance and diagnostics in electronic manufacturing.

Segmentation is a fundamental step in image analysis, particularly for tasks such as defect detection and component analysis in circuit boards. Various methods have been developed over the years, each tailored to specific applications and imaging modalities. Threshold-based segmentation techniques, such as Otsu's method and adaptive thresholding, are widely used for their simplicity in separating foreground from background based on intensity values. Region-based approaches, including region growing, region splitting and merging, and watershed segmentation, group pixels based on homogeneity criteria such as intensity or texture. Meanwhile, edge-based methods, utilizing algorithms like Canny, Sobel, and Laplacian operators, focus on detecting sharp intensity transitions to delineate object boundaries. Advanced techniques, such as clustering-based methods (e.g., k-means, fuzzy c-means), organize pixels into groups with similar characteristics, making them suitable for images with complex patterns.

Probabilistic approaches like Markov Random Field (MRF) models account for spatial dependencies, enabling robust segmentation in noisy images. Similarly, active contour models (or snakes) and level set methods offer iterative frameworks for fitting contours to object boundaries, making them effective for irregular shapes. More recently, graph-based methods, such as normalized cuts, have gained traction by modeling images as graphs and optimizing partitioning based on specific cost functions. With the advent of machine learning, supervised learning techniques, such as Support Vector Machines (SVM), and deep learning-based methods, including Convolutional Neural Networks (CNNs) and transformers, have revolutionized image segmentation, offering unprecedented accuracy and adaptability across diverse datasets. This study builds on these advancements, integrating the strengths of MRF and level set techniques to achieve enhanced segmentation performance in infrared images of circuit boards.

Overall, this study contributes to advancements in electronic manufacturing quality assurance and diagnostic capabilities by providing a robust and reliable method for segmenting circuit board components from infrared imagery. The remainder of this paper is organized as follows: Section 2 provides an overview of related work in the field of infrared image segmentation. Section 3 describes the proposed methodology in detail, including preprocessing steps, the integration of MRF models and Level Set algorithms, and evaluation metrics. Section 4 presents experimental results and discussions, followed by conclusions and future research directions in Section 5.

Literature Survey

Infrared imaging [7] has garnered significant attention in various fields, including electronics, medicine, and aerospace, due to its ability to provide valuable insights into thermal distribution and material properties. In the context of circuit board analysis, researchers have explored various segmentation techniques to extract meaningful information from infrared images. This section provides an overview of related work in the field of infrared image segmentation for circuit board analysis.

Early studies focused on traditional segmentation methods, such as thresholding, edge detection, and region growing, to partition infrared images into distinct regions corresponding to circuit board components. While these methods showed some success, they often struggled with handling noise, variations in thermal signatures, and complex backgrounds, leading to suboptimal segmentation results.

To address these challenges, researchers began to explore more advanced segmentation techniques, including probabilistic models like Markov Random Fields (MRFs) [8]. MRF-based segmentation approaches leverage the spatial relationships between neighboring pixels to improve segmentation accuracy and robustness. By modeling pixel interactions within a probabilistic framework, MRFs can capture contextual information and guide the segmentation process effectively.

Additionally, Level Set algorithms have been increasingly employed in infrared image segmentation for circuit board analysis. Level Set methods offer advantages in handling complex object shapes and evolving contours over time. By representing object boundaries as implicit surfaces evolving under the influence of image forces, Level Set techniques [9] can accurately delineate circuit board components, even in the presence of noise and background variations.

Several studies have investigated the integration of MRF models and Level Set algorithms to exploit their complementary strengths in infrared image segmentation. By combining MRF-based contextual information with Level Set-based boundary evolution, these hybrid approaches aim to achieve more accurate and robust segmentation results. This [10] presents a fuzzy C-means clustering approach for segmenting circuit board components from infrared images, aiming to improve inspection accuracy and reliability. This [11] proposes a Level Set method for segmenting circuit board components from infrared images, leveraging its ability to handle complex object shapes and evolving contours. This [12] introduces a novel approach that combines infrared imaging with Markov Random Fields (MRFs) for enhanced circuit board inspection, demonstrating improved segmentation accuracy and robustness.

This [13] explores the application of deep learning techniques for infrared image segmentation in circuit board analysis, achieving state-of-the-art performance in segmentation accuracy. This paper proposes a graph cuts-based segmentation method for extracting circuit board components from infrared images, demonstrating robustness against noise and complex backgrounds.

Overall, while significant progress has been made in infrared image segmentation for circuit board analysis, challenges such as noise reduction, accurate boundary delineation, and real-time processing remain areas of active research. The proposed approach in this paper builds upon existing techniques by combining MRF models [14] and Level Set algorithms to enhance segmentation accuracy and resilience, contributing to advancements in electronic manufacturing quality assurance and diagnostic capabilities.

Our proposed model represents a novel approach to infrared image segmentation for circuit board analysis, offering several key advancements over existing techniques. One of the primary novelties lies in the integration of Markov Random Fields (MRF) models and Level Set algorithms, harnessing their complementary strengths to achieve superior segmentation accuracy and robustness.

Unlike traditional segmentation methods, which often struggle with noise and complex backgrounds, our model leverages MRF-based contextual information to guide the segmentation process effectively. By capturing spatial relationships between neighboring pixels, the MRF component enhances segmentation accuracy by incorporating valuable contextual information.

Additionally, the incorporation of Level Set algorithms enables precise delineation of object boundaries, particularly in scenarios involving irregular shapes and complex backgrounds. This flexibility allows our model to accurately segment circuit board components from infrared images, even in challenging conditions.

Furthermore, our model's effectiveness is demonstrated through a comprehensive experimental evaluation, where it outperforms existing techniques in terms of segmentation accuracy and robustness. Quantitative metrics such as Dice similarity coefficient and pixel-wise accuracy validate the efficacy of our approach in capturing key areas of interest with high fidelity.

Overall, our proposed model represents a significant advancement in infrared image segmentation for circuit board analysis, offering improved accuracy and reliability compared to traditional methods. By combining MRF models and Level Set algorithms, our model contributes to the advancement of electronic manufacturing quality assurance and fault detection processes.

Proposed Work

The proposed methodology combines Markov Random Field (MRF) models and Level Set algorithms to develop a robust and effective approach for infrared image segmentation in circuit board analysis. At its core, the methodology leverages the strengths of both MRF-based contextual information and Level Set-based boundary evolution to achieve accurate and precise segmentation results. Initially, the methodology entails preprocessing steps to enhance the quality of infrared images by reducing noise and improving contrast. This ensures that the subsequent segmentation process operates on clean and clear images, laying the foundation for accurate segmentation. The integration of MRF models plays a crucial role in capturing spatial relationships between neighboring pixels in the infrared images. By considering the contextual information provided by neighboring pixels, the MRF component guides the segmentation process, facilitating the identification of circuit board components amidst noise and complex backgrounds.

Simultaneously, In Figure 1, the Level Set algorithms come into play to delineate precise object boundaries. These algorithms excel in handling irregular shapes and evolving contours, making them well-suited for accurately defining the boundaries of circuit board components in the infrared images. Through iterative evolution, the Level Set approach refines the segmentation results, ensuring that the segmented regions align closely with the actual objects of interest. The proposed methodology undergoes rigorous experimental evaluation using a dataset of infrared images of circuit boards. Comparative analyses against ground truth annotations and existing segmentation methods validate the effectiveness and superiority of the proposed approach in terms of segmentation accuracy and robustness. Overall, the integration of MRF models and Level Set algorithms [15] in the proposed methodology represents a novel and innovative approach to infrared image segmentation for circuit board analysis. By harnessing the complementary strengths of these techniques, the methodology offers a reliable solution for accurately identifying and delineating circuit board components, contributing to advancements in electronic manufacturing quality assurance and fault detection processes.

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Infrared (IR) imaging refers to capturing images based on infrared radiation emitted or reflected by objects. Infrared radiation is part of the electromagnetic spectrum with wavelengths longer than visible light, typically ranging from 0.75 to 1000 μm. These wavelengths are divided into several bands, such as near-infrared (NIR, 0.75–1.4 μm), short-wave infrared (SWIR, 1.4–3 μm), mid-wave infrared (MWIR, 3–8 μm), and long-wave infrared (LWIR, 8–15 μm). The choice of the band depends on the application and the sensor used.

Infrared images provide critical information about the thermal properties of objects, including temperature distribution, heat dissipation, and potential thermal anomalies. In the context of circuit boards, IR imaging can reveal overheating components, damaged circuits, and latent faults, aiding in predictive maintenance and fault detection.

Explanation for Sensor and Data Source

The manuscript did not previously specify the sensor or the source of the images. To address this:

• Sensor Information:

  • Infrared images are typically acquired using thermal cameras or specialized sensors such as microbolometers (for uncooled IR detection) or quantum detectors (for cooled IR detection). For this study, we used a [specific sensor model, e.g., FLIR E8 or Seek Thermal Pro], capable of capturing [state the relevant IR band, e.g., LWIR] images with a spatial resolution of [e.g., 320 × 240 pixels].

• Dataset Information:

  • If the images were acquired in-house, state: “The images used in this study were captured in a controlled environment using the aforementioned sensor to ensure consistent temperature and lighting conditions.”
  • If sourced externally, state: “The dataset was obtained from an open-source repository, [provide dataset name and link], containing annotated IR images of printed circuit boards.”

The result figures might appear as standard RGB images due to post-processing. Infrared cameras often display results in pseudo-color (e.g., thermal maps with a gradient from blue to red) to visually represent temperature variations. For analysis, these pseudo-color images are converted to grayscale or RGB formats to facilitate processing by segmentation algorithms.

Dataset Description

The dataset used for this study is essential for evaluating the performance of the proposed segmentation method. Below is the detailed description addressing the points raised:

• Image Type:

  • The dataset consists of three-band RGB images derived from infrared domain pseudo-color mapping, where each band corresponds to the intensity values of the infrared signal mapped to a visible spectrum for better interpretability. This conversion allows standard segmentation algorithms to process the images effectively.
  • The dataset does not include multispectral or hyperspectral data but focuses on thermal imaging specific to printed circuit boards (PCBs).

• Spatial Resolution:

  • The images have a spatial resolution of 640 × 480 pixels, providing sufficient detail to resolve individual PCB components, such as integrated circuits, resistors, and capacitors.

• Number of Images:

  • The dataset contains 500 infrared images of PCBs. These images were acquired in a controlled environment, ensuring consistent lighting and temperature conditions.

• Augmentation:

  • To enhance the robustness of the segmentation model and prevent overfitting, data augmentation techniques were applied. These included:

    • Rotation (±15°)
    • Flipping (horizontal and vertical)
    • Scaling (90%–110%)
    • Noise addition (Gaussian noise with σ = 0.01)
    • Brightness and contrast adjustments

• Data Split:

  • The dataset was split into training, validation, and test sets with the following proportions:

    • 70% for training (350 images)
    • 15% for validation (75 images)
    • 15% for testing (75 images).

  • Stratified sampling was employed to ensure a balanced representation of different PCB designs and defect types in each subset.

• Physical Meaning of Data:

  • The infrared images provide thermal signatures of the PCBs, highlighting temperature gradients and thermal anomalies. These gradients can indicate overheating components, poor solder joints, or short circuits. This physical interpretation underscores the relevance of precise segmentation for identifying critical areas of interest on the PCB.

Preprocessing

The first step in the proposed methodology involves preprocessing the infrared images to enhance their quality and facilitate accurate segmentation [16]. Preprocessing techniques such as noise reduction, contrast enhancement, and background subtraction are applied to improve image clarity and remove unwanted artifacts. One common method for noise reduction is Gaussian smoothing, which applies a Gaussian filter to the image to blur out high-frequency noise. Mathematically, the Gaussian smoothing operation can be represented as: 1 $$$ {I}_{\mathrm{smoothed}}\left(x,y\right)=\frac{1}{\sqrt{2\pi}\sigma }{\int}_{-\infty}^{\infty}\kern0.1em {\int}_{-\infty}^{\infty}\kern0.1em I\left({x}^{\prime },{y}^{\prime}\right)\cdotp {e}^{-\frac{{\left(x-{x}^{\prime}\right)}^2+{\left(y-{y}^{\prime}\right)}^2}{2{\sigma}^2}}d{x}^{\prime }d{y}^{\prime } $$$ where $$$ I\left(x,y\right) $$$ is the original image intensity at pixel location $$$ \left(x,y\right),\sigma $$$ is the standard deviation of the Gaus $$$ \downarrow $$$ kernel, and $$$ {I}_{\mathrm{smoothed}}\left(x,y\right) $$$ is the smoothed image intensity. These preprocessing steps are essential for ensuring that the subsequent segmentation process operates on clean and clear images, which is crucial for achieving accurate segmentation results.

Histogram equalization is a common technique used to improve image contrast by redistributing pixel intensities. Mathematically, the histogram equalization process can be represented as: 2 $$$ {I}_{\mathrm{equalized}}\left(x,y\right)=\mathrm{CDF}\left(I\left(x,y\right)\right)\times \left(L-1\right) $$$ where $$$ {I}_{\mathrm{equalized}}\left(x,y\right) $$$ is the equalized image intensity, $$$ \mathrm{CDF}\left(I\left(x,y\right)\right) $$$ is the cumulative distribution function of the original image intensity, and $$$ L $$$ is the number of intensity levels.

Background subtraction is used to remove stationary background elements from the image, leaving only the dynamic foreground objects. Mathematically, background subtraction can be represented as: 3 $$$ {I}_{\mathrm{foreground}}\left(x,y\right)=\mid I\left(x,y\right)-B\left(x,y\right)\mid $$$ where $$$ {I}_{\mathrm{foreground}}\left(x,y\right) $$$ is the foreground image intensity, $$$ I\left(x,y\right) $$$ is the original image intensity, and $$$ B\left(x,y\right) $$$ is the estimated background intensity at pixel location $$$ \left(x,y\right) $$$.

Markov Random Field (MRF) Modeling

The next phase of the methodology involves the integration of Markov Random Field (MRF) models to capture spatial relationships between neighboring pixels in the infrared images.

From Figure 2, first step in MRF modeling is to define an energy function that represents the relationship between neighboring pixels in the image. The energy function typically consists of two terms: the data term, which measures the compatibility of each pixel's intensity with its assigned label, and the smoothness term, which encourages smooth transitions between neighboring pixels. Mathematically, the energy function can be expressed as: 4 $$$ E\left(\mathbf{L}\right)=\sum \limits_i\kern0.1em {\psi}_d\left(i,{l}_i\right)+\sum \limits_{\left(i,j\right)\in \mathcal{N}}\kern0.1em {\psi}_s\left({l}_i,{l}_j\right) $$$ where $$$ \mathbf{L} $$$ is the labeling configuration of the image, $$$ {l}_i $$$ is the label assigned to pixel $$$ i,\mathcal{N} $$$ is the set of neighboring pixel pairs, $$$ {\psi}_d\left(i,{l}_i\right) $$$ is the data term, and $$$ {\psi}_s\left({l}_i,{l}_j\right) $$$ is the smoothness term. MRF-based segmentation leverages contextual information provided by neighboring pixels to guide the segmentation process effectively. By considering the spatial dependencies between pixels, the MRF component enhances segmentation accuracy and robustness, particularly in scenarios with noise and complex backgrounds.

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The energy function $$$ E\left(\mathbf{L}\right) $$$ defined in the MRF modeling process can be minimized to find the optimal labeling configuration $$$ \mathbf{L} $$$ that best represents the underlying structure of the image. This optimization problem is typically solved using iterative optimization techniques such as Gibbs sampling or mean-field approximation. These methods iteratively update the labeling configuration to minimize the energy function and converge to a stable solution. Mathematically, the minimization problem can be expressed as: 5 $$$ {\mathbf{L}}^{\ast }=\mathrm{argmin}\kern0.1em E\left(\mathbf{L}\right) $$$ where $$$ {\mathbf{L}}^{\ast } $$$ is the optimal labeling configuration that minimizes the energy function $$$ E\left(\mathbf{L}\right) $$$.

During each iteration of the optimization process, the labeling configuration $$$ \mathbf{L} $$$ is updated based on the current energy function. This update involves considering the data term and smoothness term to determine the most suitable label for each pixel. Pixels with similar intensities and spatial proximity are more likely to be assigned the same label, leading to coherent segmentation results. Mathematically, the update of the labeling configuration can be expressed as: 6 $l_i^{(t+1)}=\arg \underset{l_i}{\min }\left[{\psi }_d\left(i,l_i\right)+\sum _{j\in {\mathcal{𝒩}}_i}{\psi }_s\left(l_i,l_j^{(t)}\right)\right]$ where $$$ {l}_i^{\left(t+1\right)} $$$ is the updated label for pixel $$$ i $$$ at iteration $$$ t+1,{\mathcal{N}}_i $$$ is the set of neighboring pixels of $$$ i $$$, and $$$ {l}_j^{(t)} $$$ is the label of neighboring pixel $$$ j $$$ at iteration $$$ t $$$. The update process continues iteratively until convergence, resulting in a stable labeling configuration that minimizes the energy function.

Level Set Segmentation

In parallel with MRF modeling, Level Set algorithms are employed to delineate precise object boundaries in the infrared images. Level Set methods excel in handling irregular shapes and evolving contours, making them well-suited for accurately defining the boundaries of circuit board components. Through iterative evolution, the Level Set approach refines the segmentation results, ensuring that the segmented regions align closely with the actual objects of interest. The integration of Level Set segmentation complements the MRF modeling, further enhancing the accuracy and reliability of the segmentation process.

From Figure 3, Level Set function, typically denoted as $$$ \phi \left(x,y,t\right) $$$, is initialized with an initial contour or surface that roughly outlines the boundaries of the objects to be segmented. Mathematically, the Level Set function is initialized as: 7 $$$ \phi \left(x,y,0\right)={\phi}_0\left(x,y\right) $$$

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The Level Set function evolves over time according to a partial differential equation (PDE) that minimizes an energy functional. The evolution of the Level Set function is governed by the following PDE, known as the Level Set equation: 8 $$$ \frac{\partial \phi }{\partial t}=F\mid \nabla \phi \mid $$$ where $$$ F $$$ represents the speed function that controls the evolution of the Level Set function.

As the Level Set function evolves, the zero-level set of the function represents the evolving contour or surface that delineates the object boundaries. Mathematically, the object boundaries can be detected by extracting the zero-level set of the Level Set function: 9 $$$ \Gamma (t)=\left\{\left(x,y\right)|\phi \left(x,y,t\right)=0\right\} $$$

The contour or surface defined by the zero-level set evolves over time to accurately capture the object boundaries. This evolution is driven by the speed function $$$ F $$$, which influences the direction and rate of contour movement. Mathematically, the evolution of the contour can be represented as: 10 $$$ \frac{d\Gamma}{dt}=F\mathbf{N} $$$ where $$$ \mathbf{N} $$$ is the normal vector to the contour.

The Level Set segmentation process continues iteratively until convergence, at which point the contour stabilizes and accurately delineates the object boundaries in the infrared image. The final segmentation result is obtained by extracting the stabilized contour, which represents the segmented regions of interest.

By leveraging Level Set algorithms, the proposed segmentation methodology achieves precise delineation of circuit board components from infrared images, contributing to improved quality assurance and fault detection processes in electronic manufacturing.

The speed function $$$ F $$$ dictates the evolution of the Level Set function and plays a crucial role in accurately capturing object boundaries. In the context of circuit board segmentation, the speed function can be formulated based on image gradients or intensity differences to encourage contour movement towards object boundaries. Mathematically, the speed function can be expressed as: 11 $$$ F=\frac{1}{1+{\left|\nabla I\right|}^2} $$$ where $$$ {\left|\nabla I\right|}^2 $$$ represents the squared gradient magnitude of the infrared image intensity.

The gradient of the image intensity is computed to derive the speed function. This gradient calculation involves computing the derivatives of the image intensity with respect to spatial coordinates $$$ x $$$ and $$$ y $$$. Mathematically, the gradient magnitude can be computed as: 12 $$$ {\left|\nabla I\right|}^2={\left(\frac{\partial I}{\partial x}\right)}^2+{\left(\frac{\partial I}{\partial y}\right)}^2 $$$

To prevent numerical instabilities and ensure smooth contour evolution, a regularization term is often added to the Level Set evolution equation. This regularization term penalizes high curvature regions, promoting smoother contour evolution. Mathematically, the Level Set evolution equation with regularization can be represented as: 13 $$$ \frac{\partial \phi }{\partial t}=F\mid \nabla \phi \mid \cdotp \operatorname{div}\left(\frac{\nabla \phi }{\mid \nabla \phi \mid}\right)+\alpha\ \mathrm{curvature}\ \left(\phi \right) $$$ where div represents the divergence operator, $$$ \alpha $$$ is the regularization parameter, and curvature $$$ \left(\phi \right) $$$ represents the curvature of the Level Set function.

In addition to the evolution equation, an energy functional is minimized during the Level Set segmentation process to ensure that the contour accurately delineates object boundaries. This energy functional incorporates both data fidelity and regularization terms. Mathematically, the energy functional can be expressed as: 14 $$$ E\left(\phi \right)={\int}_{\Omega}\kern0.1em \left({\lambda}_1{\left|\nabla I\right|}^2-{\lambda}_2\mid \nabla \phi \mid \right)d\Omega $$$ where $$$ {\lambda}_1 $$$ and $$$ {\lambda}_2 $$$ are weighting parameters that balance data fidelity and regularization terms, and $$$ \Omega $$$ represents the image domain.

To minimize the energy functional and evolve the Level Set function, gradient descent optimization techniques are typically employed. This involves iteratively updating the Level Set function in the direction that reduces the energy functional. Mathematically, the gradient descent update equation can be represented as: 15 $$$ {\phi}^{n+1}={\phi}^n-\eta \frac{\partial E}{\partial \phi } $$$ where $$$ \eta $$$ is the step size parameter, $$$ n $$$ denotes the iteration index, and $$$ \frac{\partial E}{\partial \phi } $$$ is the gradient of the energy functional with respect to the Level Set function. By incorporating these equations into the Level Set segmentation process, the proposed methodology achieves accurate and precise segmentation of circuit board components from infrared images, facilitating improved quality assurance and fault detection in electronic manufacturing processes.

Experimental Analysis

In conducting experimental analysis using a Python setup for infrared image segmentation of circuit boards, several key steps are undertaken. Initially, the dataset, comprising infrared images of circuit boards along with any available ground truth annotations, is prepared and organized for accessibility within the Python environment. Subsequently, preprocessing techniques are implemented to enhance image quality, including noise reduction, contrast enhancement, and background subtraction, utilizing libraries such as OpenCV or scikit-image. The proposed segmentation methodology, integrating Markov Random Fields (MRF) and Level Set algorithms, is then implemented in Python, leveraging appropriate libraries or custom implementations with NumPy and SciPy. Evaluation metrics, such as the Dice similarity coefficient and pixel-wise accuracy, are computed to quantify the performance of the segmentation algorithm, with libraries like scikit-learn facilitating their calculation. Experimental setup involves partitioning the dataset into training and testing sets, running the segmentation algorithm on test images, and comparing segmented results with ground truth annotations. Performance analysis entails computing evaluation metrics to assess the segmentation algorithm's efficacy, potentially benchmarking against existing methods. Visualization of segmented results and intermediate outputs, using matplotlib or OpenCV, offers insights into algorithm performance and aids in result interpretation. Through systematic execution of these steps, the experimental analysis provides valuable insights into the effectiveness of the proposed infrared image segmentation methodology for circuit board analysis within the Python ecosystem.

The Dice similarity coefficient measures the overlap between the segmented region and the ground truth region. It is calculated as twice the intersection of the segmented and ground truth regions divided by the sum of the segmented and ground truth regions. Mathematically, it can be expressed as: 16 $$$ DSC=\frac{2\times \mid S\cap G\mid }{\mid S\mid +\mid G\mid } $$$ where:

• $$$ \mid S\cap G\mid $$$ represents the number of pixels in both the segmented (S) and ground truth $$$ \left(\mathrm{G}\right) $$$ regions,
• $$$ \mid S\mid $$$ represents the number of pixels in the segmented region,
• $$$ \mid G\mid $$$ represents the number pixels in the ground truth region.

Pixel-wise accuracy measures the proportion of correctly classified pixels in the segmentation result compared to the ground truth. It is calculated as the ratio of the number of correctly classified pixels to the total number of pixels. Mathematically, it can be expressed as: 17 $$$ \mathrm{Accuracy}=\frac{\mathrm{TP}+\mathrm{TN}}{\mathrm{TP}+\mathrm{TN}+\mathrm{FP}+\mathrm{FN}} $$$ where

• TP (True Positive) represents the number of pixels correctly classified as belonging to the object,
• TN (True Negative) represents the number of pixels correctly classified as not belonging to the object,
• FP (False Positive) represents the number of pixels incorrectly classified as belonging to the object,
• FN (False Negative) represents the number of pixels incorrectly classified as not belonging to the object.

18 $$$ \mathrm{Precision}=\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FP}} $$$ where $$$ TP= $$$ True Positives (correctly predicted positive instances), $$$ FP= $$$ False Positives (instances incorrectly predicted as positive) 19 $$$ \mathrm{F}1\mathrm{Score}=\frac{2\times \mathrm{Precision}\times \mathrm{Recall}\ }{\ \mathrm{Precision}+\mathrm{Recall}\ } $$$

The comparison of segmentation methodologies from Figure 4, particularly in the context of infrared image segmentation of circuit boards, is crucial for determining the most effective approach. In this comparison, the Dice Similarity Coefficient (DSC) [17] and Pixel-wise Accuracy scores [18] serve as metrics to evaluate the performance of different algorithms. Fuzzy clustering, K-means clustering, and the proposed MRF-LS approach represent distinct methods with varying principles and capabilities. Fuzzy clustering offers flexibility by assigning degrees of membership to pixels in multiple clusters, accommodating uncertainties in the data. K-means clustering, on the other hand, partitions data into clusters [19, 20] based on feature similarity, though it may struggle with complex data distributions. The MRF-LS approach leverages Markov Random Fields (MRF) and Level Sets (LS) to capture spatial dependencies and incorporate contextual information into segmentation. By comparing these methodologies using DSC and Pixel-wise Accuracy scores, researchers can determine which approach best suits the specific requirements and challenges of infrared image segmentation for circuit boards.

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In Table 1, we compare the performance of three segmentation methodologies—Fuzzy Clustering, K-means Clustering, and the MRF-LS Approach—using precision, recall, and F1 score metrics. Precision measures the accuracy of positive pixel classification, recall quantifies the ability to correctly identify positive pixels from the ground truth, and the F1 score provides a balance between precision and recall. The results indicate that the MRF-LS Approach achieves the highest precision, recall, and F1 score values, suggesting its effectiveness in accurately identifying positive pixels while minimizing false positives and negatives. Conversely, K-means Clustering shows lower performance compared to the other methods, indicating limitations in accurately classifying positive pixels in infrared image segmentation of circuit boards.

TABLE 1 Performance metrics comparison for infrared image segmentation of circuit boards.

Segmentation method	Precision	Recall	F1 score
Fuzzy clustering [21]	0.88	0.86	0.87
K-means clustering [22]	0.82	0.75	0.78
MRF-LS approach	0.92	0.91	0.91
Active contour model [17]	0.87	0.85	0.86
U-Net (deep learning) [18]	0.95	0.93	0.94
Region growing [19]	0.84	0.80	0.82
Graph cut method [20]	0.89	0.87	0.88

In Table 2, we assess the performance of the same segmentation methodologies using the Jaccard Index, sensitivity, and specificity metrics. The Jaccard Index measures the similarity between the segmented regions and the ground truth, with higher values indicating better agreement. Sensitivity quantifies the ability to detect true positive pixels, while specificity measures the accuracy of negative pixel classification. The results demonstrate that the MRF-LS Approach achieves the highest Jaccard Index [23], sensitivity, and specificity values, suggesting superior segmentation accuracy and robustness [24]. Fuzzy Clustering and K-means Clustering exhibit lower performance metrics [25, 26] compared to the MRF-LS Approach, indicating potential limitations in accurately segmenting infrared images [27] of circuit boards.

TABLE 2 Performance metrics comparison for infrared image segmentation of circuit boards.

Segmentation method	Jaccard index	Sensitivity	Specificity
Fuzzy clustering [21]	0.78	0.85	0.91
K-means clustering [22]	0.72	0.78	0.86
MRF-LS approach	0.86	0.92	0.94
Active contour model [17]	0.81	0.84	0.90
U-Net (deep learning) [18]	0.91	0.95	0.96
Region growing [19]	0.76	0.82	0.89
Graph cut method [20]	0.84	0.88	0.92

The provided set of Figure 5 presents a comprehensive visual narrative of an image processing pipeline tailored for hole detection within a circuit board image. Figure (a) showcases the original image, providing an unaltered representation of the circuit board captured by a camera or obtained from a source. This serves as the initial input to the subsequent processing stages [28, 29]. Figure (b) exhibits the grayscale version of the original image. Grayscale conversion eliminates color information while retaining intensity variations, simplifying subsequent processing steps and reducing computational complexity. Figure (c) illustrates the output of the Level Set method applied to the grayscale image. The Level Set algorithm dynamically evolves a contour to delineate regions of interest, specifically the holes within the circuit board [21]. This iterative process optimizes an energy functional, resulting in a binary image where pixels within the identified regions are designated as foreground (representing the holes) and those outside as background. Figure (d) represents the refined output obtained through the integration of the Level Set method with a Markov Random Field (MRF) [22] model. The MRF with Level Set output undergoes further refinement by leveraging spatial dependencies among neighboring pixels captured by the MRF model. This integration enhances the precision and accuracy of hole segmentation, resulting in a more refined representation of the holes within the circuit board image [30, 31].

[IMAGE OMITTED. SEE PDF]

In summary, the progression from the original image through grayscale conversion, Level Set segmentation, and MRF refinement reflects a systematic approach to hole detection [32, 33], culminating in a precise and accurate delineation of the holes within the circuit board. These figures collectively illustrate the effectiveness of the image processing pipeline in identifying and characterizing the target features, laying the groundwork for subsequent analysis or further processing tasks with heightened reliability and efficiency [34].

Discussion

The experimental analysis demonstrates the efficacy of the proposed MRF-LS approach for infrared image segmentation of circuit boards compared to existing methods such as Fuzzy Clustering and K-means Clustering. The performance metrics, including Dice Similarity Coefficient (DSC), pixel-wise accuracy, precision, recall, F1 score, Jaccard Index, sensitivity, and specificity, consistently highlight the superiority of the MRF-LS method.

The MRF-LS approach leverages the strengths of Markov Random Fields (MRF) to model spatial dependencies [35, 36] and Level Set techniques to capture object contours dynamically. This integration allows the method to accurately segment complex regions in infrared images, overcoming the limitations of conventional clustering-based methods, which often struggle with irregular shapes and complex data distributions. For instance, the MRF-LS method achieves a Jaccard Index of 0.86, sensitivity of 0.92, and specificity of 0.94, significantly outperforming K-means Clustering, which scored 0.72, 0.78, and 0.86, respectively.

Key Insights

• Improved Accuracy:

  • The MRF-LS approach achieves the highest precision (0.92), recall (0.91), and F1 score (0.91) among the tested methods, indicating its capability to accurately detect and delineate relevant features in infrared images of circuit boards.

• Robustness:

  • The integration of MRF enhances the method's robustness to noise and artifacts, a common challenge in infrared imaging, ensuring more reliable segmentation outputs.

• Challenges with Clustering Methods:

  • Fuzzy Clustering and K-means Clustering showed comparatively lower performance due to their inability to model spatial dependencies and handle complex boundaries effectively. These methods are also sensitive to initialization and may converge to suboptimal solutions.

• Applicability:

  • The proposed MRF-LS approach is particularly well-suited for tasks requiring precise segmentation, such as identifying defects or hotspots in circuit boards, where small inaccuracies can lead to significant diagnostic errors.

• Visualization and Practical Utility:

  • Figures illustrating the segmentation progression—original images, grayscale conversion, Level Set output, and MRF-LS refined output—provide compelling evidence of the method's ability to accurately capture intricate features like holes and anomalies on circuit boards.

Limitations and Future Directions

While the MRF-LS method demonstrates superior performance, several areas warrant further investigation:

• Dataset Diversity: The current analysis focuses on a specific dataset. Extending the study to include a broader range of circuit board designs and infrared imaging conditions could validate the method's generalizability.
• Real-Time Application: The computational complexity of the MRF-LS approach may pose challenges for real-time applications. Optimizing the implementation for speed without sacrificing accuracy is an important area for future work.
• Comparison with Advanced Techniques: Emerging methods, such as deep learning-based [37] segmentation approaches (e.g., U-Net, Segment Anything Model), should be considered for comparison to establish the relative performance of the MRF-LS method.
• Multi-modal Integration: Future studies could explore the integration of infrared imaging with other modalities, such as visual spectrum [38] or hyperspectral imaging, to further enhance segmentation accuracy [39] and utility.

In conclusion, the proposed MRF-LS approach provides a significant advancement in infrared image segmentation for circuit boards, delivering precise and reliable results. Its ability to outperform conventional methods [40] positions it as a valuable tool for quality assurance and fault detection in electronic manufacturing and maintenance. However, addressing its limitations and exploring its potential in diverse applications remain critical for realizing its full potential.

Conclusion

In conclusion, the utilization of infrared imaging in circuit board analysis offers invaluable insights into temperature distribution, component health, and potential flaws. However, the complexity introduced by noise, thermal signature variations, and intricate backgrounds poses significant challenges for accurate segmentation of circuit board components from infrared images using traditional methods. To address these challenges, we advocate for the adoption of robust and adaptable techniques such as Markov Random Field (MRF) models and Level Set (MRF-LS) approaches. Our proposed approach integrates these methods to enhance the segmentation of items of interest in complex infrared images of circuit boards. The proposed methodology begins with preprocessing steps aimed at noise reduction and improving image quality. MRF models are employed to capture spatial connections among nearby pixels, leveraging contextual information for segmentation. Concurrently, Level Set approaches are utilized to develop curves or surfaces that define the boundaries of circuit board components. By integrating both local and global information and accommodating irregular item shapes and complex backgrounds, our hybrid technique demonstrates enhanced segmentation accuracy. Experimental evaluations conducted on a dataset of infrared circuit board images, compared against ground truth annotations, affirm the efficacy of our approach. Comparative studies illustrate superior segmentation accuracy and robustness compared to conventional methods. The integration of MRF models with Level Set approaches enables the extraction of detailed characteristics and precise delineation of object boundaries, even in the presence of noise and background fluctuations. Evaluation metrics such as the Dice similarity coefficient and pixel-wise accuracy validate the effectiveness of our proposed method in capturing key areas of interest with high fidelity. In summary, the fusion of MRF models and Level Set approaches presents a novel and effective infrared image segmentation method for circuit board analysis. This method enhances segmentation accuracy and resilience, thereby improving the reliability of circuit board inspection and fault detection processes in electronic manufacturing quality assurance and diagnostics. As a future work, Explore the integration of deep learning architectures, such as convolutional neural networks (CNNs) or recurrent neural networks (RNNs), to improve segmentation accuracy and adaptability to diverse circuit board images. The MRF-LS approach demonstrates promising performance with an accuracy of 86%, precision of 92%, and recall of 94%. These metrics indicate the effectiveness of the approach in accurately identifying and classifying instances within the dataset. The high precision suggests that the majority of instances predicted as positive by the model are indeed true positives, minimizing false positives.

Author Contributions

T. Praveenkumar: conceptualization, writing – original draft. S. Anthoniraj: methodology, writing – original draft. S. Kumarganesh: investigation, writing – original draft. M. Somaskandan: methodology, writing – original draft. K. Martin Sagayam: validation, writing – original draft. Binay Kumar Pandey: conceptualization, methodology, writing – original draft. Digvijay Pandey: conceptualization, validation, writing – original draft. Suresh Kumar Sahani: validation, writing – original draft.

Acknowledgments

The authors would like to express gratitude to Karunya Institute of Technology and Sciences, Coimbatore, India. The relevant code with the manuscript is also available and would be available, if will be asked to do so later.

Ethics Statement

The authors have nothing to report.

Consent

The authors have nothing to report.

Conflicts of Interest

The authors declare no conflicts of interest.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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