A Hybrid Framework for Statistical Feature Selection and Image-Based Noise-Defect Detection

In industrial imaging, accurately detecting and distinguishing surface defects from noise is critical and challenging, particularly in complex environments with noisy data. This paper presents a hybrid framework that integrates both statistical feature selection and classification techniques to improve defect detection accuracy while minimizing false positives. The motivation of the system is based on the generation of scalar scores that represent the likelihood that a region of interest (ROI) is classified as a defect or noise. We present around 55 distinguished features that are extracted from industrial images, which are then analyzed using statistical methods such as Fisher separation, chi-squared test, and variance analysis. These techniques identify the most discriminative features, focusing on maximizing the separation between true defects and noise. Fisher's criterion ensures robust, real-time performance for automated systems. This statistical framework opens up multiple avenues for application, functioning as a standalone assessment module or as an a posteriori enhancement to machine learning classifiers. The framework can be implemented as a black-box module that applies to existing classifiers, providing an adaptable layer of quality control and optimizing predictions by leveraging intuitive feature extraction strategies, emphasizing the rationale behind feature significance and the statistical rigor of feature selection. By integrating these methods with flexible machine learning applications, the proposed framework improves detection accuracy and reduces false positives and misclassifications, especially in complex, noisy environments.

Physics Meets Pixels: PDE Models in Image Processing

Partial Differential Equations (PDEs) have long been recognized as powerful tools for image processing and analysis, providing a framework to model and exploit structural and geometric properties inherent in visual data. Over the years, numerous PDE-based models have been developed and refined, inspired by natural analogies between physical phenomena and image spaces. These methods have proven highly effective in a wide range of applications, including denoising, deblurring, sharpening, inpainting, feature extraction, and others. This work provides a theoretical and computational exploration of both fundamental and innovative PDE models applied to image processing, accompanied by extensive numerical experimentation and objective and subjective analysis. Building upon well-established techniques, we introduce novel physical-based PDE models specifically designed for various image processing tasks. These models incorporate mathematical principles and approaches that, to the best of our knowledge, have not been previously applied in this domain, showcasing their potential to address challenges beyond the capabilities of traditional and existing PDE methods. By formulating and solving these mathematical models, we demonstrate their effectiveness in advancing image processing tasks while retaining a rigorous connection to their theoretical underpinnings. This work seeks to bridge foundational concepts and cutting-edge innovations, contributing to the evolution of PDE methodologies in digital image processing and related interdisciplinary fields.