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    <subfield code="a">Accurate segmentation of objects from grayscale images is fundamental in computer  vision with diverse applications. In medical imaging, it enables precise detection of  anatomical structures, lesions, and tumors from modalities like CT, MRI, and ultrasound  for diagnosis, treatment planning, and monitoring diseases. In industrial inspection,  segmentation algorithms detect product defects, cracks, or anomalies for quality control  and safety. However, achieving accurate segmentation in grayscale images is a  challenging endeavor due to several inherent complexities. Uneven illumination, a  common issue in real-world imaging scenarios, can lead to significant variations in pixel  intensities, obscuring object boundaries and complicating the segmentation process.  Additionally, the presence of noise, whether from sensor imperfections or environmental  factors, can further degrade image quality and introduce artifacts that hinder accurate  segmentation. Moreover, complex object boundaries, particularly in scenes with  occlusions, shadows, or intricate shapes, pose significant challenges for traditional  segmentation methods. These methods often struggle to accurately delineate the intricate  contours and regions of interest, leading to under-segmentation or over-segmentation  errors. To address these challenges, the proposed thesis introduces a novel model-based  hybrid variational level-set method, termed VKMHLS, specifically tailored for object  detection in grayscale images. VKMHLS simplifies the Local Intensity Clustering (LIC)  model and introduces a novel energy functional based on the region-based pressure  function, enhancing the efficiency of segmentation for low grayscale images.  Furthermore, a fast numerical implementation strategy enables swift segmentation of  images and estimation of the offset field, significantly improving overall computational  efficiency. To robustly and accurately segment intricate object structures in challenging  grayscale datasets, VKMHLS employs a multi-layer model-based level-set structure with  adaptive scale operators. These operators dynamically determine the optimal number of  layers and precise scale parameters, overcoming issues with local minima and enabling  successful handling of severely uneven grayscale distributions. Additionally, the thesis  proposes an innovative active contour model called CER, which intelligently combines  elements from the Chan-Vese (CV) model and the Region-Scalable Fitting (RSF) model.  CER integrates information entropy calculations and minimizes the overall energy  functional, allowing successful segmentation of regions with weak edges, strong noise  interference, and uneven brightness variations across grayscale images. To tackle the  persistent challenge of segmenting grayscale images with both uneven characteristics and  high noise levels, a hybrid level-set algorithm based on kernel metrics is introduced. This  algorithm leverages an improved multi-scale mean filter to mitigate grayscale  inhomogeneity while reducing the impact of scale parameter selection. Kernel  measurements and local similarity metrics suppress noise influence, enhancing  robustness. Furthermore, a count gradient regularization term further reduces noise  impact, ensuring precise segmentation results. Comprehensive experimental evaluations  demonstrate that VKMHLS accurately segments grayscale images characterized by both  inhomogeneity and noise contamination, exhibiting robust performance across various  noise types. These attributes make VKMHLS a highly valuable tool for tackling realworld grayscale image segmentation challenges and enabling reliable object detection.</subfield>
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