This section discusses region-based image segmentation, focusing on finding coherent and homogeneous regions within an image. The basic formulation of the problem involves partitioning the image into a finite set of non-overlapping regions. The goal is to ensure that each region is homogeneous, meaning that no adjacent regions should share common features. The concept of region homogeneity is introduced, where pixels within a region are connected, and the connectivity can be defined by different criteria such as 4-connectivity or 8-connectivity. The section also covers region growing by pixel aggregation, where pixels are added to a region based on a homogeneity criterion, typically defined by a maximum allowed absolute difference \( T \). Key aspects of designing a region-growing algorithm include selecting the seed pixel, defining the similarity measure \( S \), choosing the threshold \( T \), and deciding whether to compare a pixel to its neighbor or to the entire region. The advantages and disadvantages of these approaches are discussed, highlighting the trade-offs between sensitivity to the seed pixel and the transitivity of similarity relationships. The section also introduces region merging algorithms, which start with an oversegmented image and merge adjacent regions based on a merging criterion. Two specific methods are mentioned: boundary melting, where regions merge if they are separated by weak edges, and the split-and-merge algorithm, which recursively splits and merges regions until no further changes are possible. Finally, the section includes examples and figures to illustrate the concepts, such as segmenting a gray-scale lightning image and visualizing the quadtree decomposition used in the split-and-merge algorithm.This section discusses region-based image segmentation, focusing on finding coherent and homogeneous regions within an image. The basic formulation of the problem involves partitioning the image into a finite set of non-overlapping regions. The goal is to ensure that each region is homogeneous, meaning that no adjacent regions should share common features. The concept of region homogeneity is introduced, where pixels within a region are connected, and the connectivity can be defined by different criteria such as 4-connectivity or 8-connectivity. The section also covers region growing by pixel aggregation, where pixels are added to a region based on a homogeneity criterion, typically defined by a maximum allowed absolute difference \( T \). Key aspects of designing a region-growing algorithm include selecting the seed pixel, defining the similarity measure \( S \), choosing the threshold \( T \), and deciding whether to compare a pixel to its neighbor or to the entire region. The advantages and disadvantages of these approaches are discussed, highlighting the trade-offs between sensitivity to the seed pixel and the transitivity of similarity relationships. The section also introduces region merging algorithms, which start with an oversegmented image and merge adjacent regions based on a merging criterion. Two specific methods are mentioned: boundary melting, where regions merge if they are separated by weak edges, and the split-and-merge algorithm, which recursively splits and merges regions until no further changes are possible. Finally, the section includes examples and figures to illustrate the concepts, such as segmenting a gray-scale lightning image and visualizing the quadtree decomposition used in the split-and-merge algorithm.