We propose two image segmentation algorithms: the integrated sortmap relabel with adjacent-region merging (ISARM), and the self-guided sortmap relabel with adjacent-region merging (SGSARM). Due to the integration of noise reduction and fast merging, ISARM provides a 25% improvement in processing time, as compared to leading existing algorithms such as the region adjacency graph (RAG) algorithm, on a variety of test images. ISARM also provides better segmentation accuracy than the RAG algorithm, by a measure combining the mean squared error and the number of regions obtained. SGSARM is designed for use with large images (say 1024×1024 or larger). It incorporates two levels of processing: an edge detection algorithm of linear complexity, which is applied to large images to detect regions of interest (ROIs), followed by ISARM for finer segmentation of each ROI. SGSARM therefore has significant advantages in speed and accuracy when used in large images. Simulation results are provided to demonstrate the performance of both algorithms.