This paper presents efficient and portable implementations of two useful primitives in image processing algorithms, histogramming and connected components. Our general framework is a single-address space, distributed memory programming model. We use efficient techniques for distributing and coalescing data as well as efficient combinations of task and data parallelism. Our connected components algorithm uses a novel approach for parallel merging which performs drastically limited updating during iterative steps, and concludes with a total consistency update at the final step. The algorithms have been coded in Split-C and run on a variety of platforms. Our experimental results are consistent with the theoretical analysis and provide the best known execution times for these two primitives, even when compared with machine-specific implementations. More efficient implementations of Split-C will likely result in even faster execution times.