The combination of hardware acceleration and flexibility make FPGAs important to image processing applications. There is also a need for efficient, flexible hardware/software codesign environments that can balance the benefits and costs of using FPGAs. Image processing applications often consist of a pipeline of components where each component applies a different processing algorithm. Components can be implemented for FPGAs or software. Such systems enable an image analyst to work with either FPGA or software implementations of image processing algorithms for a given problem. The pipeline assignment problem chooses from alternative implementations of pipeline components to yield the fastest pipeline. Our codesign system solves the pipeline assignment problem to provide the most effective implementation automatically, so the image analyst can focus solely on choosing components which make up the pipeline. However, the pipeline assignment problem is NP complete. An efficient, dynamic solution to the pipeline assignment problem is a desirable enabler of codesign systems which use both FPGA and software implementations. This paper is concerned with solving pipeline assignment in this context. Consequently, we focus on optimal and heuristic methods for fast (fixed time limit) runtime pipeline assignment. Exhaustive search, integer linear programming and local search methods for pipeline assignment are investigated. We present experimental findings for pipelines of 20 or fewer components which show that in our environment, optimal runtime solutions are possible for smaller pipelines and nearly optimal heuristic solutions are possible for larger pipelines.