A comprehensive finite-element model is constructed to represent a solar cell as interconnected diodes. By simulating the voltage distribution and luminescence intensity across the cell plane, and fitting them to measured voltages and luminescence images, resistance and recombination parameters related to different parts of the cell can be extracted unambiguously. Four measurement and fitting routines are described, each designed to resolve different sets of cell parameters, ranging from the edge recombination diode saturation current density, metal contact recombination, to the metal-semiconductor contact resistance and metal finger conductance statistical distribution.