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The figure of merit (FOM) is popular for testing an edge detector's performance, but there are very few reports using FOM as an evaluation method in Genetic Programming (GP). In this study, FOM is investigated as a fitness function in GP for edge detection. Since FOM has some drawbacks from type II errors, new fitness functions are developed based on FOM in order to address these weaknesses. Experimental results show that FOM can be used to evolve GP edge detectors that perform better than the Sobel detector, and the new fitness functions clearly improve the ability of GP edge detectors to find edge points and give a single response on edges, compared with the fitness function using FOM.