Straight lines are important features in images, and their detection plays a major role in the compression, representation and analysis of visual information. The visual system of spiders from the Salticidae family is especially effective for straight line detection, due to their elongated and moveable retinae, which are used to scan the visual field. This paper presents a method for straight line motivated by the visual system of the Salticidae, which uses an optimization strategy (namely Nelder and Mead’s amoeba with simulated annealing) to find maxima on the continuous ρ-θ parameter space that correspond to straight lines in the image. The method considers the spatially quantized nature of the image spaces and allows unlimited parametric resolution without the need to sample large regions of the parameter space.