We describe several techniques for detecting object boundaries in images immersed in speckle noise. Based on the assumption that the image speckle is uncorrelated, optimal statistical procedures are formulated using local tests for changes in intensity. The first method described is parametric: the average values taken from adjacent image neighborhoods are ratioed and compared to a threshold statistic. A cooperative scheme is then described in which the parametric statistic is applied only at the zero crossings of the image resulting from a convolution with a narrowband differential operator. A non-parametric procedure based on a linear rank statistic is also described, which can be shown to be locally most powerful (among rank tests) under the noise assumption. Examples illustrate the effectiveness of each method.