Border extraction is an important procedure associated with recognition and interpretation tasks in digital image processing and computer vision. Since local processing schemes (i.e., spatial filltering) are not appropriate for border extraction in noisy images, global and intelligent mechanisms are required to deal with this situation. Some heuristic algorithms that apply jointly local operators and some kind of optimization criterion have been successfully applied to treat images corrupted by additive noise. However, the behavior of these mechanisms is considerably undermined when managing images with multiplicative (speckle) noise. In this paper we present a gradient-based evolutionary algorithm that can achieve convenient boundary extraction in digital images with additive noise, and that can be successfully extended to operate with non-additive noisy images as well.