The speckle produces severe degradations in digital images, which could be introduced by technological devices during the acquisition, capture or transmission of the images. This perturbation affects, for instance, medical and satellite images. Recently, some methods defined in the bi-geometric structure have presented significant improvements in the processing of image with speckle. In this work, we review some aspects of the bi-geometric structure including a discussion about some of the applications found in the literature focused in the detection of contours in grey scale images with speckle.