In this paper a new operator is presented for the detection of contours in images with multiplicative noise, by using the operations introduced in the bi-geometric calculus, since recent results in the literature show that multiplicative operators tend to make more accurate approximations of the reality in images with multiplicative noise. The operator introduced corresponds to a multiplicative multi-directional gradient. The Global Efficiency was used as performance function to make a comparison about the effectiveness in the detection of contours, between the multi-gradient and its multiplicative version. These operators are applied on some images (one synthetic and another real), under a threshold for each noise level, then the function of optimal performance is obtained over a continuous range of noise, and thus an objective comparison between both operators is presented. According to the results obtained from the objective comparison, the multiplicative multi-directional gradient operator presents improved efficiency in obtaining contours versus its classical version.