After researching the anti-monitoring problem on mobile objects in the heterogeneous sensory field, a new Exposure model is proposed, which can be used to estimate the approximate risk of a mobile object moving along a path to traverse the sensory field deployed with anisotropic sensor nodes. Based on the newly proposed Exposure model, a novel decision algorithm for path selection is designed by combing the Anisotropic Voronoi Tessellation schemes, which guarantee that the mobile object can select a suitable path with a minimal approximately risk of traveling across the anisotropic sensory field. Theoretical analyses and simulation results show that the new algorithm has a good anti-monitoring performance and requires only that the mobile object should know the local information in its detection radius, so it is distributed and practical.