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This paper presents a global diffeomorphism from a visible set of rigid-body configurations, a subset of SE(3), to an image space. Using the diffeomorphism, we develop an image-based, essentially global, dynamic visual servoing algorithm that keeps features in the field of view and avoids self-occlusions. The approach is geometric in the sense that the visible set and its corresponding image are differentiable manifolds, and the diffeomorphism is global. The mapping to image space and the resulting Jacobian rely on a specific target geometry, a sphere with a known radius marked with an "arrow" feature point. The paper presents simulation experiments for a more typical visual target comprised of a collection of isolated feature points. In this setting, the diffeomorphism to image space is approximate, nevertheless, the simulations converge for a wide variety of target geometries and initial conditions.