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This paper presents a silhouette-slice theorem for convex opaque 3-D objects. The theorem states that the 2-D Curvature Transform (CT) of any silhouette contour is a slice of the 3-D CT of the object surface at some appropriate orientation. The 2-D and 3- D CT's are defined as curvature functions on the Gaussian circle and sphere of the silhouette and object, respectively. The new theorem and transforms are shown to be the counterparts in silhouette imaging of the projection-slice theorem and Fourier Transforms of line-integral projection imaging.