We present a novel variational approach to top-down image segmentation, which accounts for significant projective transformations between a single prior image and the image to be segmented. The proposed segmentation process is coupled with reliable estimation of the transformation parameters, without using point correspondences. The prior shape is represented by a generalized cone that is based on the contour of the reference object. Its unlevel sections correspond to possible instances of the visible contour under perspective distortion and scaling. We extend the Chan-Vese energy functional by adding a shape term. This term measures the distance between the currently estimated section of the generalized cone and the region bounded by the zero-crossing of the evolving level set function. Promising segmentation results are obtained for images of rotated, translated, corrupted and partly occluded objects. The recovered transformation parameters are compatible with the ground truth.