Non-uniformly sampled images represented on irregular content-based meshes are central to the developments in image compression techniques and in efficient motion tracking. We present a general approach to the development of systematic design procedures for scalable and adaptive low level image processing operators that can be applied to such non-uniformly sampled images. We provide algorithms that use the content-based mesh to address the usually difficult issue of local operator scale selection. The operator scale is therefore automatically matched to the local scale of the image features as embodied in the mesh. In this way we are able to apply a range of operators directly to compressed images. We demonstrate the approach with the design of image derivative operators that enable image feature detection to be implemented directly on compressed images.