Techniques for improving the resolution of images (either analog images, analytic images, or images having a higher resolution than that of a display device) to be rendered on patterned displays. In one aspect of the present invention, an overscaling or oversampling process may accept analytic character information, such as contours for example, and a scale factor or grid and overscale or oversample the analytic character information to produce an overscaled or oversampled image. The overscaled or oversampled image generated has a higher resolution than the display upon which the character is to be rendered. Displaced samples of the overscaled or oversampled image are then combined (or filtered). An analytic image, such as a line drawing for example, may be applied to the oversampling / overscaling process as was the case with the character analytic image. However, since the analytic image may have different units than that of the character analytic image, the scale factor applied may be different. Since an ultra resolution image is already "digitized", that is, not merely mathematically expressed contours or lines between points, it may be applied directly to a process for combining displaced samples of the ultra-resolution image to generate another ultra-resolution image (or an image with sub-pixel information). The functionality of the overscaling / oversampling process and the processes for combining displaced samples may be combined into a single step analytic to digital sub-pixel resolution conversion process.