A platenless book scanner with line buffering performs electronic perspective correction to account for rotation of the spine of a non-planar bound document relative to a reference line in a support plane of the platenless book scanner. A pre-scan of the non-planar bound document is performed to provide a geometrical contour map of the bound document. The geometrical contour map, which identifies displacement of the bound document from the support plane, is analyzed to calculate an angular offset between a spine of the bound document and the reference line in the support plane. The angular offset is used to identify a minimum number of scan line buffers for recording image data, from a set of scan line buffers. Once the minimum number of scan line buffers is filled with recorded image data, distortions caused by displacements of the non-planar bound document from the support plane and skew of the bound document relative to the reference line in the support plane are corrected. A scan line of image data is corrected by polling locations in the set of scan line buffers in accordance with the geometrical contour map, and by interpolating the polled locations to provide output pixels. To correct additional scan lines of image data some of the image data stored in the minimum number of image buffers is replaced after recording more image data.