This paper addresses the problem of deducing the surface shape of an object given just the surface normals. Many shape measurement algorithms such as shape from shading and shape from texture only return the surface normals of an object, often with an ambiguity of π in the surface tilt. The surface shape has to be inferred from these normals, typically via some integration process. However, reconstruction through the integration of surface gradients is sensitive to noise and the choice of integration paths across the surface. In addition, existing techniques cannot accommodate ambiguities in tilt. This paper presents a new approach to the reconstruction of surfaces from surface normals using basis functions, referred to here as shapelets. The surface gradients of the shapelets are correlated with the gradients of the surface and the correlations summed to form the reconstruction. This results in a simple reconstruction process that is very robust to noise. Where there is an ambiguity of π in the surface tilt, reconstructions of reduced quality are still possible up to a positive/negative shape ambiguity. Intriguingly, some form of reconstruction is also possible using just slant information.