We present a method for determining the skeletal shape description for letters in texts faded due to ageing and/or poor ink quality. The proposed algorithm is interesting in that it neither involves assumptions about demarcation of object regions from the background, nor does it require pixel connectivity in the text regions. Consequently, it may be applied for obtaining the shape descriptions of sparse regions, which are characteristic of letters in faded documents. Given the pixel distribution for a letter or a word from a faded document, the method involves an iterative evolution of a piecewise-linear approximation of the principal curve of this pixel distribution. By constraining the principal curve to lie on the edges of the Delaunay triangulation of the shape distribution, the adjacency relationships between regions in the shape can be detected and used in evolving the skeleton. The approximation of the principal curve, on convergence, gives the final skeletal shape. The skeletonization is invariant to Euclidean transformations and is adaptive in terms of the topology of the underlying shape distribution as well as in the number of units needed for the piece-wise approximation of the principal curve.