1. A range-image processing apparatus, comprising: input means for inputting a range image; generating means for generating a plurality of range images having different resolutions from the range image input by said input means; calculation means for calculating normal vectors for each of the plurality of range images having different resolutions generated by said generation means; edge-map formation means for forming an edge map for each of the plurality of range images based on the normal vectors corresponding to different resolutions calculated by said calculation means; synthesis means for forming a single edge map by synthesizing the plurality of edge maps corresponding to different resolutions formed by said edge-map formation means; and polygon-data formation means for forming polygon data for describing the surface shape of the object represented by the range image input by said input means based on the edge map formed by said synthesis means.