The spin-resolved density of states of Co atoms on a noncollinear magnetic support displays a distinct shape contrast, which is superimposed on the regular height contrast in spin-polarized scanning tunneling microscopy. The apparent atom height follows the well-known cosine dependence on the angle formed by the tip and adatom local magnetization directions, whereas the shape contrast exhibits a sine dependence. We explain this effect in terms of a noncollinear spin density induced by the substrate, which in our case is the spin spiral of the Mn monolayer on W(110). The two independent contrast channels, apparent height and shape, are identified with the Co magnetization projections onto two orthogonal axes. As a result, all components of the overall atom magnetic moment vector can be determined with a single spin-sensitive tip in the absence of an external magnetic field. This result should be general for any atom deposited on noncollinear magnetic layers.