We predict a bias-voltage dependent corrugation reversal for scanning tunneling microscopy (STM) images with atomic resolution of bcc-(110) transition metal surfaces: Atoms which appear usually on STM images of metal surfaces as protrusions, may appear on these images anticorrugated, e.g., as hollow sites and vice versa hollow sites may appear as atoms. This makes the absolute determination of atom sites by STM unreliable. We investigate the image-reversal in detail for the W(110) surface and explain its origin on the basis of the electronic structure. We found, the image is determined by a competition between surface resonance states with ${d}_{\mathrm{xz}}$ and ${d}_{{z}^{2}}$ character contributing to a direct image of atomic sites and surface-state bands around the $\overline{S}$ point of the two-dimensional Brillouin zone with $\mathrm{pd}$ bonding character and bonding charge between the surface atoms. The surface states contribute to anticorrugated images. Finally the image depends on the bias voltage. For W(110) and positive bias voltages the surface resonances dominate over the surface states leading to a direct image of atomic sites. For negative voltages below a critical value of $\ensuremath{-}0.4$ V calculations show a reversed image, i.e., anticorrugation. The critical bias voltage depends slightly on the tip-sample separation. For bias voltages around the critical value corrugating and anticorrugating contributions to the STM image compensate each other, the corrugation amplitudes become extremely small, the atomic resolution disappears, which is consistent with the experimental difficulties in achieving atomic resolution on W(110) for negative voltages and stripelike images are predicted. For positive bias voltages we found a good agreement between the theoretical results and our measured STM images. The competition between surface resonances and surface states is a quite general mechanism and anticorrugation is expected to occur on (110) surfaces of other bcc transition-metals [i.e., Nb(110), Mo(110), Ta(110)]. We demonstrated this explicitly for Ta(110), anticorrugation occurs practically over the entire bias-voltage range available by a STM and an image reversal from an anticorrugated to a corrugated image is predicted for 1.3 V. For magnetic surfaces the image reversal may occur twice, once for majority and once for minority states. For Fe(110) we show that the minority spin channel controls the STM image. We predict a direct image for majority states and an anticorrugated image for minority states below a bias voltage of 0.7 V, and we predict only one image reversal at about 0.4 V for an ordinary non-spin-polarized STM. Employing the full-potential linearized augmented plane wave method in film geometry, the electronic structure is determined by first principles calculations within the framework of the density functional theory in the local (spin) density approximation. The STM analysis is carried out within the s-orbital tip-model of Tersoff and Hamann. An efficient analysis of the corrugation amplitude in terms of two-dimensional star coefficients of the vacuum density of states is presented. The tip-sample distance dependent ${\mathbf{k}}_{\ensuremath{\parallel}}$-point selection to the tunneling current is analyzed. The enhancement of the corrugation amplitude due to ${p}_{z}$- and ${d}_{{z}^{2}}$-type tip-orbitals are determined. We show that the enhancement factors calculated are close to the analytical factors given by Chen.