Figure 3.

Markers were semiautomatically detected in 2D projection images. Based on a manually identified marker position in 3 to 5 projection images and Eq. 3, an initial estimate of ($\overline{\mathrm{x}},\overline{\mathrm{y}},\overline{\mathrm{z}}$) was acquired in Step (i). The initial ($\overline{\mathrm{x}},\overline{\mathrm{y}},\overline{\mathrm{z}}$) was forward-projected onto a projection image using a projection matrix. A radial search around the forward-projected point (${\overline{\mathrm{u}}}_{\mathrm{j}},{\overline{\mathrm{v}}}_{\mathrm{j}}$) shown as an open circle was conducted to locate (u_j, v_j) shown as a solid circle. Step (iv) updated ($\overline{\mathrm{x}},\overline{\mathrm{y}},\overline{\mathrm{z}}$) using the identified (u_j, v_j) from every projection and Eq. 3. The updated ($\overline{\mathrm{x}},\overline{\mathrm{y}},\overline{\mathrm{z}}$) provides a reference for the following motion correction methods.