We investigate location dependent lesion detectability of cone beam computed tomography images for different background types (i.e., uniform and anatomical), image planes (i.e., transverse and longitudinal) and slice thicknesses. Anatomical backgrounds are generated using a power law spectrum of breast anatomy, 1/f3. Spherical object with a 5mm diameter is used as a signal. CT projection data are acquired by the forward projection of uniform and anatomical backgrounds with and without the signal. Then, projection data are reconstructed using the FDK algorithm. Detectability is evaluated by a channelized Hotelling observer with dense difference-of-Gaussian channels. For uniform background, off-centered images yield higher detectability than iso-centered images for the transverse plane, while for the longitudinal plane, detectability of iso-centered and off-centered images are similar. For anatomical background, off-centered images yield higher detectability for the transverse plane, while iso-centered images yield higher detectability for the longitudinal plane, when the slice thickness is smaller than 1.9mm. The optimal slice thickness is 3.8mm for all tasks, and the transverse plane at the off-center (iso-center and off-center) produces the highest detectability for uniform (anatomical) background.