The computational framework, basedon the conformal camera, is developedfor processingvisual information duringsmooth pursuit movements of a robotic eye. During smooth pursuit, the image of the tracked object remains nearly stationary while the image of a stationary background sweeps across the image plane of the camera. The background's image transformation derived in the second-order approximation enable the anticipation of the perceptual outcome of the camera pursuit. This can be used to support the correct visual information of the moving object in front of the stationary background, These results complement the author's previous study on the predictive image processingfor visual stability duringthe conformalcameramovementsresembling primate's saccadiceye rotations. The visual information processing algorithms that can support visual stability during smooth pursuit and saccadic movements of an anthropomorphic robotic camera are neededfor an autonomousrobot efficient interactions with the real world, in real time.