1. An imaging device, comprising: an image sensor that includes imaging pixels, which generate image outputs, disposed in a two-dimensional array and focus detection pixels, which generate outputs for focus detection, disposed along a specific direction over part of the array of the imaging pixels; a recognizing circuit that recognizes an image pattern indicating a pixel image output change of the imaging pixels along a direction perpendicular to the specific direction in which the focus detection pixels are disposed using the image outputs from the imaging pixels present around each focus detection pixel; and a determining circuit that determines an image output for an interpolation at each focus detection pixel using an output from the focus detection pixel and the image outputs from the imaging pixels present around the focus detection pixel through a first arithmetic operation method if the image pattern has been recognized by the recognizing circuit and using the image outputs from the imaging pixels present around the focus detection pixel without the output from the focus detection pixel through a second arithmetic operation method if the image pattern has not been recognized by the recognizing circuit.