1. An image processing apparatus comprising: a calculating unit that generates, for each of a plurality of color separation images, an edge gradient image that comprises a gradient direction for each pixel in the color separation image and an edge intensity image that comprises an edge intensity for each pixel in the color separation image, the plurality of color separation images resulting from separation of a color captured image into a plurality of color components; an edge-position detecting unit that, for each color separation image, detects edge pixels on the basis of the edge gradient image and the edge intensity image of the color separation image, and for each color separation image, generates a binary edge image indicating the detected edge pixels; a combining unit that generates a combined edge image that combines the plurality of binary edge images; a combined edge intensity image that combines the edge intensity images, and a combined edge gradient image that combines the edge gradient images; and a subject-region detecting unit that detects a subject region in the color captured image on the basis of the combined edge intensity image, the combined edge gradient image, and the edge pixels indicated by the combined edge image.