An extraneous-matter detecting apparatus according to an embodiment includes a first extraction unit, a second extraction unit, and a detection unit. The first extraction extracts a first pixel group of first pixels included in a captured image captured by an image capturing device. Each of the first pixels has a luminance gradient directed outward from a predetermined center region. The second extraction unit extracts a second pixel group of second pixels included in the captured image. Each of the second pixels has a luminance gradient directed inward toward the predetermined center region. The detection unit combines the first pixel group, extracted by the first extraction unit, and the second pixel group, extracted by the second extraction unit, with each other so as to detect an extraneous matter adhered to the image capturing device.