1. A vehicle periphery monitoring apparatus for monitoring a vehicle periphery comprising: a detection unit detecting a brightness change of a pixel along a detection line, the detection line extending in a right-left axis of a captured image captured by an in-vehicle camera, and the brightness change of the pixel being caused by a movement of a moving object; a parameter table defining a parameter regarding brightness change being detected along the detection line, as a predefined brightness change of the pixel along the detection line; and a moving object detector detecting the moving object, wherein the detection line has multiple portions that include a center portion at a center of the captured image and multiple side portions on a right and left side of the center portion, the side portions are positioned on far-off spots farther from the in-vehicle camera relative to a spot on which the center portion is positioned, the parameter table defines a different parameter for each of the multiple portions of the detection line, the parameter table defines, as the parameter, a size (W) of the predefined brightness change as a number of pixels, and the size of the predefined brightness change is defined smaller for the pixels along the side portions of the detection line than for the pixels along the center portion of the detection line, the parameter table defines, as the parameter, a per-unit-time movement amount of the predefined brightness change as a number of pixels (D), and the per-unit-time movement amount of the predefined brightness change is defined smaller for the pixels along the side portions of the detection line than for the pixels along the center portion of the detection line, and the moving object detector detects the moving object based on the brightness change of the pixel detected by the detection unit and the predefined brightness change of the pixel defined by the parameter table for the multiple portions of the detection line.