1. A wafer inspection apparatus for inspecting a processed face of a wafer processed by grinding and polishing, comprising: a chuck table configured to hold a wafer thereon; image pickup means for picking up an image of the processed face of the wafer held by the chuck table; a first image creation unit configured to delimit picked up image data obtained by the image pickup by the image pickup means for each predetermined region and extract only pixels having a pixel value higher than those of peripheral pixels as a characteristic point in the predetermined region to create a first image; a second image creation unit configured to extract only pixels having a pixel value lower than those of peripheral pixels as a characteristic point in the predetermined region to create a second image; and a selection unit configured to select one of the first image creation unit and the second image creation unit in response to an inspection target; wherein the image pickup means is configured from a line sensor having a linear image pickup range of a predetermined length in a radial direction of the wafer; the wafer inspection apparatus further comprises rotation means for rotating the chuck table and the image pickup means relative to each other around the center of the wafer, and horizontally moving means for moving the chuck table and the image pickup means relative to each other in a diametrical direction of the wafer; and every time an image of the wafer is picked up by the image pickup means while the wafer is rotated by 360 degrees by the rotation means, the image pickup means is moved in a diametrical direction of the wafer by a distance corresponding to a length of the image pickup range by the horizontally moving means and then the pieces of picked up image data obtained by the image pickup of an overall area of the processed face are used to inspect the processed face of the wafer.