This invention provides a system for measuring displacement of an object surface having a displacement sensor that projects a line on the object surface and receives light from the projected line at an imager in a manner defines a plurality of displacement values in a height direction. A vision system processor operates on rows of imager pixels to determine a laser line center in columns of imager pixels in each of a plurality of regions of interest. Each region of interest defines a plurality of rows that correspond with expected locations of the projected line on the object surface. A GUI can be used to establish the regions. In further embodiments, the system generates grayscale images with the imager. These grayscale images can be compared to a generated height image to compensate for contrast-induced false height readings. Imager pixels can be compared to a reference voltage to locate the line.