This thesis describes a measurement methodology and set of tools for measuring scanning tunneling microscope images of crystals at picometer length scales. We use the crystal structure present in high-quality scanning tunneling microscope images as an internal standard to measure distortion caused by thermal drift of the scanning tunneling microscope tip and piezoelectric actuator nonlinearities introduced during the scan. Using a model for these sources of distortion, we calculate an inverse distortion transform and apply it to the image. By taking advantage of spatial and temporal averaging of corrected images, we can make high-precision measurements of the surface structure and its aggregate noise. We applied this technique to images of graphite and alkanethiol self-assembled monolayers on Au(111). Our measurements of graphite were consistent with our expectations, with noise level as low as ±3.5 pm. Preliminary results for alkanethiol self-assembled monolayers show measurements of their tilt direction and twist structure, confirmation of the 4-molecule-basis lattice, and a strong dependence of image results on the condition of the probe tip.