Abstract: In a digitized picture, the orientation of the line is made nearly, but not exactly, parallel to a coordinate axis. Statistical analysis of the grid points or of the lattice points forming the line, preferably the former, gives the position and orientation of the line with high accuracy. Repeated measurements after small displacements of the line allows further improvement of the accuracy. Rectangular objects can be measured by taking differences between positions of opposite edges. The method can be extended to deal with curved lines, areas or the detection and measurement of edge or line features such as angles or properties of arcs. Measurement apparatus for practicing the method is also disclosed.