Problems with automated techniques for measuring boundary fractal dimensions using structured walks are described and a new method is proposed, coordinate averaging. The actual polygon generated by a structured walk is variable and depends upon the chosen starting point. This noise is apparent in the resulting Richardson plots. The use of multiple starting points enhances the Fast (equipaced) method but is less productive with the Hybrid (fixed step) method because the paths followed around the perimeter tend to converge. Coordinate averaging uses perimeters that have been mapped as a list of sequential coordinates. They are then examined by averaging every coordinate with an increasing number of neighbours. The resulting family of shapes progressively shed detail and can be used to generate fractal dimensions. Coordinate averaging appears to be free from the noise found with structured walks and is able to examine highly convoluted shapes. In addition it appears well suited to the examination of the homogeneity of boundaries and can follow the detailed evolution of individual features.