This is the first of two papers on the morphological analysis of H I features. In this first paper, we use the so-called metric space technique, developed by F. C. Adams and J. Wiseman. The metric space technique is an image analysis, mathematical formalism used to quantitatively compare astrophysical maps according to complexity. Instead of comparing maps on a pixel-by-pixel basis, we compare the maps' one-dimensional "output functions," which characterize specific morphological/physical aspects of the maps. The tool is used to analyze 28 H I features of known origin taken from the Canadian Galactic Plane Survey (CGPS), where the maps are scaled at 18'' per pixel (resolution of 1 cos δ arcmin). Technical and mathematical improvements to the formalism are presented. After classifying the 28 maps according to complexity, we searched for correlations between this complexity ranking and other quantifiable aspects of the H I features such as age, area, H I area, distance, flux from the ionizing star(s), fractal dimension, H I mass, and |z| (the absolute value of the height of the objects, above or below the Galactic plane). The most interesting correlations are (1) the higher the flux of UV photons, the more complex is the photodissociated H I feature, and (2) the older the supernova remnant, the more complex the H I associated with it. There is no correlation between the fractal dimension of the maps and their complexity or their physical characteristics, thus showing that the metric space technique could be used as a solution to the degeneracy of the fractal dimension.