Accurate measurements of galaxy structure are prerequisites for quantitative investigation of galaxy properties or evolution. Yet galaxy inclination, through projection and varying dust effects, strongly affects many commonly used metrics of galaxy structure. Here we demonstrate that collapsing a galaxy's light distribution onto its major axis gives a "linear brightness profile" that is unaffected by projection. In analogy to widely used half-light radius and concentrations, we use two metrics to describe this light distribution: x_50_, the linear distance containing half of the galaxy's luminosity, and c_x_=x_90_/x_50_, the ratio between the 90% light distance and the 50% light distance. In order to minimize the effects of dust, we apply this technique to a diverse sample of galaxies with moderately deep and high-resolution K-band imaging from the UKIDSS Large Area Survey. Using simulated galaxy images, we find that while our measurements are primarily limited by the surface brightness in the outer parts of galaxies, most local galaxies have high enough surface brightnesses to result in reliable measurements. When applied to real data, our metrics vary from face-on to edge-on by typically ~5% in c_x_ and ~12% in x_50_, representing factors of several to 10 improvement over existing optical and some infrared catalog measures of galaxy structure. We release a sample of 23804 galaxies with inclination-independent and dust-penetrated observational proxies for stellar mass, specific star formation rate, half-light size, and concentration.