We present an nD image processing paradigm to obtain high precision estimates of geometric object properties such as volume, surface area, and length from digitized data. We prove that the weighted sum of all pixel values after a suitable transformation is a sampling compatible measurement technique. Applied to binary images, which are hampered by aliasing and discretization errors, a weighted sum of pixels yields a limited precision, which depends heavily on the sampling density. Applied to gray-scale images we show that our measurement procedure yields order(s) of magnitude better precision than its binary counterpart, due to absence of discretization effects.