Quantification of the structure and composition of biomaterials using micro-CT requires image segmentation due to the low contrast and overlapping radioopacity of biological materials. The amount of bias introduced by segmentation procedures is generally unknown. We aim to develop software that generates three-dimensional models of fibrous and porous structures with known volumes, surfaces, lengths, and object counts in fibrous materials and to provide a software tool that calibrates quantitative micro-CT assessments. Virtual image stacks were generated using the newly developed software TeIGen, enabling the simulation of micro-CT scans of unconnected tubes, connected tubes, and porosities. A realistic noise generator was incorporated. Forty image stacks were evaluated using micro-CT, and the error between the true known and estimated data was quantified. Starting with geometric primitives, the error of the numerical estimation of surfaces and volumes was eliminated, thereby enabling the quantification of volumes and surfaces of colliding objects. Analysis of the sensitivity of the thresholding upon parameters of generated testing image sets revealed the effects of decreasing resolution and increasing noise on the accuracy of the micro-CT quantification. The size of the error increased with decreasing resolution when the voxel size exceeded 1/10 of the typical object size, which simulated the effect of the smallest details that could still be reliably quantified. Open-source software for calibrating quantitative micro-CT assessments by producing and saving virtually generated image data sets with known morphometric data was made freely available to researchers involved in morphometry of three-dimensional fibrillar and porous structures in micro-CT scans.