Flow behavior in complex three-dimensional (3D) microscale domains is the key in the development of microcirculatory pathologies and the design of 3D microfluidics. While numerical simulations are common practice for the derivation of velocity fields in such domains, they are limited to known geometries. Current experimental methods such as micron-scale particle tracing comprise of intricate algorithmic approaches for the accurate tracing of numerous particles in a dense moving liquid suspension and are fundamentally limited in resolution to the finite size of the interrogated steps. Here, we introduce 3D streamlines image velocimetry (3D-SIV), a method to derive fluid velocity fields in arbitrary resolution for fully developed laminar flow in 3D geometries. Our approach utilizes 3D geometrical fitting and superimposed Delaunay triangulation to reconstruct streamtubes and to trace their volumetric changes. Our algorithm has applications in out-of-plane velocimetries, which we demonstrate in a 3D dilated curved geometry and in an ascending aorta. The 3D-SIV can be applied for high-resolution derivation of velocity fields in microcirculatory pathologies and to 3D microfluidic circuits, extending the potential of out-of-plane velocimetries to complex geometries and arbitrary resolution.