Cell migration is commonly quantified by tracking the speed of the cell layer interface in wound healing assays. This quantification is often hampered by low signal to noise ratio, in particular when complex substrates are employed to emulate in vivo cell migration in geometrically complex environments. Moreover, information about the cell motion, readily available inside the migrating cell layers, is not usually harvested. We introduce Cell Image Velocimetry (CIV), a combination of cell layer segmentation and image velocimetry algorithms, to drastically enhance the quantification of cell migration by wound healing assays. The resulting software analyses the speed of the interface as well as the detailed velocity field inside the cell layers in an automated fashion. CIV is shown to be highly robust for images with low signal to noise ratio, low contrast and frame shifting and it is portable across various experimental settings. The modular design and parametrization of CIV is not restricted to wound healing assays and allows for the exploration and quantification of flow phenomena in any optical microscopy dataset. Here, we demonstrate the capabilities of CIV in wound healing assays over topographically engineered surfaces and quantify the relative merits of differently aligned gratings on cell migration.