We report a method of imaging of the magnetization reversal process using analysis of real-time images of magnetic domain structures in cylindrically shaped microwires. This method uses wide-field polarizing optical microscopy and is based on the magneto-optical Kerr effect (MOKE). The aperture diaphragm in MOKE microscope was used to control the incident angles of the light rays that reached the non-planar surface of the microwire and also determined the MOKE geometries. The movement of the non-central position of the hole in this diaphragm leads to a change in the orientation of the plane of incidence of the light along the perpendicular or the parallel direction to the axial direction of the wire. The visualization of the surface magnetic domain structures is obtained using polar and longitudinal MOKE geometries. The hysteresis loops were obtained by plotting the averaged image contrast as a function of the external magnetic field. The separation of the all-magnetization components is performed using different MOKE geometries in a microscope. We demonstrate the use of vector magnetometry to analyze the orientation of the magnetization in a cylindrically shaped microwire under the influence of an external magnetic field.