System comprising a control unit and an apparatus for spatially capturing the surface of an object by means of stereo image recordings, having at least one colour camera oriented towards a recording region for arranging the object, wherein the at least one colour camera enables the recording of at least two images of the object at a triangulation angle from different recording directions, wherein furthermore - at least two illumination devices (21, 22, 23, 24) are provided, - the illumination devices (21, 22, 23, 24) are oriented towards the recording region from different illumination directions, - the illumination devices (21, 22, 23, 24) are configured to fully illuminate the recording region in each case two-dimensionally, - the at least two illumination devices (21, 22, 23, 24) are configured to emit light in different colours, wherein a highly resolved colour texture can be achieved in objects having a locally strong curvature, wherein colour regions are formed in the colours of the different illumination devices and also in mixed colours formed therefrom, - the control unit is assigned to the apparatus, - the mutually assigned image recordings produced at the triangulation angle are fed to the control unit, - the control unit is designed to assign correspondence points to one another at least on the basis of the colour of a respective location on the surface of a recorded object, - the at least one colour camera is configured as a line-scan camera, the line and/or lines of which is/are aligned transversely to a scanning direction of the line-scan camera, - the illumination devices (21, 22, 23, 24) are arranged transversely to the line and/or the lines of the line-scan camera and are oriented towards the recording region at an angle with respect to one another, and/or the illumination devices (21, 22, 23, 24) are arranged in the scanning direction and are oriented towards the recording region at an angle with respect to one another, and - at least one illumination device (21, 22, 23, 24) is arranged on one side and at least one second illumination device (21, 22, 23, 24) is arranged on the opposite side of an epipolar plane, and - the control unit is configured to capture a height profile along a line of the surface of the object transversely to the scanning direction from two recordings of the at least one line-scan camera from at least two recording directions and to perform three-dimensional capturing of the surface by combining successive height profiles. - at least two illumination devices (21, 22, 23, 24) are provided, - the illumination devices (21, 22, 23, 24) are oriented towards the recording region from different illumination directions, - the illumination devices (21, 22, 23, 24) are configured to fully illuminate the recording region in each case two-dimensionally, - the at least two illumination devices (21, 22, 23, 24) are configured to emit light in different colours, wherein a highly resolved colour texture can be achieved in objects having a locally strong curvature, wherein colour regions are formed in the colours of the different illumination devices and also in mixed colours formed therefrom, - the control unit is assigned to the apparatus, - the mutually assigned image recordings produced at the triangulation angle are fed to the control unit, - the control unit is designed to assign correspondence points to one another at least on the basis of the colour of a respective location on the surface of a recorded object, - the at least one colour camera is configured as a line-scan camera, the line and/or lines of which is/are aligned transversely to a scanning direction of the line-scan camera, - the illumination devices (21, 22, 23, 24) are arranged transversely to the line and/or the lines of the line-scan camera and are oriented towards the recording region at an angle with respect to one another, and/or the illumination devices (21, 22, 23, 24) are arranged in the scanning direction and are oriented towards the recording region at an angle with respect to one another, and - at least one illumination device (21, 22, 23, 24) is arranged on one side and at least one second illumination device (21, 22, 23, 24) is arranged on the opposite side of an epipolar plane, and - the control unit is configured to capture a height profile along a line of the surface of the object transversely to the scanning direction from two recordings of the at least one line-scan camera from at least two recording directions and to perform three-dimensional capturing of the surface by combining successive height profiles.