one camera 22 is shown in fig1 although a plurality of preferably identical cameras 22 can be provided at different positions the at least one camera 22 can generate an image preferably a three dimensional image of the item 10 of laundry at the transfer point 21 this image reproduces the surface profile or topography of at least one part of the item 10 of laundry in the region of the transfer point 21 accordingly the clamp 20 of the transport device 18 located in each case at the transfer point 21 can grip an arbitrary corner 23 of the item 10 of laundry the end 24 of the rail 19 of the transport device 18 situated opposite the gripping device 15 shown to the right in fig1 is located at a reorientation point 25 at this reorientation point 25 the item 10 of laundry held at a corner 23 by the clamp 20 initially hangs down freely the surface profile or topography of the item 10 of laundry hanging down from the clamp 20 at the reorientation point 25 is in turn determined by at least one camera 22 to generate preferably a three dimensional image in the shown exemplary embodiment two opposite preferably identical cameras 22 are shown which record the surface profile or topography of the item 10 of laundry from opposite sides of the item 10.