How do you cut out a high resolution photo? It depends on the picture of course. If you are cutting out a product – a mobile phone, say – then use the pen tool in Photoshop. Blow the image up big and follow the edge one or two pixels in using Bézier curves. Bézier is a town in the south of France that I’ve been through on a train from Calais to Perpignan. The name comes from Renault employee Pierre Bézier who invented a method of describing the cars’ curves mathematically with vectors.
If, however, you are cutting out a person with frizzy hair, then softened edges are needed. Feather selections by a few pixels or create an extra channel and paint with soft brushes.