We look at the structure of the family of perfect sets from an ideal I on the real line . We restrict our attention to ideals on which are dense on perfect sets (i.e. each perfect set contains a perfect subset from the ideal). To compare different ideals from the point of view of their perfect members we use perfect isomorphisms. A bijection f from onto is a perfect isomorphism if and only if it is measurable with respect to the field of Marczewski's sets. We describe canonical perfect isomorphisms of and apply this description to build some examples. Further we look at intersections of families of ideals and their traces on perfect sets.