The author has the exclusive right to allow or forbid the modification of their work, whether or not this change is substantial or appropriate. This means you need the author’s permission, even if you think you have only changed minor details which make the photo look better.
However, a large number of Flickr users have chosen to place their works under the protection of Creative Commons licences. The “ND” (NoDerivs) attribution means that modification of the work is not authorised. If the author has not listed their work under this attribution, the licence allows users to publish retouched versions of the photo.