The palace had come under mounting pressure to reveal the truth behind the image after international picture agencies withdrew it over claims that it had been manipulated.
Kate, in a statement released on social media, said this morning: "Like many amateur photographers, I do occasionally experiment with editing. I wanted to express my apologies for any confusion the family photograph we shared yesterday caused. I hope everyone celebrating had a very happy Mother's Day."
The photograph of Kate and her children, taken by the Prince of Wales, was the first to be issued since the princess's abdominal surgery and was released by the palace to mark Mothering Sunday.
It is understood William and Kate wanted to offer an informal picture of the family together, with the princess making "minor adjustments".
It was withdrawn with a "Kill" notice by picture agencies last night and the UK's PA news agency this morning because of suspicions it had been manipulated. The controversy the palace's initial reluctance to comment served to fuel online speculation about Kate since her abdominal surgery in January.
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