We spoke in another thread about crossovers between figure sudoku and skyscraper. Possibly figure sudoku are not so well-known. So I'm giving an own puzzle of this variant. I guess that inventor of this variant is Vladimir Portugalov. He used letters. They can be repeated. But here are the rules for my puzzle:

Fill the grid with the digits 1 to 9. Each row, column and 3x3-box has exactly one of each digit. All occurrences of each shape outlined in black (rotated and/or mirrored) must contain the same set of digits (possibly in different orders). None shape contains a repeated digit.