I start by using the dots at the edge of the grid to place the 1s in the first two rows and the bottom row, and the extra lines that that leads to. This fully determines the shape of the top left region, so I am also able to place the 2 in the top row. The 2 can also be placed in the second row, and the lower line from this fully determines the shape of the top right region. I can now use the dots to place the 2 in the third row, and the lower line from that. The remaining two 1s can be placed, along with the extra lines they tell us. It is now straightforward to place all of the other lines. This fixes the 2, 3 and 4 of the lower right shape (and so therefore also the 5). The final 2 can be placed in the bottom corner. The dot tells us the position of the 3 in the backwards L region, and the lack of dot tells us where the 3 goes in the S region. The last two 3s can now also be placed. From here on in, there is always a row, column or shape that only needs one more number to be complete.