Remove a set of grids taking into account its overall geometry

Question

I have a bunch of grids (100x100m) and I need to remove some of them considering the linear shape that forms some sets forms.

I've blue circled the set of grids I need to remove.

What I thought since now is to count the number of adjacent vertex of each one of the grids. Considering that a square has 4 vertex, if a grid only share two sides (having the id of 2 different grids 4 times one for each vertex shared) that means only have 2 adjancents grids what forms the linear shape. I thought as well dissolving the grid by his adjacents to set the sets of geometries (1, 2, 3 in image) to remove the whole grids with a dissolved geometry. Also if I do a dissolve, I could aggregate the total number of vertex and get a score considering how many vertex the grid shares.

Any theorical ideas or any script/tool you know that do something similar?

Answer 1

1. Dissolve (with keep disjoint feature separate)
2. Buffer with a negative distance. My grid size is 2000*2000 m and i buffer with -1400
3. Extracy by location the input grid cells intersecting the buffer

Answer 2

Dissolve all cells to get one large polygon, buffer with a negative value, corresponding to the size of each cell, thus eliminating those parts just one cell thick, then again buffer with the same value as before, but positive.

You can do that with this expression in one step:

case 
when $id=maximum($id) 
then 
    collect_geometries(
        buffer (
            buffer (
                buffer (collect ($geometry),0), -- dissolve all cells to one large polygon
                -100, 
                join:='miter'
            ),
            100, 
            join:='miter'
        )
    )
end