How to divide the image into several irregular parts according to this grid

Question

I see the method of image segmentation here.

I can use the ImagePartition function to divide the image into several regular sub images

img=Import["https://i.stack.imgur.com/vn5ot.jpg"]
ImagePartition[img, 120] // Grid

But how to divide the image into several irregular parts according to this grid:

Answer 1

Rather than trying to process the puzzle image, we can work with the procedure that produced it (from Vasiliy Kaurov's wonderful blog page Designing Jigsaw Puzzles with Mathematica).

Two things we need to add: (1) We need to get polygon primitives with wiggled edges rather than lines, and (2) We need to use the input image as Texture for polygon primitives rather than graphics background.

ClearAll[bSF, jiggedlines, match, jiggedfaces, vtc, jiggle]

bSF[{p1_, p2_}] := With[{pm = Mean[{p1, p2}], dp = (p2 - p1)/5, 
   rc = RandomChoice[3 {-1, 1}/4]}, 
  BSplineFunction[{p1, pm, pm - dp + rc {1, -1} Reverse[dp], 
    pm + dp + rc {1, -1} Reverse[dp], pm, p2}, 
   SplineWeights -> {1, 15, 25, 25, 15, 1}]]

jiggedlines[mesh_] := Join[MeshPrimitives[mesh, {"Lines", "Boundary"}],
   (Join @@ (MeshPrimitives[mesh, {"Lines", #}] & /@ {"Interior", "Frontier"})) /. 
     Line[x_] /; ArcLength[Line[x]] > 0.25 :> (bSF[x] /@ Subdivide[50])] /. Line[x_] :> x;

match[coords_] := If[#[[{1, -1}]] == coords, #, Reverse@#] &@*
  SelectFirst[#[[{1, -1}]] == coords || #[[{-1, 1}]] == coords &]

jiggedfaces[mesh_] := Module[{jl = jiggedlines[mesh]}, 
   MeshPrimitives[mesh, "Polygons"] /. 
     Polygon[x_] :> Join @@ (match[#][jl] & /@ Partition[x, 2, 1, 1])];

Examples:

image = Import["https://i.stack.imgur.com/MVClL.jpg"];
image = ImageCrop[image, {448, 448}];

id = ImageDimensions[image];
SeedRandom[1]
vm = VoronoiMesh[Transpose[RandomReal[{0, #}, 9] & /@ id],
  Thread[{0, id}], ImageSize -> id];

Row[{Graphics[lines, ImageSize -> 400],
  Graphics[{Opacity[.7], RandomColor[], EdgeForm[Gray], Polygon@#} & /@
     jiggedfaces[vm], ImageSize -> 400]}]

To use the input image as Texture for individual polygons, we need a function to determine VertexTextureCoordinates:

vtc[mesh_] := Transpose[MapThread[Rescale[#, #2] &,
      {Transpose[#], CoordinateBounds[mesh]}]] &;

Texturized puzzle pieces:

pieces = Graphics[{Texture@image, EdgeForm[Gray], 
      Polygon[#, VertexTextureCoordinates -> vtc[vm][#]]}] & /@ jiggedfaces[vm];

Row[Panel /@ {image, 
   Pane[Grid[Partition[pieces, 3]], ImageSize -> {Automatic, 448}, 
    ImageSizeAction -> "ShrinkToFit"]}, Spacer[5]]

Show the pieces together or jiggle location/scale/orientation randomly:

ClearAll[jiggle]
jiggle[ctr_] := Function[{x, y}, Rotate[Translate[Scale[x[[1]], {.95, .95}, y], 
     RandomReal[{.05, .2}] (y - ctr)], RandomReal[{-Pi/16, Pi/16}], y]];

centroids = RegionCentroid @ jiggedfaces[vm];
center = RegionCentroid[vm];

SeedRandom[1]
Row[{Show[pieces, ImageSize -> 400], 
  Graphics[MapThread[jiggle[center], {pieces, centroids}], ImageSize -> 400]}, Spacer[10]]

Replace Texture @ image with

Texture @ Rasterize[Show[RemoveBackground@image, 
   Background -> Opacity[.5, ColorData["Rainbow"][RandomReal[]]]]]

to make pieces with different background colors:

Replace Texture @ image with

Texture @ ImageMultiply[image, Append[ RandomColor[], .3]]

to tint each piece with a random color: