How to segment rectangular photographs on a table?

Here's an idea, but it only works (partially) with the easiest of the test cases.

img = CloudGet[CloudObject["https://www.wolframcloud.com/objects/068cf32f-b753-4c38-bc01-
f378bc64d54a"]][[5]]

(* Binarize - this step depends a lot on the background in the image *)
img2 = ChanVeseBinarize[img, Automatic, {Automatic, Automatic, 2, 1}]

(* Find hulls, and discard ones that are tiny or touching a border *)
comps = MorphologicalComponents[img2, Method -> "ConvexHull"];
comps2 = SelectComponents[comps, #AdjacentBorderCount == 0 && #Count > 50 &];

(* show perimeters, to see how it's working *)
perims = ComponentMeasurements[comps2, "PerimeterPositions"];
HighlightImage[img, {PointSize[Medium], Red, Point @@@ perims[[All, 2]]}]

(* Extract the single images *)
singleimgs = ComponentMeasurements[ {comps2, img} , "MaskedImage"][[All, 2]]

transform[img_] := 
 Module[{img2, frame, comp, p, c, c2, cornerdemo, t, img3},
  
  (*add some padding,to make the corner detection work better*)
  img2 = ImagePad[img, 2];
  
  (*get the perimeter of the image*)
  frame = AlphaChannel[img2];
  comp = MorphologicalComponents[frame, Method -> "ConvexHull"];
  p = Flatten[
    ComponentMeasurements[comp, "PerimeterPositions"][[1, 2]], 1];
  
  (*find the corners of the image*)
  c = Sort[ImageCorners[frame, 5, 0.01]];
  
  (*the desired new corners*)
  c2 = Sort[Tuples[MinMax /@ Transpose[p]]];
  
  (*just to demonstrate the corner detection*)
  colors = {Red, Orange, Yellow, Blue};
  cornerdemo = 
   Show[frame, 
    Graphics[{Table[{colors[[n]], Disk[c2[[n]], 5]}, {n, 4}]}], 
    Graphics[Table[{colors[[n]], Circle[c[[n]], 5]}, {n, 4}]]];
  
  (*transform such that the image corners are mapped to the desired corners*)
  t = Last[FindGeometricTransform[c2, c]];
  img3 = ImagePerspectiveTransformation[img2, t, DataRange -> Full];
  
  {cornerdemo, img3}]

transform /@ singleimgs

With some of the examples given, we can bring all the images in the correct position at once, before extracting them. Here I chose 4 points using the coordinates tool.

imgs = CloudGet@
   CloudObject[
    "https://www.wolframcloud.com/objects/068cf32f-b753-4c38-bc01-
f378bc64d54a"];

fourPoints = {{43.8398, 70.2148}, {336.398, 68.4375}, {342.199, 219.031}, {56.6094,209.16}}

This function processes the image. It takes the image and the four points.

processImage[img_, pts_List] := (
  rect = {{pts[[1]][[1]], pts[[1]][[2]]}, {pts[[3]][[1]], 
     pts[[1]][[2]]}, {pts[[3]][[1]], pts[[3]][[2]]}, {pts[[1]][[1]], 
     pts[[3]][[2]]}};
  transform = FindGeometricTransform[rect, pts][[2]];
  Show[fullImage = 
    Sharpen[ImagePerspectiveTransformation[img, transform, 
      PlotRange -> Full], 1], 
   Graphics[{PointSize[Large], Green, Point[rect], Transparent, 
     EdgeForm[Green], Polygon[rect]}], ImageSize -> Medium]
  )

processImage[imgs[[1]],fourPoints];

Now we isolate the pictures.

perim = MorphologicalPerimeter[fullImage, 60];
i2 = DeleteSmallComponents[perim];
morphBox = MorphologicalTransform[i2, {"BoundingBoxes", "Clean"}, Infinity]; 
ima=ImageMultiply[fullImage,morphBox];

Extract as a list of images and discard those not meeting a certain dimensions.

singles = ComponentMeasurements[ima, "MaskedImage"][[All, 2]];
validSingles = 
 Select[singles, 
  0.4 < Min[ImageDimensions[#]]/Max[ImageDimensions[#]] &]

Go through the list of images and attempt to trim the borders. It is difficult to get something that will work for all images, particularly when the border is the same color as the background of the photo. This works for some images, but not all of them.

imageList = {};
n = 1;
While[n <= Length[validSingles],
 v = validSingles[[n]];
 dim = ImageDimensions[v];
 bd = BorderDimensions[ImageAdjust[v, {-0.1, 0.1}], 0.04];
 crop1 = ImageCrop[v, 
   dim - {bd[[1]][[1]], bd[[2]][[1]]}, {Left, Bottom}];
 dim2 = ImageDimensions[crop1];
 crop2 = ImageCrop[crop1, 
   dim2 - {bd[[1]][[2]], bd[[2]][[2]]}, {Right, Top}];
 AppendTo[imageList, crop2];
 n++;
 ]
Row[imageList, "  "]

Better with a black background.