Image processing: Floor plan - detecting rooms' borders (area) and room names' texts

Question

Here is a simple building floor plan. I would like to derive the rooms as (rectangular) components and the names of the rooms. This is very common representation of building floor plans.

The problem

So far I could clean up the floor plan. However, only the walls are left as one component but I would like to derive the rooms as rectangular components. In the solution - The rooms may have polygonal shapes as well as rectangles with small rectangular components called circulation areas, corridors or an other function name... alternatively they could added to living room or any other near function. My Question is how to proceed from here?

Code to start with

img = Import["https://i.sstatic.net/qDhl7.jpg"]
nsc = DeleteSmallComponents[Binarize[img, {0, .2}]];
m = MorphologicalTransform[nsc, {"Min", "Max"}]

Cleaned up floor plan

EDIT 1

Some further information about the image.

The image contains 2 types of information.

1. The geometric
2. The Spatial

The Spatial information; it is important to abstract the room names for defining adjacency of spaces. The door and windows helps to define the adjacency matrix. The adjacency matrix with the geometric information can be used to calculate areas or boundaries. For example :

Answer 1

EDIT: Updated the algorithm, new part below

Fun problem!

Ok, my first would be to find the room centers. This is relatively easy using a distance transform and geodesic erosion.

distTransform = DistanceTransform[ColorNegate@m];
ImageAdjust[distTransform]

The distance transform image contains for every pixel the distance to the closest wall. We're looking for the bright "peak" in the distance transform, i.e. the center of each room.

centerAreas = ImageDifference[
    GeodesicDilation[Image[ImageData[distTransform] - 10], 
    distTransform], distTransform]

EDIT: The next part is new

With this, we can use a watershed transform to find the rooms. The watershed transform (intuitively speaking) finds "basins" in a 3d landscape. We'll invert the distance transform image to turn the "peaks" into "basins" and use the room centers as markers:

watershed = 
 DeleteSmallComponents[
  DeleteBorderComponents[
   Binarize[
    Image[WatershedComponents[ColorNegate[distTransform], 
      centerAreas]]]], 1000]

This segments the rooms quite well. Unfortunately, the watershed transform ignores the walls - the components we found are too big. But they're close enough that this simple "grow the room rectangle until it hits the wall"-algorithm finds the actual room areas:

rooms = ComponentMeasurements[watershed, "BoundingBox"];

Clear[growRect]
growRect[{{x1_, y1_}, {x2_, y2_}}] := 
 Module[{checkRectEmpty, growSingleDirection, growSingleStep, cx, cy, 
   left, top, right, bottom, sizeEstimate, size},
  (
   {cx, cy} = Round[{x1 + x2, y1 + y2}/2];

   checkRectEmpty[{left_, top_, right_, bottom_}] := 
    Max[ImageValue[
       m, {cx - left ;; cx + right, cy - top ;; cy + bottom}]] == 0;
   growSingleDirection[size_, grow_] := 
    If[checkRectEmpty[size + grow], size + grow, size];
   growSingleStep[size_] := 
    Fold[growSingleDirection, size, IdentityMatrix[4]];

   sizeEstimate = 
    Abs[Round[{x2 - x1, y2 - y1, x2 - x1, y2 - y1}/2 - 20]];
   {left, top, right, bottom} = 
    FixedPoint[growSingleStep, sizeEstimate, 20];
   Rectangle[{cx - left, cy - top}, {cx + right, cy + bottom}]
   )]

Using this, all that's left is to display the results:

finalRectangles = growRect /@ rooms[[All, 2]];

feetAndInch[n_] := ToString[Round[n/12]] <> "'" <> ToString[Mod[n, 12]]
Show[m,
 Graphics[
  {
   finalRectangles[[ ;; ]] /. 
    rect : Rectangle[{x1_, y1_}, {x2_, y2_}] :>
     {
      {EdgeForm[Red], Transparent, rect},
      {Red, 
       Text[StringForm["`` x ``\n``", feetAndInch@(x2 - x1), 
         feetAndInch@(y2 - y1), (x2 - x1)*(y2 - y1)/(144.)], {x1 + x2,
           y1 + y2}/2]}
      }
   }]]

or, using the original floor plan as background:

Answer 2

img = Import["https://i.sstatic.net/qDhl7.jpg"];
nsc = DeleteSmallComponents[Binarize[img, {0, .2}]];
iD = ImageDimensions[img];
mWS = 70; (*Max window span*)
sLT = 5;(*Straight line tolerance*)
i4 = Thinning@(i1 = Closing[MorphologicalTransform[nsc, {"Min", "Max"}], 3])

Now let's find the endpoints for each door and window by using HitMissTransform[] . We define some masks first:

k1 = ConstantArray[-1, 8];
v = {k1, {-1, -1, 0, 0, 1, 0, -1, -1}};
h = {k1[[;; 4]], {-1, -1, 1, 1}, {-1, -1, 0, 0}};

Now we find the candidate endpoints:

p = Position[ImageData@HitMissTransform[i4, #], 1] & /@ {v, Reverse@v, h, Reverse /@ h};
ListPlot[(Union @@ p) /. {a_, b_} -> {b, iD[[2]] - a}, Axes -> False, Frame -> True]  

Now we select only paired endpoints:

lin = Union[
 Select[Tuples[p[[1;;2]]], 0 < #[[1,1]] - #[[2,1]] < mWS && Abs[#[[1,2]] - #[[2,2]]] < sLT &],
 Select[Tuples[p[[3;;4]]], 0 < #[[1,2]] - #[[2,2]] < mWS && Abs[#[[1,1]] - #[[2,1]]] < sLT &]] /. 
                                     {{a_, b_}, {c_, d_}} -> {{b, iD[[2]] - a}, {d, iD[[2]] - c}};
Graphics[{Point@(Union @@ lin), Line@lin}, 
          PlotRange -> iD /. {x_, y_} -> {{1, x}, {1, y}}, Axes -> False, Frame -> True]

We finally "close" the doors and windows and use MorphologicalComponents[] to identify the rooms:

ColorNegate@ImageSubtract[img, Colorize@MorphologicalComponents@ Binarize@
            Erosion[Show[ColorNegate@i1, 
                   Graphics[Line@lin, PlotRange -> iD /. {x_, y_} -> {{1, x}, {1, y}}]], 1]]

Answer 3

first of all, this is a very interesting problem. I cannot provide you with a complete answer, however, if you apply

m = MorphologicalTransform[nsc, {"Max", "Min", "Max"}]

you can use

(mc = MorphologicalComponents[ColorNegate@m]) // Colorize

to find a fair number of the rooms. The expressions

lines = ImageLines[m, Method -> "RANSAC", MaxFeatures -> 15];
Show[m, Graphics[{Thickness[0.01], Blue, Line /@ lines}]]

actually let you find the walls. ImageLines has more options, so

lines = ImageLines[m, Method -> "Hough", "Segmented" -> True];
Show[m, Graphics[{Thickness[0.01], Blue, Line /@ lines}]]

can restrict the search to walls inside the house.