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Extracting road curves from an image


I have taken several gps readings while driving around town.


gpsPositions=GeoPosition[{{33.657, -84.5197}, {33.6687, -84.4977}, 
{33.692, -84.4907}, {33.7057, -84.4287}, {33.7431, -84.4027}, {33.7285, 
-84.3493}}]

map = GeoGraphics[GeoMarker[gpsPositions], 
  GeoRange ->Entity["City",{"Atlanta","Georgia","UnitedStates"}],ImageSize->Large]

Mathematica graphics



Were are able to extract the main roads by the following functions:


    bgnd = GeoGraphics[ GeoRange ->Entity["City",{"Atlanta","Georgia","UnitedStates"}],ImageSize->Large];
    roads = DeleteSmallComponents@
      Thinning@ImageAdd[
        Dilation[#, DiskMatrix[3]] & /@ 
         DominantColors[bgnd, 7, {"CoverageImage", "Color"}][[5 ;; 6, 1]]];
    ImageCompose[map, ColorNegate@SetAlphaChannel[roads, roads]]

Mathematica graphics


Road Extraction worked fine. Now convert the gpsPositions and map them to the road image.



range = Abs[#1 - #2] & @@@ map[[8, 2]]    
origin = #1 & @@@ map[[8, 2]];
max = Reverse@ImageDimensions[roads];
waypoints = gpsPositions[[1]];
points = Reverse@(Round[(max (#)/range), 1]) & /@ ((# - origin) & /@ 
     waypoints);
Show[ColorNegate@roads, 
 Graphics[{Red, PointSize[Large], Point[points]}]]

Mathematica graphics



I would like to be able to segment the lines between the dots. Then, set up an interpolation function between each dot so we can simulate the placement of the vehicle at any point of the road as needed.


Any thoughts on how this can be achieved?



Answer



I'm not 100% sure what you want: "segmentation" has a well-defined meaning in image processing, and I think that's not what you want. Also, I couldn't reproduce your results (I think DominantColors isn't guaranteed to give the same order or even the same results every time it's run). So this may or may not help...


First, this seems more reproducible than DominantColors:


roadColors = List @@@ {Yellow, Blue};

colorDist = 
  Total[(# - 
        Transpose[

         ImageData[bgnd][[All, All, ;; 3]], {2, 3, 1}])^2] & /@ 
   roadColors;

roads = Thinning[
  MorphologicalBinarize[
   Closing[Image[1 - MapThread[Min, colorDist, 2]], 
    DiskMatrix[3]], {0.43, 0.8}]]

Next, I convert the white pixel locations to a graph:


whitePixels = PixelValuePositions[roads, 1];


nearestFn = Nearest[whitePixels -> Automatic];

edges = MapThread[
   Function[{point, potentialNeighbors}, 
    point <-> # & /@ 
     Select[potentialNeighbors, 
      0 < EuclideanDistance[whitePixels[[#]], whitePixels[[point]]] < 
        2 &]],
   {Range[Length[whitePixels]], nearestFn[#, 10] & /@ whitePixels}];


g = Graph[DeleteDuplicates@Flatten[edges]];

Now, if I choose point locations in the image:


pts = {{133, 97}, {464, 461}};
LocatorPane[Dynamic[pts], ColorNegate@roads]

I can use nearestFn to find the nearest road pixel, and FindShortestPath to find the shortest path between two points:


path = FindShortestPath[g, nearestFn[pts[[1]]][[1]], 
   nearestFn[pts[[2]]][[1]]];


Show[Image@bgnd, 
 Graphics[{Red, Line[whitePixels[[path]]], PointSize[Large], 
   Point[whitePixels[[path[[;; ;; 10]]]]]}]]

enter image description here


We can even make a little Indiana Jones-style animation:


Animate[Show[Image@bgnd, 
  Graphics[{Red, Thick, Line[whitePixels[[path[[;; i ;; 2]]]]]}]], {i,
   1, Length[path], 1}]


(unfortunately, I don't think I can upload videos to Mathematica.SE)


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