Fill in an incomplete outline of an image

Question

I have an outline which I have extracted from an image, which may well not entirely closed, for instance:

I now want to fill the inside of this, as another image, using the convex hull if it is not closed.

For instance:

img = Import["https://i.stack.imgur.com/yC9ym.png"];
ConvexHullMesh[PixelValuePositions[img, 1]]

is the right shape, but is a mesh rather than an image and now in a different coordinate system.

FillingTransform doesn't seem to work, presumably because the outline is not complete. ComponentMeasurements[img, "ConvexVertices"] gives me the points that make up the convex hull, but I can't manage to fill in the middle in an easy (and ideally fast way).

Rasterizing the ConvexHullMesh has been suggested in the comments, but that doesn't appear to work for me, as the ConvexHullMesh zooms into the image.

HighlightImage[Rasterize[ConvexHullMesh[PixelValuePositions[img, 1]], 
    RasterSize -> ImageDimensions[img]], img]

$Version
(* "11.3.0 for Mac OS X x86 (64-bit) (March 7, 2018)" *)

Answer 1

pvp = PixelValuePositions[img, 1];
Graphics[{LightBlue, EdgeForm[Blue], Polygon[pvp[[FindShortestTour[pvp][[2]]]]]}]

ImageAdd[img, 
 Graphics[{Red, EdgeForm[Blue], Polygon[pvp[[FindShortestTour[pvp][[2]]]]]}, 
  PlotRange -> Thread[{0, ImageDimensions[img]}]]

Answer 2

Turns out that MorphologicalComponents will give the convex hull:

imageHull = Image@MorphologicalComponents[img, Method -> "ConvexHull"]

HighlightImage[imageHull, img]

I am still interested in a solution that doesn't require ConvexHull for the whole image, but just fills in the missing hole where there is a gap.

Answer 3

First, extract the points from the image and take the convex hull mesh:

ClearAll["Global`*"]
img = Import["https://i.stack.imgur.com/yC9ym.png"];
allpts = PixelValuePositions[img, 1];
chmesh = ConvexHullMesh@allpts;

Use MeshPrimitives to extract the boundary lines. Extract their endpoints. Since the endpoints are not unique, take every other end point to obtain a set of unique points on the convex hull:

endpts = Flatten[MeshPrimitives[chmesh, 1] /. Line -> List, 2];
hullpts = Take[endpts, {1, -1, 2}];

Plot the results:

Graphics[{Black, PointSize[1/300], Point@allpts,
  Red, Line[hullpts],
  Opacity[1/8], Blue, FilledCurve@Line[hullpts] }]

EDIT:

What we are really after is an image of the filled curve that will overlay the original image, which has ImageDimensions of {1024,1024}. We want to use ImagePadding to position the filled image on the original image. The amount of padding is first estimated by looking at the minimum and maximum coordinates in allpts, then adjusting by a small $\delta$. Instead of the original image let's work with its negative.

MinMax/@Transpose[allpts]
δ = 16;
filled = Image[Graphics[
    {Opacity[1/8], Red, FilledCurve@Line[hullpts]},
    ImagePadding -> {{137 - δ, 
       1024 - 895 - δ}, {114 - δ, 
       1024 - 917 - δ}}], 
   ImageSize -> ImageDimensions[reverse]];
reverse = ColorNegate[img];
Show[{reverse, filled}, ImageSize -> 200]

(*   {{137, 895}, {114, 917}}   *)

To verify that $\delta = 16$ is optimal, we can use ImageTake to zoom in on the left edge, say,

β = 20;
Show[ImageTake[#, {512 - β, 512 + β}, {137 - β, 
     137 + β}] & /@ {reverse, filled}, ImageSize -> 200, 
 Frame -> True]

Here we have zoomed in on both the reverse image and the filled image at about 137 pixels from the left and 512 pixels from the top. Our view frame is $2\beta$ square. We could adjust $\delta$ a little to see how the filled image shifts relative to the reverse image. We can also zoom in to check the fit at other critical points of the image.

Answer 4

As stated in the comments, ConvexHullMesh works as desired for me on Windows.

Windows 7

$Version
(* "11.3.0 for Microsoft Windows (64-bit) (March 7, 2018)" *)

img = Import["https://i.stack.imgur.com/yC9ym.png"];
meshraster = Rasterize[ConvexHullMesh[PixelValuePositions[img, 1]], RasterSize -> ImageDimensions[img]];
HighlightImage[meshraster, img]

Mac OS

I just ran it on Mac OS 10.13. I have no words.

$Version
(* "11.3.0 for Mac OS X x86 (64-bit) (March 7, 2018)" *)