Added SRG algorithm

[annimesh2809]

An Implementation of the Seeded Region Growing Algorithm (Improved version) as explained in this paper. It can currently be used with various color models (like RGB, RGBA, GrayA etc) and also works with arrays having custom indices (like OffsetArrays). Multiple points can be given the same label to indicate that they belong to the same region. The srg function can be used as:

img_seg = srg(img, seeds, diff_fn)

Here, img is the input image seeds is a vector of Tuple{CartesianIndex{2}, Int}. Each seed corresponds to a point on the image along with a label (which is of type Int). This label is used to identify a region uniquely in the segmented image. diff_fn is a function to calculate δ between a region and a neighboring point.

Currently, the output is an array having indices similar to that of the input image. Each point of this array contains a label corresponding to the region to which it belongs. The label can be any of the seed labels or a special value (-4) that corresponds to a point that has same δ value for two (or more) neighbors (boundary tied points).

An example:

using Images, ImageSegmentation, ImageView

img = load("img.jpg")
img = centered(img)
imshow(img)
seeds = [(CartesianIndex(-54,-14),1), (CartesianIndex(66,-14), 2), (CartesianIndex(1,77), 3), (CartesianIndex(85,-83),4), (CartesianIndex(-79,96), 4)]
img_s = srg(img, seeds)
imshow(map(i->((i==3)?RGB(0,1,0):(i==2)?RGB(0,0,0):(i==1)?RGB(1,0,0):RGB(1,1,1)), img_s))

Original:

After segmentation (before changes):

After segmentation (after changes):

There are a few things which need to be discussed:

• We could give the user more control by adding some more features like custom neighborhood (which would default to 8-connectivity) and unrestricted labels (which would mean labels could be String, Float or anything else)
• The algorithm is restricted to 2-dimensional arrays but can be modified to be used with general N-dimensional arrays.
• Currently, the output is an array containing seed labels for segmented regions and a special value (-4) for tied points. This needs to changed as the user can provide (-4) as a seed label. I was thinking of a new return type

  type SegmentedImage{T<:AbstractArray,U}
  img::T
  segment_labels::Vector{U}
  segment_means::Dict{U,eltype(T)}
  segment_pixel_count::Dict{U,Int}
  end

  where, img::T is the result array that we get as output now. We can label the tied boundary points as -Inf or something like that.

Once we settle for an API, the documentation and tests could be added.

[annimesh2809]

UPDATES:

• The data type of region_means has been rectified, the output is much better now (see here).
• Support for N-dimensional images has been added (tested for 1-d, 2-d and 3-d arrays)
• Support for custom neighborhood has been added. Now users can define the neighborhood of each point of the image as a function of that point.
• Support for custom neighborhood as an N-dimensional kernel has also been added.
• User defined seed labels have been restricted to be positive integers and tied boundary points are labeled with '0'.
• The function returns a SegmentedImage type object that carries useful information regarding the segments like segment_means and segment_pixel_count along with the array containing the labels.

A nice demo:

Original:

After segmentation:

[timholy]

Sweet! That looks really nice!

[annimesh2809]

Docstring and tests have been added!

The improvement can be seen by comparing these to the previous outputs:

Original:

After segmentation (7 labels, 7 seeds):

---

Original:

After segmentation (2 labels, 8 seeds):

The color of the ith segment corresponds to seg.segment_means[i]

[codecov[bot]]

Codecov Report

:exclamation: No coverage uploaded for pull request base (master@582387a). Click here to learn what that means. The diff coverage is 100%.

@@           Coverage Diff           @@
##             master     #1   +/-   ##
=======================================
  Coverage          ?   100%           
=======================================
  Files             ?      2           
  Lines             ?     95           
  Branches          ?      0           
=======================================
  Hits              ?     95           
  Misses            ?      0           
  Partials          ?      0

Impacted Files	Coverage Δ
src/region_growing.jl	100% <100%> (ø)
src/core.jl	100% <100%> (ø)

---

Continue to review full report at Codecov.

Legend - Click here to learn more Δ = absolute <relative> (impact), ø = not affected, ? = missing data Powered by Codecov. Last update 582387a...32b5c9e. Read the comment docs.

[annimesh2809]

I think it is ready to merge. The travis and appveyor builds are fine with Julia 0.5, although they fail with Julia 0.7 due to LoadError in MacroTools.jl. Just wanted to ask, is the field-name img of SegmentedImage descriptive enough or should we change it? I could not think of any nice word to describe a map from indices to labels.

[timholy]

labeled_image comes to mind, although if I understand correctly that might be a bit misleading because it's really the indices to the labels. Would it make sense to bundle both img and segment_labels together into an IndirectArray? If you don't want to do that, perhaps image_indexmap?

[timholy]

And by all means hit "merge" when you are ready.