The morphological hit-or-miss operator can detect nodes in a skeleton (green). When changing the SE, it's possible to extract the end points (blue) of the skeleton ex: [image: EndPointsBranchedPoints-ConvexHullFails.png] using different kind of pixels configuration (structuring elements): [image: SE_branchedpoints.png] Several libs provides hit-or-miss operator, and mathematical morphologyl operators: - scipy (never get how to use it) <https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.ndimage.mo...> - opencv <https://vovkos.github.io/doxyrest-showcase/opencv/sphinx_rtd_theme/page_tuto...> (callable from python ?) - my favorite was mahotas <https://mahotas.readthedocs.io/en/latest/api.html#mahotas.hitmiss> - imagej has some plugins (Landini) implementing several morphological operators (hit-or-miss) - mamba <http://www.mamba-image.org/> - the very first lib, I tried <https://dip4fish.blogspot.com/2010/12/building-yayi-under-ubuntu-maverick.ht...> was yayi <http://raffi.enficiaud.free.fr/index.html> - pymorph ( pure python lib, mahotas ancestor) Iterative morphological erosion on a skeleton or on an edge can gives an anisotropy of a particle <https://dip4fish.blogspot.com/2011/12/how-to-rotate-faster-chromosomes.html> : [image: Spectrum orientation 06.png] I was interested in morphological skeleton to classify binary shapes on their skeleton. A first try can be to prune a skeleton <https://dip4fish.blogspot.com/2013/05/an-endpoints-spectrumpossible-features...> one end points pixel after another: [image: skelEP.png] to get a kind of end-point spectrum: [image: spectrum01.png] Of course, it's slow, that's why converting a skeleton into a graph could be useful. Regarding the edge, opencv provides things such convexhull, convexity (I found it incomplete <https://dip4fish.blogspot.com/2012/07/convexity-defects-in-cluster-of-mouse....> ). For example to analyse the bending of a contour, skimage provides a polygonal approximation, it's possible to get positive/negative (red/yellow points) "bending" domains of a contour curve <https://dip4fish.blogspot.com/2012/10/contour-looking-for-negatively-curved....> : [image: contour01.png] Le ven. 30 nov. 2018 à 11:48, Deepa <deepamahm.iisc@gmail.com> a écrit :

Just to be clear, I am just looking for ways of parsing the nodes and edges from the image

Thanks

On Fri, Nov 30, 2018 at 3:06 PM Deepa <deepamahm.iisc@gmail.com> wrote:

...

I checked the sknw package . I'm using the input matrix data of the skeleton image that is created using Mathematica. Here is my code that is written to highlight all the nodes and edges

from skimage.morphology import skeletonize from skimage import data import sknw import numpy as np import matplotlib.pyplot as plt import scipy.io as spio import networkx as nx from networkx.drawing.nx_pydot import write_dot mat = spio.loadmat('file.mat', squeeze_me=True) print(type(mat)) print(type(mat.get('Expression1'))) print(mat.get('Expression1')) img1 = mat.get('Expression1') print(img1) ske = skeletonize(img1).astype(np.uint16) # build graph from skeleton graph = sknw.build_sknw(ske)

# draw image plt.imshow(img1, cmap='gray')

# draw edges by pts for (s,e) in graph.edges(): ps = graph[s][e]['pts'] plt.plot(ps[:,1], ps[:,0], 'green')

# draw node by o node, nodes = graph.node, graph.nodes() ps = np.array([node[i]['o'] for i in nodes]) plt.plot(ps[:,1], ps[:,0], 'r.') #pos = nx.nx_agraph.graphviz_layout(graph) #print(pos) #plt.findpath(img1) # title and show plt.title('Build Graph') plt.show()

Please find the input file <http://goog_1659607921>.mat <https://github.com/DeepaMahm/cytoscape/blob/master/file.mat> file here. Even with sknw package I face the same problem when there are multiple edges.Please the output image attached. Some edges are not highlighted in green.

Could you please suggest how this can be improved?

On Thu, Nov 29, 2018 at 7:33 PM <imagepy@sina.com> wrote:

...

please see my mail earlier，skan and sknw on github.

----- 原始邮件 ----- 发件人: Leena Chourey<leenagour@gmail.com> 收件人: Mailing list for scikit-image (http://scikit-image.org)<; scikit-image@python.org> 主题: [scikit-image] Re: Converting an image to a skeleton 日期: 2018-11-29 19:40

I need solution for same. Pls share.

On Thu, 29 Nov 2018, 16:37 Deepa, <deepamahm.iisc@gmail.com> wrote:

I would like to generate a skeleton out of an image. The resulting output of the skeleton image has disconnected edges.

import skimage from skimage import data,io,filters import numpy as np import cv2 import matplotlib.pyplot as plt from skimage.filters import threshold_adaptive,threshold_mean from skimage.morphology import binary_dilation from skimage import feature from skimage.morphology import skeletonize_3d

imgfile = "Bagah.jpeg" im = cv2.imread(imgfile) image = cv2.cvtColor(im, cv2.COLOR_BGR2GRAY) thresh = threshold_mean(image) thresh = threshold_mean(thresh)

binary = image > thresh #dilate = skimage.morphology.binary_dilation(binary) gaussian = skimage.filters.gaussian(binary) edges = filters.sobel(gaussian) #dilate = feature.canny(edges)#binary,sigma=0) skeleton = skeletonize_3d(gaussian)#binary) fig, axes = plt.subplots(nrows=2,ncols=2, figsize=(8, 2))

ax = axes.ravel() ax[0].imshow(gaussian, cmap=plt.cm.gray)

ax[0].set_title('gaussian')

ax[1].imshow(skeleton, cmap=plt.cm.gray) ax[1].set_title('skeleton')

for a in ax: a.axis('off')

plt.show()

Please find the attachments of my input and output files.

I would like to translate this skeleton into a graph with nodes and edges.

Could someone suggest how to obtain a skeleton with connected edges?

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