What is skeletor?\n\nUnlike its namesake, this skeletor\ndoes not (yet) seek to conquer Eternia but to turn meshes into skeletons.
\n\nBefore we get started some terminology:
\n\n\n- a mesh is something that consists of vertices and faces
\n- a skeleton is a (hierarchical) tree-like structure consisting of vertices\n(also called nodes) and edges that connect them
\n
\n\nSkeletons are useful for a range of reasons. For example:
\n\n\n- Typically smaller (less vertices) than the mesh
\n- Have an implicit sense of topology (e.g. \"this node is distal to that node\")
\n
\n\nExtracting skeletons from meshes (or other types of data such as voxels) is\nnon-trivial and there are a great many research papers exploring various\ndifferent approaches (see Google scholar).
\n\nskeletor implements some algorithms that I found useful in my work with\nneurons. In my experience there is unfortuntely no magic bullet when it\ncomes to skeletonization and chances are you will have to fiddle around a bit\nto get decent results.
\n\nInstallation
\n\nFrom PyPI:
\n\n\n
pip3 install skeletor\n
\n
For the bleeding-edge version from Github:
\n\n\n
pip3 install git+https://github.com/navis-org/skeletor@master\n
\n
Getting started
\n\nA skeletonization pipeline typically consists of:
\n\n\n- Some pre-processing of the mesh (e.g. fixing some potential errors like\ndegenerate faces, unreferenced vertices, etc.)
\n- The skeletonization itself
\n- Some post-processing of the skeleton (e.g. adding radius information, smoothing, etc.)
\n
\n\n
\n\nHere is a complete list of available functions:
\n\n\n\n\n | function | \n description | \n
\n\n\n\n | example data | \n | \n
\n\n skeletor.example_mesh() | \n load an example mesh | \n
\n\n | pre-processing | \n | \n
\n\n skeletor.pre.fix_mesh() | \n fix some common errors found in meshes | \n
\n\n skeletor.pre.remesh() | \n re-generate mesh (uses Blender 3D) | \n
\n\n skeletor.pre.simplify() | \n reduce mesh complexity (uses Blender 3D) | \n
\n\n skeletor.pre.contract() | \n contract mesh to facilitate skeletonization [1] | \n
\n\n | skeletonization | \n | \n
\n\n skeletor.skeletonize.by_wavefront() | \n very fast, works well for tubular meshes (like neurons) | \n
\n\n skeletor.skeletonize.by_vertex_clusters() | \n very fast but needs mesh to be contracted (see above) | \n
\n\n skeletor.skeletonize.by_edge_collapse() | \n presented in [1] but never got this to work well | \n
\n\n skeletor.skeletonize.by_teasar() | \n very fast and robust, works on mesh surface | \n
\n\n skeletor.skeletonize.by_tangent_ball() | \n very fast, best on smooth meshes | \n
\n\n | postprocessing | \n | \n
\n\n skeletor.post.clean_up() | \n fix some potential errors in the skeleton | \n
\n\n skeletor.post.radii() | \n add radius information using various method | \n
\n\n skeletor.post.smooth() | \n smooth the skeleton | \n
\n\n skeletor.post.remove_bristles() | \n remove single-node bristles from the skeleton | \n
\n\n skeletor.post.despike() | \n smooth out jumps in the skeleton | \n
\n\n
\n\n
\n\nSee docstrings of the respective functions for details.
\n\nA pipeline might look like this:
\n\n\nskeletor.pre.fix_mesh() to fix the meshskeletor.pre.simplify() to simplify the meshskeletor.pre.contract() to contract the mesh [1]skeletor.skeletonize.by_vertex_clusters() to generate a skeletonskeletor.post.clean_up() to clean up some potential issues with the skeletonskeletor.post.smooth() to smooth the skeletonskeletor.post.radii() to extract radii either by k-nearest neighbours or ray-casting
\n\nIn my experience there is no one-size-fits-all. You will have to play around to\nfind the right approach and parameters to get nice skeletons for your meshes.\nIf you need help just open an issue.
\n\nAlso check out the Gotchas below!
\n\nExamples
\n\nFirst load the example mesh (a fruit fly neuron):
\n\n\n
>>> import skeletor as sk\n>>> mesh = sk.example_mesh()\n>>> mesh\n<trimesh.Trimesh(vertices.shape=(6582, 3), faces.shape=(13772, 3))>\n
\n
Next see if there is stuff to fix in the mesh (degenerate faces, duplicate\nvertices, etc.):
\n\n\n
>>> fixed = sk.pre.fix_mesh(mesh, remove_disconnected=5, inplace=False)\n>>> fixed\n<trimesh.Trimesh(vertices.shape=(6213, 3), faces.shape=(12805, 3))>\n
\n
Now for tubular meshes like this neuron, the \"wave front\" skeletonization method\nperforms really well: it works by casting waves across the mesh and collapsing\nthe resulting rings into a skeleton (kinda like when you throw a stone in a\npond and track the expanding ripples).
\n\n\n
>>> skel = sk.skeletonize.by_wavefront(fixed, waves=1, step_size=1)\n>>> skel\n<Skeleton(vertices=(1258, 3), edges=(1194, 2), method=wavefront)>\n
\n
All skeletonization methods return a Skeleton object. These are just\nconvenient objects to bundle the various outputs of the skeletonization.
\n\n\n
>>> # x/y/z location of skeleton vertices (nodes)\n>>> skel.vertices\narray([[16744, 36720, 26407],\n ...,\n [22076, 23217, 24472]])\n>>> # child -> parent edges\n>>> skel.edges\narray([[ 64, 31],\n ...,\n [1257, 1252]])\n>>> # Mapping for mesh to skeleton vertex indices\n>>> skel.mesh_map\narray([ 157, 158, 1062, ..., 525, 474, 547])\n>>> # SWC table\n>>> skel.swc.head()\n node_id parent_id x y z radius\n0 0 -1 16744.005859 36720.058594 26407.902344 0.000000\n1 1 -1 5602.751953 22266.756510 15799.991211 7.542587\n2 2 -1 16442.666667 14999.978516 10887.916016 5.333333\n
\n
SWC is a commonly used format for saving skeletons. Skeleton objects\nhave a method for quickly saving a correctly formatted SWC file:
\n\n\n
>>> skel.save_swc('~/Documents/my_skeleton.swc')\n
\n
If you installed pyglet (see above) you can also use trimesh's plotting\ncapabilities to inspect the results:
\n\n\n
>>> skel.show(mesh=True)\n
\n
![\"skeletor_example\"](\"https://github.com/navis-org/skeletor/raw/master/_static/example1.png\")
\n\nThat looks pretty good already but let's run some pro-forma postprocessing.
\n\n\n
>>> sk.post.clean_up(skel, inplace=True)\n<Skeleton(vertices=(1071, 3), edges=(1070, 2))>\n
\n
So that would be a full pipeline mesh to skeleton. Don't expect your own meshes\nto produce such nice results off the bat though. Chances are you will need to\nplay around to find the right recipe. If you don't know where to start, I suggest\nyou try out mesh contraction + vertex clustering first:
\n\n\n
>>> import skeletor as sk\n>>> # Load the example mesh that ships with skeletor\n>>> mesh = sk.example_mesh()\n>>> # Alternatively use trimesh to load/construct your own mesh:\n>>> # import trimesh as tm\n>>> # mesh = tm.Trimesh(vertices, faces)\n>>> # mesh = tm.load_mesh('some/mesh.obj')\n>>> # Run some general clean-up (see docstring for details)\n>>> fixed = sk.pre.fix_mesh(mesh, remove_disconnected=5, inplace=False)\n>>> # Contract mesh to 10% (0.1) of original volume\n>>> cont = sk.pre.contract(fixed, epsilon=0.1)\n>>> # Skeletonize\n>>> skel = sk.skeletonize.by_vertex_clusters(cont, sampling_dist=100)\n>>> # Replace contracted mesh with original for postprocessing and plotting\n>>> skel.mesh = fixed\n>>> # Add radii (vertex cluster method does not do that automatically)\n>>> sk.post.radii(skel, method='knn')\n>>> skel.show(mesh=True)\n
\n
Gotchas
\n\n\n- while this is a general purpose library, my personal focus is on neurons and\nthis has certainly influenced things like default parameter values and certain\npost-processing steps
\n- meshes need to be triangular (we are using
trimesh) \n- use
sk.pre.simplify if your mesh is very complex (half a million vertices is\nwhere things start getting sluggish) \n- a good mesh contraction is often half the battle but it can be tricky to get\nto work
\n- if the mesh consists of multiple disconnected pieces the skeleton will\nlikewise be fragmented (i.e. will have multiple roots)
\n- it's often a good idea to fix issues with the skeleton in postprocessing rather\nthan trying to get the skeletonization to be perfect
\n
\n\nBenchmarks
\n\n![\"skeletor_benchmark\"](\"https://github.com/navis-org/skeletor/raw/master/benchmarks/benchmark_2.png\")
\n\nBenchmarks\nwere run on a 2018 MacBook Pro (2.2 GHz Core i7, 32Gb memory) with optional\nfastremap dependency installed. Note some of these functions (e.g.\ncontraction and TEASAR/vertex cluster skeletonization) vary a lot in\nspeed based on parameterization.
\n\nWhat about algorithm X?
\n\nskeletor contains some algorithms that I found easy enough to implement\nand useful for my work with neurons. If you have some interesting paper/approach\nthat could make a nice addition to skeletor, please get in touch on Github.\nPull requests are always welcome!
\n\nReferences
\n\n[1] Au OK, Tai CL, Chu HK, Cohen-Or D, Lee TY. Skeleton extraction by mesh contraction. ACM Transactions on Graphics (TOG). 2008 Aug 1;27(3):44.
\n\nThe abstract and the paper can be found here.\nAlso see this YouTube video.
\n\nSome of the code in skeletor was modified from the\nPy_BL_MeshSkeletonization\naddon created by #0K Srinivasan Ramachandran and published under GPL3.
\n\nTop-level functions and classes
\n\nAt top-level we only expose example_mesh() and the Skeleton class (which\nyou probably won't ever need to touch manually). Everything else is neatly\ntucked away into submodules (see side-bar or above table).
\n"}, "skeletor.Skeleton": {"fullname": "skeletor.Skeleton", "modulename": "skeletor", "qualname": "Skeleton", "kind": "class", "doc": "Class representing a skeleton.
\n\nTypically returned as results from a skeletonization.
\n\nAttributes
\n\n\n- swc (pd.DataFrame, optional):\nSWC table.
\n- vertices ((N, 3) array):\nVertex (node) positions.
\n- edges ((M, 2) array):\nIndices of connected vertex pairs.
\n- radii ((N, ) array, optional):\nRadii for each vertex (node) in the skeleton.
\n- mesh (trimesh, optional):\nThe original mesh.
\n- mesh_map (array, optional):\nSame length as
mesh. Maps mesh vertices to vertices (nodes)\nin the skeleton. \n- skel_map (array of arrays, optional):\nInverse of
mesh_map: maps skeleton vertices (nodes) to mesh\nvertices. \n- method (str, optional):\nWhich method was used to generate the skeleton.
\n
\n"}, "skeletor.Skeleton.__init__": {"fullname": "skeletor.Skeleton.__init__", "modulename": "skeletor", "qualname": "Skeleton.__init__", "kind": "function", "doc": "\n", "signature": "(swc, mesh=None, mesh_map=None, method=None)"}, "skeletor.Skeleton.swc": {"fullname": "skeletor.Skeleton.swc", "modulename": "skeletor", "qualname": "Skeleton.swc", "kind": "variable", "doc": "\n"}, "skeletor.Skeleton.mesh": {"fullname": "skeletor.Skeleton.mesh", "modulename": "skeletor", "qualname": "Skeleton.mesh", "kind": "variable", "doc": "\n"}, "skeletor.Skeleton.mesh_map": {"fullname": "skeletor.Skeleton.mesh_map", "modulename": "skeletor", "qualname": "Skeleton.mesh_map", "kind": "variable", "doc": "\n"}, "skeletor.Skeleton.method": {"fullname": "skeletor.Skeleton.method", "modulename": "skeletor", "qualname": "Skeleton.method", "kind": "variable", "doc": "\n"}, "skeletor.Skeleton.edges": {"fullname": "skeletor.Skeleton.edges", "modulename": "skeletor", "qualname": "Skeleton.edges", "kind": "variable", "doc": "Return skeleton edges.
\n"}, "skeletor.Skeleton.vertices": {"fullname": "skeletor.Skeleton.vertices", "modulename": "skeletor", "qualname": "Skeleton.vertices", "kind": "variable", "doc": "Return skeleton vertices (nodes).
\n"}, "skeletor.Skeleton.radius": {"fullname": "skeletor.Skeleton.radius", "modulename": "skeletor", "qualname": "Skeleton.radius", "kind": "variable", "doc": "Return radii.
\n"}, "skeletor.Skeleton.skeleton": {"fullname": "skeletor.Skeleton.skeleton", "modulename": "skeletor", "qualname": "Skeleton.skeleton", "kind": "variable", "doc": "Skeleton as trimesh Path3D.
\n"}, "skeletor.Skeleton.skel_map": {"fullname": "skeletor.Skeleton.skel_map", "modulename": "skeletor", "qualname": "Skeleton.skel_map", "kind": "variable", "doc": "Skeleton vertex (nodes) to mesh vertices. Based on mesh_map.
\n"}, "skeletor.Skeleton.leafs": {"fullname": "skeletor.Skeleton.leafs", "modulename": "skeletor", "qualname": "Skeleton.leafs", "kind": "variable", "doc": "Leaf nodes (includes root).
\n"}, "skeletor.Skeleton.reindex": {"fullname": "skeletor.Skeleton.reindex", "modulename": "skeletor", "qualname": "Skeleton.reindex", "kind": "function", "doc": "Clean up skeleton.
\n", "signature": "(self, inplace=False):", "funcdef": "def"}, "skeletor.Skeleton.copy": {"fullname": "skeletor.Skeleton.copy", "modulename": "skeletor", "qualname": "Skeleton.copy", "kind": "function", "doc": "Return copy of the skeleton.
\n", "signature": "(self):", "funcdef": "def"}, "skeletor.Skeleton.get_graph": {"fullname": "skeletor.Skeleton.get_graph", "modulename": "skeletor", "qualname": "Skeleton.get_graph", "kind": "function", "doc": "Generate networkX representation of the skeletons.
\n\nDistance between nodes will be used as edge weights.
\n\nReturns
\n\n\n", "signature": "(self):", "funcdef": "def"}, "skeletor.Skeleton.get_segments": {"fullname": "skeletor.Skeleton.get_segments", "modulename": "skeletor", "qualname": "Skeleton.get_segments", "kind": "function", "doc": "Generate a list of linear segments while maximizing segment lengths.
\n\nParameters
\n\n\n- weight ('weight' | None, optional):\nIf
\"weight\" use physical, geodesic length to determine\nsegment length. If None use number of nodes (faster). \n- return_lengths (bool):\nIf True, also return lengths of segments according to
weight. \n
\n\nReturns
\n\n\n- segments (list):\nSegments as list of lists containing node IDs. List is\nsorted by segment lengths.
\n- lengths (list):\nLength for each segment according to
weight. Only provided\nif return_lengths is True. \n
\n", "signature": "(self, weight='weight', return_lengths=False):", "funcdef": "def"}, "skeletor.Skeleton.save_swc": {"fullname": "skeletor.Skeleton.save_swc", "modulename": "skeletor", "qualname": "Skeleton.save_swc", "kind": "function", "doc": "Save skeleton in SWC format.
\n\nParameters
\n\n\n- filepath (path-like):\nFilepath to save SWC to.
\n
\n", "signature": "(self, filepath):", "funcdef": "def"}, "skeletor.Skeleton.scene": {"fullname": "skeletor.Skeleton.scene", "modulename": "skeletor", "qualname": "Skeleton.scene", "kind": "function", "doc": "Return a Scene object containing the skeleton.
\n\nReturns
\n\n\n- scene (trimesh.scene.scene.Scene):\nContains the skeleton and optionally the mesh.
\n
\n", "signature": "(self, mesh=False, **kwargs):", "funcdef": "def"}, "skeletor.Skeleton.show": {"fullname": "skeletor.Skeleton.show", "modulename": "skeletor", "qualname": "Skeleton.show", "kind": "function", "doc": "Render the skeleton in an opengl window. Requires pyglet.
\n\nParameters
\n\n\n- mesh (bool):\nIf True, will render transparent mesh on top of the\nskeleton.
\n
\n\nReturns
\n\n\n- scene (trimesh.scene.Scene):\nScene with skeleton in it.
\n
\n", "signature": "(self, mesh=False, **kwargs):", "funcdef": "def"}, "skeletor.Skeleton.mend_breaks": {"fullname": "skeletor.Skeleton.mend_breaks", "modulename": "skeletor", "qualname": "Skeleton.mend_breaks", "kind": "function", "doc": "Mend breaks in the skeleton using the original mesh.
\n\nThis works by comparing the connectivity of the original mesh with that\nof the skeleton. If the shortest path between two adjacent vertices on the mesh\nis shorter than the distance between the nodes in the skeleton, a new edge\nis added to the skeleton.
\n\nParameters
\n\n\n- dist_mult (float, optional):\nFactor by which the new edge should be shorter than the\ncurrent shortest path between two nodes to be added.\nLower values = fewer false negatives; higher values = fewer\nfalse positive edges.
\n- dist_min (float, optional):\nMinimum distance between nodes to consider adding an edge.\nUse this to avoid adding very short edges.
\n- dist_max (float, optional):\nMaximum distance between nodes to consider adding an edge.\nUse this to avoid adding very long edges.
\n
\n\nReturns
\n\n\n- edges ((N, 2) array):\nEdges connecting the skeleton nodes.
\n- vertices ((N, 3) array):\nPositions of the skeleton nodes.
\n
\n", "signature": "(self, dist_mult=5, dist_min=0, dist_max=inf):", "funcdef": "def"}, "skeletor.example_mesh": {"fullname": "skeletor.example_mesh", "modulename": "skeletor", "qualname": "example_mesh", "kind": "function", "doc": "Load and return example mesh.
\n\nThe example mesh is a fruit fly neuron (an olfactory projection neuron of\nthe DA1 glomerulus) segmented from an EM image data set. It is part of the\nJanelia hemibrain data set (see here) [1].
\n\nReferences
\n\n[1] Louis K. Scheffer et al., eLife. 2020. doi: 10.7554/eLife.57443\nA connectome and analysis of the adult Drosophila central brain
\n\nReturns
\n\n\n\nExamples
\n\n\n
>>> import skeletor as sk\n>>> # Load this example mesh\n>>> mesh = sk.example_mesh()\n
\n
The skeletor.post module contains functions to post-process skeletons after\nskeletonization.
\n\nFixing issues with skeletons
\n\nDepending on your mesh, pre-processing and the parameters you chose for\nskeletonization, chances are that your skeleton will not come out perfectly.
\n\nskeletor.post.clean_up can help you solve some potential issues:
\n\n\n- skeleton nodes (vertices) that outside or right on the surface instead of\ncentered inside the mesh
\n- superfluous \"hairs\" on otherwise straight bits
\n
\n\nskeletor.post.smooth will smooth out the skeleton.
\n\nskeletor.post.despike can help you remove spikes in the skeleton where\nsingle nodes are out of aligment.
\n\nskeletor.post.remove_bristles will remove bristles from the skeleton.
\n\n\n\nOnly skeletor.skeletonize.by_wavefront() provides radii off the bat. For all\nother methods, you might want to run skeletor.post.radii can help you\n(re-)generate radius information for the skeletons.
\n"}, "skeletor.post.radii": {"fullname": "skeletor.post.radii", "modulename": "skeletor.post", "qualname": "radii", "kind": "function", "doc": "Extract radii for given skeleton table.
\n\nImportant
\n\nThis function really only produces useful radii if the skeleton is centered\ninside the mesh. by_wavefront does that by default whereas all other\nskeletonization methods don't. Your best bet to get centered skeletons is\nto contract the mesh first (sk.pre.contract).
\n\nParameters
\n\n\n\nFor method \"knn\"::
\n\nn : int (default 5)\n Radius will be the mean over n nearest-neighbors.\n
\n\nFor method \"ray\"::
\n\nn_rays : int (default 20)\n Number of rays to cast for each node.\nprojection : \"sphere\" (default) | \"tangents\"\n Whether to cast rays in a sphere around each node or in a\n circle orthogonally to the node's tangent vector.\nfallback : \"knn\" (default) | None | number\n If a point is outside or right on the surface of the mesh\n the raycasting will return nonesense results. We can either\n ignore those cases (``None``), assign a arbitrary number or\n we can fall back to radii from k-nearest-neighbors (``knn``).\n
\n\nReturns
\n\n\n- None: But attaches
radius to the skeleton's SWC table. Existing\nvalues are replaced! \n
\n", "signature": "(\ts,\tmesh=None,\tmethod='knn',\taggregate='mean',\tvalidate=False,\t**kwargs):", "funcdef": "def"}, "skeletor.post.clean_up": {"fullname": "skeletor.post.clean_up", "modulename": "skeletor.post", "qualname": "clean_up", "kind": "function", "doc": "Clean up the skeleton.
\n\nThis function bundles a bunch of procedures to clean up the skeleton:
\n\n\n- Remove twigs that are running parallel to their parent branch
\n- Move nodes outside the mesh back inside (or at least snap to surface)
\n
\n\nNote that this is not a magic bullet and some of this will not work (well)\nif the original mesh was degenerate (e.g. internal faces or not watertight)\nto begin with.
\n\nParameters
\n\n\n- s (skeletor.Skeleton):\nSkeleton to clean up.
\n- mesh (trimesh.Trimesh, optional):\nOriginal mesh (e.g. before contraction). If not provided will\nuse the mesh associated with
s. \n- validate (bool):\nIf True, will try to fix potential issues with the mesh\n(e.g. infinite values, duplicate vertices, degenerate faces)\nbefore cleaning up. Note that this might change your mesh\ninplace!
\n- inplace (bool):\nIf False will make and return a copy of the skeleton. If True,\nwill modify the
s inplace. \n- **kwargs: Keyword arguments are passed to the bundled function.
\n
\n\nFor skeletor.postprocessing.drop_parallel_twigs::
\n\ntheta : float (default 0.01)\n For each twig we generate the dotproduct between the tangent\n vectors of it and its parents. If these line up perfectly the\n dotproduct will equal 1. theta determines how much that\n value can differ from 1 for us to still prune the twig: higher\n theta = more pruning.
\n\nReturns
\n\n\n- s_clean (skeletor.Skeleton):\nHopefully improved skeleton.
\n
\n", "signature": "(s, mesh=None, validate=False, inplace=False, **kwargs):", "funcdef": "def"}, "skeletor.post.smooth": {"fullname": "skeletor.post.smooth", "modulename": "skeletor.post", "qualname": "smooth", "kind": "function", "doc": "Smooth skeleton using rolling windows.
\n\nParameters
\n\n\n- s (skeletor.Skeleton):\nSkeleton to be processed.
\n- window (int, optional):\nSize (N observations) of the rolling window in number of\nnodes.
\n- to_smooth (list):\nColumns of the node table to smooth. Should work with any\nnumeric column (e.g. 'radius').
\n- inplace (bool):\nIf False will make and return a copy of the skeleton. If\nTrue, will modify the
s inplace. \n
\n\nReturns
\n\n\n- s (skeletor.Skeleton):\nSkeleton with smoothed node table.
\n
\n", "signature": "(\ts,\twindow: int = 3,\tto_smooth: list = ['x', 'y', 'z'],\tinplace: bool = False):", "funcdef": "def"}, "skeletor.post.despike": {"fullname": "skeletor.post.despike", "modulename": "skeletor.post", "qualname": "despike", "kind": "function", "doc": "Remove spikes in skeleton.
\n\nFor each node A, the euclidean distance to its next successor (parent)\nB and that node's successor C (i.e A->B->C) is computed. If\n\\( \\frac{dist(A,B)}{dist(A,C)}>sigma \\), node B is considered a spike\nand realigned between A and C.
\n\nParameters
\n\n\n- x (skeletor.Skeleton):\nSkeleton to be processed.
\n- sigma (float | int, optional):\nThreshold for spike detection. Smaller sigma = more\naggressive spike detection.
\n- max_spike_length (int, optional):\nDetermines how long (# of nodes) a spike can be.
\n- inplace (bool, optional):\nIf False, a copy of the neuron is returned.
\n- reverse (bool, optional):\nIf True, will also walk the segments from proximal\nto distal. Use this to catch spikes on e.g. terminal\nnodes.
\n
\n\nReturns
\n\n\n- s skeletor.Skeleton: Despiked neuron.
\n
\n", "signature": "(s, sigma=5, max_spike_length=1, inplace=False, reverse=False):", "funcdef": "def"}, "skeletor.post.remove_bristles": {"fullname": "skeletor.post.remove_bristles", "modulename": "skeletor.post", "qualname": "remove_bristles", "kind": "function", "doc": "Remove \"bristles\" that sometimes occurr along the backbone.
\n\nWorks by finding terminal twigs that consist of only a single node.
\n\nParameters
\n\n\n- s (skeletor.Skeleton):\nSkeleton to clean up.
\n- mesh (trimesh.Trimesh, optional):\nOriginal mesh (e.g. before contraction). If not provided will\nuse the mesh associated with
s. \n- los_only (bool):\nIf True, will only remove bristles that are in line of sight of\ntheir parent. If False, will remove all single-node bristles.
\n- inplace (bool):\nIf False will make and return a copy of the skeleton. If True,\nwill modify the
s inplace. \n
\n\nReturns
\n\n\n- s (skeletor.Skeleton):\nSkeleton with single-node twigs removed.
\n
\n", "signature": "(s, mesh=None, los_only=False, inplace=False):", "funcdef": "def"}, "skeletor.pre": {"fullname": "skeletor.pre", "modulename": "skeletor.pre", "kind": "module", "doc": "The skeletor.pre module contains functions to pre-process meshes before\nskeletonization.
\n\nFixing faulty meshes
\n\nSome skeletonization methods are susceptible to faulty meshes (degenerate faces,\nwrong normals, etc.). If your skeleton looks off, it might be worth a shot\ntrying to fix the mesh using skeletor.pre.fix_mesh().
\n\nMesh contraction
\n\nAs a rule of thumb: the more your mesh looks like a skeleton, the easier it is\nto extract one (duh). Mesh contraction using skeletor.pre.contract() [1] can\nhelp you to get your mesh \"in shape\".
\n\nReferences
\n\n[1] Au OK, Tai CL, Chu HK, Cohen-Or D, Lee TY. Skeleton extraction by mesh\n contraction. ACM Transactions on Graphics (TOG). 2008 Aug 1;27(3):44.
\n"}, "skeletor.pre.fix_mesh": {"fullname": "skeletor.pre.fix_mesh", "modulename": "skeletor.pre", "qualname": "fix_mesh", "kind": "function", "doc": "Try to fix some common problems with mesh.
\n\n\n- Remove infinite values
\n- Merge duplicate vertices
\n- Remove duplicate and degenerate faces
\n- Remove unreference vertices
\n- Drop winglets (faces that have only one adjacent face)
\n- Fix normals (Optional)
\n- Remove disconnected fragments (Optional)
\n
\n\nParameters
\n\n\n- mesh (mesh-like object):\nMesh to fix. Must have
.vertices and .faces\nproperties. \n- remove_disconnected (False | int):\nIf a number is given, will iterate over the mesh's\nconnected components and remove those consisting of\nless than the given number of vertices. For example,\n
remove_disconnected=5 will drop parts of the\nmesh that consist of five or less connected\nvertices. \n- inplace (bool):\nIf True, will perform fixes on the input mesh.\nIf False, will make a copy first. This is silently\nignored if
mesh is not already a trimesh. \n
\n\nReturns
\n\n\n- fixed mesh (trimesh.Trimesh):
\n
\n", "signature": "(\tmesh,\tremote_infinite=True,\tmerge_duplicate_verts=True,\tremove_degenerate_faces=True,\tremove_unreferenced_verts=True,\tdrop_winglets=True,\tfix_normals=False,\tremove_disconnected=False,\tinplace=False):", "funcdef": "def"}, "skeletor.pre.simplify": {"fullname": "skeletor.pre.simplify", "modulename": "skeletor.pre", "qualname": "simplify", "kind": "function", "doc": "Simplify mesh using Blender 3D.
\n\nUses Blender's \"decimate\" modifier in \"collapse\" mode.
\n\nParameters
\n\n\n- mesh (trimesh.Trimesh):\nMesh to simplify.
\n- ratio (float):\nFactor to which to reduce faces. For example, a ratio of 0.5 will\nreduce the number of faces to 50%.
\n
\n\nReturns
\n\n\n- trimesh.Trimesh: Simplified mesh.
\n
\n", "signature": "(mesh, ratio):", "funcdef": "def"}, "skeletor.pre.remesh": {"fullname": "skeletor.pre.remesh", "modulename": "skeletor.pre", "qualname": "remesh", "kind": "function", "doc": "Remesh mesh using Blender 3D.
\n\nUses Blender's \"remesh\" modifier in \"voxel\" mode.
\n\nParameters
\n\n\n- mesh (trimesh.Trimesh):\nMesh to remesh.
\n- voxel_size (float):\nSize of individual voxels (edge length).
\n- adaptivity (float):\nReduces final face count where detail is not important.
\n
\n\nReturns
\n\n\n- trimesh.Trimesh: Remeshed mesh.
\n
\n", "signature": "(mesh, voxel_size=50, adaptivity=5):", "funcdef": "def"}, "skeletor.pre.contract": {"fullname": "skeletor.pre.contract", "modulename": "skeletor.pre", "qualname": "contract", "kind": "function", "doc": "Contract mesh.
\n\nIn a nutshell: this function contracts the mesh by applying rounds of\n_constraint_ Laplacian smoothing. This function can be fairly expensive\nand I highly recommend you play around with SL to contract the\nmesh in as few steps as possible. The contraction doesn't have to be perfect\nfor good skeletonization results (<10%, i.e. epsilon<0.1).
\n\nAlso: parameterization matters a lot! Default parameters will get you there\nbut playing around with SL and WH0 might speed things up by an order of\nmagnitude.
\n\nParameters
\n\n\n\nReturns
\n\n\n- trimesh.Trimesh: Contracted copy of original mesh. The final contraction rate\nis attached to the mesh as
.epsilon property. \n
\n\nReferences
\n\n[1] Au OK, Tai CL, Chu HK, Cohen-Or D, Lee TY. Skeleton extraction by mesh\n contraction. ACM Transactions on Graphics (TOG). 2008 Aug 1;27(3):44.
\n", "signature": "(\tmesh,\tepsilon=1e-06,\titer_lim=100,\ttime_lim=None,\tprecision=1e-07,\tSL=2,\tWH0=1,\tWL0='auto',\toperator='cotangent',\tprogress=True,\tvalidate=True):", "funcdef": "def"}, "skeletor.skeletonize": {"fullname": "skeletor.skeletonize", "modulename": "skeletor.skeletonize", "kind": "module", "doc": "The skeletor.skeletonize module contains functions to for skeletonization\nof meshes.
\n\nThere are several approaches to skeletonizing a mesh. Which one to pick depends\n(among other things) on the shape of your mesh and the skeleton quality you want\nto get out of it. In general, unless you mesh already looks like a tube I\nrecommend looking into mesh contraction .
\n\nPlease see the documentation of the individual functions for details but here\nis a quick summary:
\n\n\n\n\n | function | \n speed | \n robust | \n radii | \n mesh map | \n description | \n
\n\n\n\n skeletor.skeletonize.by_wavefront() | \n +++ | \n ++ | \n yes | \n yes | \n works well for tubular meshes | \n
\n\n skeletor.skeletonize.by_vertex_clusters() | \n ++ | \n + | \n no | \n yes | \n best with contracted meshes | \n
\n\n skeletor.skeletonize.by_teasar() | \n + | \n ++ | \n no | \n yes | \n works on mesh surface | \n
\n\n skeletor.skeletonize.by_tangent_ball() | \n ++ | \n 0 | \n yes | \n yes | \n works with mesh normals | \n
\n\n skeletor.skeletonize.by_edge_collapse() | \n - | \n 0 | \n no | \n no | \n published with [1] - never got this to work well | \n
\n\n
\n\nReferences
\n\n[1] Au OK, Tai CL, Chu HK, Cohen-Or D, Lee TY. Skeleton extraction by mesh contraction. ACM Transactions on Graphics (TOG). 2008 Aug 1;27(3):44.
\n\n\n"}, "skeletor.skeletonize.by_teasar": {"fullname": "skeletor.skeletonize.by_teasar", "modulename": "skeletor.skeletonize", "qualname": "by_teasar", "kind": "function", "doc": "Skeletonize a mesh mesh using the TEASAR algorithm [1].
\n\nThis algorithm finds the longest path from a root vertex, invalidates all\nvertices that are within inv_dist. Then picks the second longest (and\nstill valid) path and does the same. Rinse & repeat until all vertices have\nbeen invalidated. It's fast + works very well with tubular meshes, and with\ninv_dist you have control over the level of detail. Note that by its\nnature the skeleton will be exactly on the surface of the mesh.
\n\nBased on the implementation by Sven Dorkenwald, Casey Schneider-Mizell and\nForrest Collman in meshparty (https://github.com/sdorkenw/MeshParty).
\n\nParameters
\n\n\n- mesh (mesh obj):\nThe mesh to be skeletonize. Can an object that has\n
.vertices and .faces properties (e.g. a\ntrimesh.Trimesh) or a tuple (vertices, faces) or a\ndictionary {'vertices': vertices, 'faces': faces}. \n- inv_dist (int | float):\nDistance along the mesh used for invalidation of vertices.\nThis controls how detailed (or noisy) the skeleton will be.
\n- min_length (float, optional):\nIf provided, will skip any branch that is shorter than\n
min_length. Use this to get rid of noise but note that\nit will lead to vertices not being mapped to skeleton nodes.\nSuch vertices will show up with index -1 in\nSkeleton.mesh_map. \n- root (int, optional):\nVertex ID of a root. If not provided will use
0. \n- progress (bool, optional):\nIf True, will show progress bar.
\n
\n\nReturns
\n\n\n- skeletor.Skeleton: Holds results of the skeletonization and enables quick\nvisualization.
\n
\n\nReferences
\n\n[1] Sato, M., Bitter, I., Bender, M. A., Kaufman, A. E., & Nakajima, M.\n (n.d.). TEASAR: tree-structure extraction algorithm for accurate and\n robust skeletons. In Proceedings the Eighth Pacific Conference on\n Computer Graphics and Applications. IEEE Comput. Soc.\n https://doi.org/10.1109/pccga.2000.883951
\n", "signature": "(mesh, inv_dist, min_length=None, root=None, progress=True):", "funcdef": "def"}, "skeletor.skeletonize.by_wavefront": {"fullname": "skeletor.skeletonize.by_wavefront", "modulename": "skeletor.skeletonize", "qualname": "by_wavefront", "kind": "function", "doc": "Skeletonize a mesh using wave fronts.
\n\nThe algorithm tries to find rings of vertices and collapse them to\ntheir center. This is done by propagating a wave across the mesh starting at\na single seed vertex. As the wave travels across the mesh we keep track of\nwhich vertices are are encountered at each step. Groups of connected\nvertices that are \"hit\" by the wave at the same time are considered rings\nand subsequently collapsed. By its nature this works best with tubular meshes.
\n\nParameters
\n\n\n- mesh (mesh obj):\nThe mesh to be skeletonize. Can an object that has\n
.vertices and .faces properties (e.g. a\ntrimesh.Trimesh) or a tuple (vertices, faces) or a\ndictionary {'vertices': vertices, 'faces': faces}. \n- waves (int):\nNumber of waves to run across the mesh. Each wave is\ninitialized at a different vertex which produces slightly\ndifferent rings. The final skeleton is produced from a mean\nacross all waves. More waves produce higher resolution\nskeletons but also introduce more noise.
\n- origins (int | list of ints, optional):\nVertex ID(s) where the wave(s) are initialized. If we run\nout of origins (either because less
origins than waves\nor because no origin for one of the connected components)\nwill fall back to semi-random origin. \n- step_size (int):\nValues greater 1 effectively lead to binning of rings. For\nexample a stepsize of 2 means that two adjacent vertex rings\nwill be collapsed to the same center. This can help reduce\nnoise in the skeleton (and as such counteracts a large\nnumber of waves).
\n- radius_agg (\"mean\" | \"median\" | \"max\" | \"min\" | \"percentile75\" | \"percentile25\"):\nFunction used to aggregate radii over sample (i.e. the\nvertices forming a ring that we collapse to its center).
\n- progress (bool):\nIf True, will show progress bar.
\n
\n\nReturns
\n\n\n- skeletor.Skeleton: Holds results of the skeletonization and enables quick\nvisualization.
\n
\n", "signature": "(\tmesh,\twaves=1,\torigins=None,\tstep_size=1,\tradius_agg='mean',\tprogress=True):", "funcdef": "def"}, "skeletor.skeletonize.by_vertex_clusters": {"fullname": "skeletor.skeletonize.by_vertex_clusters", "modulename": "skeletor.skeletonize", "qualname": "by_vertex_clusters", "kind": "function", "doc": "Skeletonize a (contracted) mesh by clustering vertices.
\n\nThe algorithm traverses the mesh graph and groups vertices together that\nare within a given distance to each other. This uses the geodesic\n(along-the-mesh) distance, not simply the Euclidean distance. Subsequently\nthese groups of vertices are collapsed and re-connected respecting the\ntopology of the input mesh.
\n\nThe graph traversal is fast and scales well, so this method is well suited\nfor meshes with lots of vertices. On the downside: this implementation is\nnot very clever and you might have to play around with the parameters\n(mostly sampling_dist) to get decent results.
\n\nParameters
\n\n\n\nExamples
\n\n\n
>>> import skeletor as sk\n>>> mesh = sk.example_mesh()\n>>> cont = sk.pre.contract(mesh, epsilon=0.1)\n>>> skel = sk.skeletonize.vertex_cluster(cont)\n>>> skel.mesh = mesh\n
\n
Returns
\n\n\n- skeletor.Skeleton: Holds results of the skeletonization and enables quick\nvisualization.
\n
\n", "signature": "(mesh, sampling_dist, cluster_pos='median', progress=True):", "funcdef": "def"}, "skeletor.skeletonize.by_edge_collapse": {"fullname": "skeletor.skeletonize.by_edge_collapse", "modulename": "skeletor.skeletonize", "qualname": "by_edge_collapse", "kind": "function", "doc": "Skeletonize a (contracted) mesh by iteratively collapsing edges.
\n\nThis algorithm (described in [1]) iteratively collapses edges that are part\nof a face until no more faces are left. Edges are chosen based on a cost\nfunction that penalizes collapses that would change the shape of the object\nor would introduce long edges.
\n\nThis is somewhat sensitive to the dimensions of the input mesh: too large\nand you might experience slow-downs or numpy OverflowErrors; too low and\nyou might get skeletons that don't quite match the mesh (e.g. too few nodes).\nIf you experience either, try down- or up-scaling your mesh, respectively.
\n\nParameters
\n\n\n- mesh (mesh obj):\nThe mesh to be skeletonize. Can an object that has\n
.vertices and .faces properties (e.g. a\ntrimesh.Trimesh) or a tuple (vertices, faces) or a\ndictionary {'vertices': vertices, 'faces': faces}. \n- shape_weight (float, optional):\nWeight for shape costs which penalize collapsing edges that\nwould drastically change the shape of the object.
\n- sample_weight (float, optional):\nWeight for sampling costs which penalize collapses that\nwould generate prohibitively long edges.
\n- progress (bool):\nIf True, will show progress bar.
\n
\n\nReturns
\n\n\n- skeletor.Skeleton: Holds results of the skeletonization and enables quick\nvisualization.
\n
\n\nReferences
\n\n[1] Au OK, Tai CL, Chu HK, Cohen-Or D, Lee TY. Skeleton extraction by mesh\n contraction. ACM Transactions on Graphics (TOG). 2008 Aug 1;27(3):44.
\n", "signature": "(mesh, shape_weight=1, sample_weight=0.1, progress=True):", "funcdef": "def"}, "skeletor.skeletonize.by_tangent_ball": {"fullname": "skeletor.skeletonize.by_tangent_ball", "modulename": "skeletor.skeletonize", "qualname": "by_tangent_ball", "kind": "function", "doc": "Skeletonize a mesh by finding the maximal tangent ball.
\n\nThis algorithm casts a ray from every mesh vertex along its inverse normals\n(requires ncollpyde). It then creates a sphere that is tangent to the\nvertex and to where the ray hit the inside of a face on the opposite side.\nNext it drops spheres that overlap with another, larger sphere. Modified\nfrom [1].
\n\nThe method works best on smooth meshes and is rather sensitive to errors in\nthe mesh such as incorrect normals (see skeletor.pre.fix_mesh), internal\nfaces, noisy surface (try smoothing or downsampling) or holes in the mesh.
\n\nParameters
\n\n\n- mesh (mesh obj):\nThe mesh to be skeletonize. Can an object that has\n
.vertices and .faces properties (e.g. a\ntrimesh.Trimesh) or a tuple (vertices, faces) or a\ndictionary {'vertices': vertices, 'faces': faces}. \n
\n\nReturns
\n\n\n- skeletor.Skeleton: Holds results of the skeletonization and enables quick\nvisualization.
\n
\n\nExamples
\n\n\n
>>> import skeletor as sk\n>>> mesh = sk.example_mesh()\n>>> fixed = sk.pre.fix_mesh(mesh, fix_normals=True, remove_disconnected=10)\n>>> skel = sk.skeletonize.by_tangent_ball(fixed)\n
\n
References
\n\n[1] Ma, J., Bae, S.W. & Choi, S. 3D medial axis point approximation using\n nearest neighbors and the normal field. Vis Comput 28, 7\u201319 (2012).\n https://doi.org/10.1007/s00371-011-0594-7
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\n\nUnlike its namesake, this skeletor\ndoes not (yet) seek to conquer Eternia but to turn meshes into skeletons.
\n\nBefore we get started some terminology:
\n\n\n- a mesh is something that consists of vertices and faces
\n- a skeleton is a (hierarchical) tree-like structure consisting of vertices\n(also called nodes) and edges that connect them
\n
\n\nSkeletons are useful for a range of reasons. For example:
\n\n\n- Typically smaller (less vertices) than the mesh
\n- Have an implicit sense of topology (e.g. \"this node is distal to that node\")
\n
\n\nExtracting skeletons from meshes (or other types of data such as voxels) is\nnon-trivial and there are a great many research papers exploring various\ndifferent approaches (see Google scholar).
\n\nskeletor implements some algorithms that I found useful in my work with\nneurons. In my experience there is unfortuntely no magic bullet when it\ncomes to skeletonization and chances are you will have to fiddle around a bit\nto get decent results.
\n\nInstallation
\n\nFrom PyPI:
\n\n\n
pip3 install skeletor\n
\n
For the bleeding-edge version from Github:
\n\n\n
pip3 install git+https://github.com/navis-org/skeletor@master\n
\n
Getting started
\n\nA skeletonization pipeline typically consists of:
\n\n\n- Some pre-processing of the mesh (e.g. fixing some potential errors like\ndegenerate faces, unreferenced vertices, etc.)
\n- The skeletonization itself
\n- Some post-processing of the skeleton (e.g. adding radius information, smoothing, etc.)
\n
\n\n
\n\nHere is a complete list of available functions:
\n\n\n\n\n | function | \n description | \n
\n\n\n\n | example data | \n | \n
\n\n skeletor.example_mesh() | \n load an example mesh | \n
\n\n | pre-processing | \n | \n
\n\n skeletor.pre.fix_mesh() | \n fix some common errors found in meshes | \n
\n\n skeletor.pre.remesh() | \n re-generate mesh (uses Blender 3D) | \n
\n\n skeletor.pre.simplify() | \n reduce mesh complexity (uses Blender 3D) | \n
\n\n skeletor.pre.contract() | \n contract mesh to facilitate skeletonization [1] | \n
\n\n | skeletonization | \n | \n
\n\n skeletor.skeletonize.by_wavefront() | \n very fast, works well for tubular meshes (like neurons) | \n
\n\n skeletor.skeletonize.by_vertex_clusters() | \n very fast but needs mesh to be contracted (see above) | \n
\n\n skeletor.skeletonize.by_edge_collapse() | \n presented in [1] but never got this to work well | \n
\n\n skeletor.skeletonize.by_teasar() | \n very fast and robust, works on mesh surface | \n
\n\n skeletor.skeletonize.by_tangent_ball() | \n very fast, best on smooth meshes | \n
\n\n | postprocessing | \n | \n
\n\n skeletor.post.clean_up() | \n fix some potential errors in the skeleton | \n
\n\n skeletor.post.radii() | \n add radius information using various method | \n
\n\n skeletor.post.smooth() | \n smooth the skeleton | \n
\n\n skeletor.post.remove_bristles() | \n remove single-node bristles from the skeleton | \n
\n\n skeletor.post.despike() | \n smooth out jumps in the skeleton | \n
\n\n
\n\n
\n\nSee docstrings of the respective functions for details.
\n\nA pipeline might look like this:
\n\n\nskeletor.pre.fix_mesh() to fix the meshskeletor.pre.simplify() to simplify the meshskeletor.pre.contract() to contract the mesh [1]skeletor.skeletonize.by_vertex_clusters() to generate a skeletonskeletor.post.clean_up() to clean up some potential issues with the skeletonskeletor.post.smooth() to smooth the skeletonskeletor.post.radii() to extract radii either by k-nearest neighbours or ray-casting
\n\nIn my experience there is no one-size-fits-all. You will have to play around to\nfind the right approach and parameters to get nice skeletons for your meshes.\nIf you need help just open an issue.
\n\nAlso check out the Gotchas below!
\n\nExamples
\n\nFirst load the example mesh (a fruit fly neuron):
\n\n\n
>>> import skeletor as sk\n>>> mesh = sk.example_mesh()\n>>> mesh\n<trimesh.Trimesh(vertices.shape=(6582, 3), faces.shape=(13772, 3))>\n
\n
Next see if there is stuff to fix in the mesh (degenerate faces, duplicate\nvertices, etc.):
\n\n\n
>>> fixed = sk.pre.fix_mesh(mesh, remove_disconnected=5, inplace=False)\n>>> fixed\n<trimesh.Trimesh(vertices.shape=(6213, 3), faces.shape=(12805, 3))>\n
\n
Now for tubular meshes like this neuron, the \"wave front\" skeletonization method\nperforms really well: it works by casting waves across the mesh and collapsing\nthe resulting rings into a skeleton (kinda like when you throw a stone in a\npond and track the expanding ripples).
\n\n\n
>>> skel = sk.skeletonize.by_wavefront(fixed, waves=1, step_size=1)\n>>> skel\n<Skeleton(vertices=(1258, 3), edges=(1194, 2), method=wavefront)>\n
\n
All skeletonization methods return a Skeleton object. These are just\nconvenient objects to bundle the various outputs of the skeletonization.
\n\n\n
>>> # x/y/z location of skeleton vertices (nodes)\n>>> skel.vertices\narray([[16744, 36720, 26407],\n ...,\n [22076, 23217, 24472]])\n>>> # child -> parent edges\n>>> skel.edges\narray([[ 64, 31],\n ...,\n [1257, 1252]])\n>>> # Mapping for mesh to skeleton vertex indices\n>>> skel.mesh_map\narray([ 157, 158, 1062, ..., 525, 474, 547])\n>>> # SWC table\n>>> skel.swc.head()\n node_id parent_id x y z radius\n0 0 -1 16744.005859 36720.058594 26407.902344 0.000000\n1 1 -1 5602.751953 22266.756510 15799.991211 7.542587\n2 2 -1 16442.666667 14999.978516 10887.916016 5.333333\n
\n
SWC is a commonly used format for saving skeletons. Skeleton objects\nhave a method for quickly saving a correctly formatted SWC file:
\n\n\n
>>> skel.save_swc('~/Documents/my_skeleton.swc')\n
\n
If you installed pyglet (see above) you can also use trimesh's plotting\ncapabilities to inspect the results:
\n\n\n
>>> skel.show(mesh=True)\n
\n
\n\nThat looks pretty good already but let's run some pro-forma postprocessing.
\n\n\n
>>> sk.post.clean_up(skel, inplace=True)\n<Skeleton(vertices=(1071, 3), edges=(1070, 2))>\n
\n
So that would be a full pipeline mesh to skeleton. Don't expect your own meshes\nto produce such nice results off the bat though. Chances are you will need to\nplay around to find the right recipe. If you don't know where to start, I suggest\nyou try out mesh contraction + vertex clustering first:
\n\n\n
>>> import skeletor as sk\n>>> # Load the example mesh that ships with skeletor\n>>> mesh = sk.example_mesh()\n>>> # Alternatively use trimesh to load/construct your own mesh:\n>>> # import trimesh as tm\n>>> # mesh = tm.Trimesh(vertices, faces)\n>>> # mesh = tm.load_mesh('some/mesh.obj')\n>>> # Run some general clean-up (see docstring for details)\n>>> fixed = sk.pre.fix_mesh(mesh, remove_disconnected=5, inplace=False)\n>>> # Contract mesh to 10% (0.1) of original volume\n>>> cont = sk.pre.contract(fixed, epsilon=0.1)\n>>> # Skeletonize\n>>> skel = sk.skeletonize.by_vertex_clusters(cont, sampling_dist=100)\n>>> # Replace contracted mesh with original for postprocessing and plotting\n>>> skel.mesh = fixed\n>>> # Add radii (vertex cluster method does not do that automatically)\n>>> sk.post.radii(skel, method='knn')\n>>> skel.show(mesh=True)\n
\n
Gotchas
\n\n\n- while this is a general purpose library, my personal focus is on neurons and\nthis has certainly influenced things like default parameter values and certain\npost-processing steps
\n- meshes need to be triangular (we are using
trimesh) \n- use
sk.pre.simplify if your mesh is very complex (half a million vertices is\nwhere things start getting sluggish) \n- a good mesh contraction is often half the battle but it can be tricky to get\nto work
\n- if the mesh consists of multiple disconnected pieces the skeleton will\nlikewise be fragmented (i.e. will have multiple roots)
\n- it's often a good idea to fix issues with the skeleton in postprocessing rather\nthan trying to get the skeletonization to be perfect
\n
\n\nBenchmarks
\n\n
\n\nBenchmarks\nwere run on a 2018 MacBook Pro (2.2 GHz Core i7, 32Gb memory) with optional\nfastremap dependency installed. Note some of these functions (e.g.\ncontraction and TEASAR/vertex cluster skeletonization) vary a lot in\nspeed based on parameterization.
\n\nWhat about algorithm X?
\n\nskeletor contains some algorithms that I found easy enough to implement\nand useful for my work with neurons. If you have some interesting paper/approach\nthat could make a nice addition to skeletor, please get in touch on Github.\nPull requests are always welcome!
\n\nReferences
\n\n[1] Au OK, Tai CL, Chu HK, Cohen-Or D, Lee TY. Skeleton extraction by mesh contraction. ACM Transactions on Graphics (TOG). 2008 Aug 1;27(3):44.
\n\nThe abstract and the paper can be found here.\nAlso see this YouTube video.
\n\nSome of the code in skeletor was modified from the\nPy_BL_MeshSkeletonization\naddon created by #0K Srinivasan Ramachandran and published under GPL3.
\n\nTop-level functions and classes
\n\nAt top-level we only expose example_mesh() and the Skeleton class (which\nyou probably won't ever need to touch manually). Everything else is neatly\ntucked away into submodules (see side-bar or above table).
\n"}, "skeletor.Skeleton": {"fullname": "skeletor.Skeleton", "modulename": "skeletor", "qualname": "Skeleton", "kind": "class", "doc": "Class representing a skeleton.
\n\nTypically returned as results from a skeletonization.
\n\nAttributes
\n\n\n- swc (pd.DataFrame, optional):\nSWC table.
\n- vertices ((N, 3) array):\nVertex (node) positions.
\n- edges ((M, 2) array):\nIndices of connected vertex pairs.
\n- radii ((N, ) array, optional):\nRadii for each vertex (node) in the skeleton.
\n- mesh (trimesh, optional):\nThe original mesh.
\n- mesh_map (array, optional):\nSame length as
mesh. Maps mesh vertices to vertices (nodes)\nin the skeleton. \n- skel_map (array of arrays, optional):\nInverse of
mesh_map: maps skeleton vertices (nodes) to mesh\nvertices. \n- method (str, optional):\nWhich method was used to generate the skeleton.
\n
\n"}, "skeletor.Skeleton.__init__": {"fullname": "skeletor.Skeleton.__init__", "modulename": "skeletor", "qualname": "Skeleton.__init__", "kind": "function", "doc": "\n", "signature": "(swc, mesh=None, mesh_map=None, method=None)"}, "skeletor.Skeleton.swc": {"fullname": "skeletor.Skeleton.swc", "modulename": "skeletor", "qualname": "Skeleton.swc", "kind": "variable", "doc": "\n"}, "skeletor.Skeleton.mesh": {"fullname": "skeletor.Skeleton.mesh", "modulename": "skeletor", "qualname": "Skeleton.mesh", "kind": "variable", "doc": "\n"}, "skeletor.Skeleton.mesh_map": {"fullname": "skeletor.Skeleton.mesh_map", "modulename": "skeletor", "qualname": "Skeleton.mesh_map", "kind": "variable", "doc": "\n"}, "skeletor.Skeleton.method": {"fullname": "skeletor.Skeleton.method", "modulename": "skeletor", "qualname": "Skeleton.method", "kind": "variable", "doc": "\n"}, "skeletor.Skeleton.edges": {"fullname": "skeletor.Skeleton.edges", "modulename": "skeletor", "qualname": "Skeleton.edges", "kind": "variable", "doc": "Return skeleton edges.
\n"}, "skeletor.Skeleton.vertices": {"fullname": "skeletor.Skeleton.vertices", "modulename": "skeletor", "qualname": "Skeleton.vertices", "kind": "variable", "doc": "Return skeleton vertices (nodes).
\n"}, "skeletor.Skeleton.radius": {"fullname": "skeletor.Skeleton.radius", "modulename": "skeletor", "qualname": "Skeleton.radius", "kind": "variable", "doc": "Return radii.
\n"}, "skeletor.Skeleton.skeleton": {"fullname": "skeletor.Skeleton.skeleton", "modulename": "skeletor", "qualname": "Skeleton.skeleton", "kind": "variable", "doc": "Skeleton as trimesh Path3D.
\n"}, "skeletor.Skeleton.skel_map": {"fullname": "skeletor.Skeleton.skel_map", "modulename": "skeletor", "qualname": "Skeleton.skel_map", "kind": "variable", "doc": "Skeleton vertex (nodes) to mesh vertices. Based on mesh_map.
\n"}, "skeletor.Skeleton.leafs": {"fullname": "skeletor.Skeleton.leafs", "modulename": "skeletor", "qualname": "Skeleton.leafs", "kind": "variable", "doc": "Leaf nodes (includes root).
\n"}, "skeletor.Skeleton.reindex": {"fullname": "skeletor.Skeleton.reindex", "modulename": "skeletor", "qualname": "Skeleton.reindex", "kind": "function", "doc": "Clean up skeleton.
\n", "signature": "(self, inplace=False):", "funcdef": "def"}, "skeletor.Skeleton.copy": {"fullname": "skeletor.Skeleton.copy", "modulename": "skeletor", "qualname": "Skeleton.copy", "kind": "function", "doc": "Return copy of the skeleton.
\n", "signature": "(self):", "funcdef": "def"}, "skeletor.Skeleton.get_graph": {"fullname": "skeletor.Skeleton.get_graph", "modulename": "skeletor", "qualname": "Skeleton.get_graph", "kind": "function", "doc": "Generate networkX representation of the skeletons.
\n\nDistance between nodes will be used as edge weights.
\n\nReturns
\n\n\n", "signature": "(self):", "funcdef": "def"}, "skeletor.Skeleton.get_segments": {"fullname": "skeletor.Skeleton.get_segments", "modulename": "skeletor", "qualname": "Skeleton.get_segments", "kind": "function", "doc": "Generate a list of linear segments while maximizing segment lengths.
\n\nParameters
\n\n\n- weight ('weight' | None, optional):\nIf
\"weight\" use physical, geodesic length to determine\nsegment length. If None use number of nodes (faster). \n- return_lengths (bool):\nIf True, also return lengths of segments according to
weight. \n
\n\nReturns
\n\n\n- segments (list):\nSegments as list of lists containing node IDs. List is\nsorted by segment lengths.
\n- lengths (list):\nLength for each segment according to
weight. Only provided\nif return_lengths is True. \n
\n", "signature": "(self, weight='weight', return_lengths=False):", "funcdef": "def"}, "skeletor.Skeleton.save_swc": {"fullname": "skeletor.Skeleton.save_swc", "modulename": "skeletor", "qualname": "Skeleton.save_swc", "kind": "function", "doc": "Save skeleton in SWC format.
\n\nParameters
\n\n\n- filepath (path-like):\nFilepath to save SWC to.
\n
\n", "signature": "(self, filepath):", "funcdef": "def"}, "skeletor.Skeleton.scene": {"fullname": "skeletor.Skeleton.scene", "modulename": "skeletor", "qualname": "Skeleton.scene", "kind": "function", "doc": "Return a Scene object containing the skeleton.
\n\nReturns
\n\n\n- scene (trimesh.scene.scene.Scene):\nContains the skeleton and optionally the mesh.
\n
\n", "signature": "(self, mesh=False, **kwargs):", "funcdef": "def"}, "skeletor.Skeleton.show": {"fullname": "skeletor.Skeleton.show", "modulename": "skeletor", "qualname": "Skeleton.show", "kind": "function", "doc": "Render the skeleton in an opengl window. Requires pyglet.
\n\nParameters
\n\n\n- mesh (bool):\nIf True, will render transparent mesh on top of the\nskeleton.
\n
\n\nReturns
\n\n\n- scene (trimesh.scene.Scene):\nScene with skeleton in it.
\n
\n", "signature": "(self, mesh=False, **kwargs):", "funcdef": "def"}, "skeletor.Skeleton.mend_breaks": {"fullname": "skeletor.Skeleton.mend_breaks", "modulename": "skeletor", "qualname": "Skeleton.mend_breaks", "kind": "function", "doc": "Mend breaks in the skeleton using the original mesh.
\n\nThis works by comparing the connectivity of the original mesh with that\nof the skeleton. If the shortest path between two adjacent vertices on the mesh\nis shorter than the distance between the nodes in the skeleton, a new edge\nis added to the skeleton.
\n\nParameters
\n\n\n- dist_mult (float, optional):\nFactor by which the new edge should be shorter than the\ncurrent shortest path between two nodes to be added.\nLower values = fewer false negatives; higher values = fewer\nfalse positive edges.
\n- dist_min (float, optional):\nMinimum distance between nodes to consider adding an edge.\nUse this to avoid adding very short edges.
\n- dist_max (float, optional):\nMaximum distance between nodes to consider adding an edge.\nUse this to avoid adding very long edges.
\n
\n\nReturns
\n\n\n- edges ((N, 2) array):\nEdges connecting the skeleton nodes.
\n- vertices ((N, 3) array):\nPositions of the skeleton nodes.
\n
\n", "signature": "(self, dist_mult=5, dist_min=0, dist_max=inf):", "funcdef": "def"}, "skeletor.example_mesh": {"fullname": "skeletor.example_mesh", "modulename": "skeletor", "qualname": "example_mesh", "kind": "function", "doc": "Load and return example mesh.
\n\nThe example mesh is a fruit fly neuron (an olfactory projection neuron of\nthe DA1 glomerulus) segmented from an EM image data set. It is part of the\nJanelia hemibrain data set (see here) [1].
\n\nReferences
\n\n[1] Louis K. Scheffer et al., eLife. 2020. doi: 10.7554/eLife.57443\nA connectome and analysis of the adult Drosophila central brain
\n\nReturns
\n\n\n\nExamples
\n\n\n
>>> import skeletor as sk\n>>> # Load this example mesh\n>>> mesh = sk.example_mesh()\n
\n
The skeletor.post module contains functions to post-process skeletons after\nskeletonization.
\n\nFixing issues with skeletons
\n\nDepending on your mesh, pre-processing and the parameters you chose for\nskeletonization, chances are that your skeleton will not come out perfectly.
\n\nskeletor.post.clean_up can help you solve some potential issues:
\n\n\n- skeleton nodes (vertices) that outside or right on the surface instead of\ncentered inside the mesh
\n- superfluous \"hairs\" on otherwise straight bits
\n
\n\nskeletor.post.smooth will smooth out the skeleton.
\n\nskeletor.post.despike can help you remove spikes in the skeleton where\nsingle nodes are out of aligment.
\n\nskeletor.post.remove_bristles will remove bristles from the skeleton.
\n\n\n\nOnly skeletor.skeletonize.by_wavefront() provides radii off the bat. For all\nother methods, you might want to run skeletor.post.radii can help you\n(re-)generate radius information for the skeletons.
\n"}, "skeletor.post.radii": {"fullname": "skeletor.post.radii", "modulename": "skeletor.post", "qualname": "radii", "kind": "function", "doc": "Extract radii for given skeleton table.
\n\nImportant
\n\nThis function really only produces useful radii if the skeleton is centered\ninside the mesh. by_wavefront does that by default whereas all other\nskeletonization methods don't. Your best bet to get centered skeletons is\nto contract the mesh first (sk.pre.contract).
\n\nParameters
\n\n\n- s (skeletor.Skeleton):\nSkeleton to clean up.
\n- mesh (trimesh.Trimesh, optional):\nOriginal mesh (e.g. before contraction). If not provided will\nuse the mesh associated with
s. \nmethod (\"knn\" | \"ray\"):\nWhether and how to add radius information to each node::
\n\n- \"knn\" uses k-nearest-neighbors to get radii: fast but\n potential for being very wrong\n- \"ray\" uses ray-casting to get radii: slower but sometimes\n less wrong\n
- aggregate (\"mean\" | \"median\" | \"max\" | \"min\" | \"percentile75\"):\nFunction used to aggregate radii over sample (i.e. across\nk nearest-neighbors or ray intersections)
\n- validate (bool):\nIf True, will try to fix potential issues with the mesh\n(e.g. infinite values, duplicate vertices, degenerate faces)\nbefore skeletonization. Note that this might make changes to\nyour mesh inplace!
\n- **kwargs: Keyword arguments are passed to the respective method:
\n
\n\nFor method \"knn\"::
\n\nn : int (default 5)\n Radius will be the mean over n nearest-neighbors.\n
\n\nFor method \"ray\"::
\n\nn_rays : int (default 20)\n Number of rays to cast for each node.\nprojection : \"sphere\" (default) | \"tangents\"\n Whether to cast rays in a sphere around each node or in a\n circle orthogonally to the node's tangent vector.\nfallback : \"knn\" (default) | None | number\n If a point is outside or right on the surface of the mesh\n the raycasting will return nonesense results. We can either\n ignore those cases (``None``), assign a arbitrary number or\n we can fall back to radii from k-nearest-neighbors (``knn``).\n
\n\nReturns
\n\n\n- None: But attaches
radius to the skeleton's SWC table. Existing\nvalues are replaced! \n
\n", "signature": "(\ts,\tmesh=None,\tmethod='knn',\taggregate='mean',\tvalidate=False,\t**kwargs):", "funcdef": "def"}, "skeletor.post.clean_up": {"fullname": "skeletor.post.clean_up", "modulename": "skeletor.post", "qualname": "clean_up", "kind": "function", "doc": "Clean up the skeleton.
\n\nThis function bundles a bunch of procedures to clean up the skeleton:
\n\n\n- Remove twigs that are running parallel to their parent branch
\n- Move nodes outside the mesh back inside (or at least snap to surface)
\n
\n\nNote that this is not a magic bullet and some of this will not work (well)\nif the original mesh was degenerate (e.g. internal faces or not watertight)\nto begin with.
\n\nParameters
\n\n\n- s (skeletor.Skeleton):\nSkeleton to clean up.
\n- mesh (trimesh.Trimesh, optional):\nOriginal mesh (e.g. before contraction). If not provided will\nuse the mesh associated with
s. \n- validate (bool):\nIf True, will try to fix potential issues with the mesh\n(e.g. infinite values, duplicate vertices, degenerate faces)\nbefore cleaning up. Note that this might change your mesh\ninplace!
\n- inplace (bool):\nIf False will make and return a copy of the skeleton. If True,\nwill modify the
s inplace. \n- **kwargs: Keyword arguments are passed to the bundled function.
\n
\n\nFor skeletor.postprocessing.drop_parallel_twigs::
\n\ntheta : float (default 0.01)\n For each twig we generate the dotproduct between the tangent\n vectors of it and its parents. If these line up perfectly the\n dotproduct will equal 1. theta determines how much that\n value can differ from 1 for us to still prune the twig: higher\n theta = more pruning.
\n\nReturns
\n\n\n- s_clean (skeletor.Skeleton):\nHopefully improved skeleton.
\n
\n", "signature": "(s, mesh=None, validate=False, inplace=False, **kwargs):", "funcdef": "def"}, "skeletor.post.smooth": {"fullname": "skeletor.post.smooth", "modulename": "skeletor.post", "qualname": "smooth", "kind": "function", "doc": "Smooth skeleton using rolling windows.
\n\nParameters
\n\n\n- s (skeletor.Skeleton):\nSkeleton to be processed.
\n- window (int, optional):\nSize (N observations) of the rolling window in number of\nnodes.
\n- to_smooth (list):\nColumns of the node table to smooth. Should work with any\nnumeric column (e.g. 'radius').
\n- inplace (bool):\nIf False will make and return a copy of the skeleton. If\nTrue, will modify the
s inplace. \n
\n\nReturns
\n\n\n- s (skeletor.Skeleton):\nSkeleton with smoothed node table.
\n
\n", "signature": "(\ts,\twindow: int = 3,\tto_smooth: list = ['x', 'y', 'z'],\tinplace: bool = False):", "funcdef": "def"}, "skeletor.post.despike": {"fullname": "skeletor.post.despike", "modulename": "skeletor.post", "qualname": "despike", "kind": "function", "doc": "Remove spikes in skeleton.
\n\nFor each node A, the euclidean distance to its next successor (parent)\nB and that node's successor C (i.e A->B->C) is computed. If\n\\( \\frac{dist(A,B)}{dist(A,C)}>sigma \\), node B is considered a spike\nand realigned between A and C.
\n\nParameters
\n\n\n- x (skeletor.Skeleton):\nSkeleton to be processed.
\n- sigma (float | int, optional):\nThreshold for spike detection. Smaller sigma = more\naggressive spike detection.
\n- max_spike_length (int, optional):\nDetermines how long (# of nodes) a spike can be.
\n- inplace (bool, optional):\nIf False, a copy of the neuron is returned.
\n- reverse (bool, optional):\nIf True, will also walk the segments from proximal\nto distal. Use this to catch spikes on e.g. terminal\nnodes.
\n
\n\nReturns
\n\n\n- s skeletor.Skeleton: Despiked neuron.
\n
\n", "signature": "(s, sigma=5, max_spike_length=1, inplace=False, reverse=False):", "funcdef": "def"}, "skeletor.post.remove_bristles": {"fullname": "skeletor.post.remove_bristles", "modulename": "skeletor.post", "qualname": "remove_bristles", "kind": "function", "doc": "Remove \"bristles\" that sometimes occurr along the backbone.
\n\nWorks by finding terminal twigs that consist of only a single node.
\n\nParameters
\n\n\n- s (skeletor.Skeleton):\nSkeleton to clean up.
\n- mesh (trimesh.Trimesh, optional):\nOriginal mesh (e.g. before contraction). If not provided will\nuse the mesh associated with
s. \n- los_only (bool):\nIf True, will only remove bristles that are in line of sight of\ntheir parent. If False, will remove all single-node bristles.
\n- inplace (bool):\nIf False will make and return a copy of the skeleton. If True,\nwill modify the
s inplace. \n
\n\nReturns
\n\n\n- s (skeletor.Skeleton):\nSkeleton with single-node twigs removed.
\n
\n", "signature": "(s, mesh=None, los_only=False, inplace=False):", "funcdef": "def"}, "skeletor.pre": {"fullname": "skeletor.pre", "modulename": "skeletor.pre", "kind": "module", "doc": "The skeletor.pre module contains functions to pre-process meshes before\nskeletonization.
\n\nFixing faulty meshes
\n\nSome skeletonization methods are susceptible to faulty meshes (degenerate faces,\nwrong normals, etc.). If your skeleton looks off, it might be worth a shot\ntrying to fix the mesh using skeletor.pre.fix_mesh().
\n\nMesh contraction
\n\nAs a rule of thumb: the more your mesh looks like a skeleton, the easier it is\nto extract one (duh). Mesh contraction using skeletor.pre.contract() [1] can\nhelp you to get your mesh \"in shape\".
\n\nReferences
\n\n[1] Au OK, Tai CL, Chu HK, Cohen-Or D, Lee TY. Skeleton extraction by mesh\n contraction. ACM Transactions on Graphics (TOG). 2008 Aug 1;27(3):44.
\n"}, "skeletor.pre.fix_mesh": {"fullname": "skeletor.pre.fix_mesh", "modulename": "skeletor.pre", "qualname": "fix_mesh", "kind": "function", "doc": "Try to fix some common problems with mesh.
\n\n\n- Remove infinite values
\n- Merge duplicate vertices
\n- Remove duplicate and degenerate faces
\n- Remove unreference vertices
\n- Drop winglets (faces that have only one adjacent face)
\n- Fix normals (Optional)
\n- Remove disconnected fragments (Optional)
\n
\n\nParameters
\n\n\n- mesh (mesh-like object):\nMesh to fix. Must have
.vertices and .faces\nproperties. \n- remove_disconnected (False | int):\nIf a number is given, will iterate over the mesh's\nconnected components and remove those consisting of\nless than the given number of vertices. For example,\n
remove_disconnected=5 will drop parts of the\nmesh that consist of five or less connected\nvertices. \n- inplace (bool):\nIf True, will perform fixes on the input mesh.\nIf False, will make a copy first. This is silently\nignored if
mesh is not already a trimesh. \n
\n\nReturns
\n\n\n- fixed mesh (trimesh.Trimesh):
\n
\n", "signature": "(\tmesh,\tremote_infinite=True,\tmerge_duplicate_verts=True,\tremove_degenerate_faces=True,\tremove_unreferenced_verts=True,\tdrop_winglets=True,\tfix_normals=False,\tremove_disconnected=False,\tinplace=False):", "funcdef": "def"}, "skeletor.pre.simplify": {"fullname": "skeletor.pre.simplify", "modulename": "skeletor.pre", "qualname": "simplify", "kind": "function", "doc": "Simplify mesh using Blender 3D.
\n\nUses Blender's \"decimate\" modifier in \"collapse\" mode.
\n\nParameters
\n\n\n- mesh (trimesh.Trimesh):\nMesh to simplify.
\n- ratio (float):\nFactor to which to reduce faces. For example, a ratio of 0.5 will\nreduce the number of faces to 50%.
\n
\n\nReturns
\n\n\n- trimesh.Trimesh: Simplified mesh.
\n
\n", "signature": "(mesh, ratio):", "funcdef": "def"}, "skeletor.pre.remesh": {"fullname": "skeletor.pre.remesh", "modulename": "skeletor.pre", "qualname": "remesh", "kind": "function", "doc": "Remesh mesh using Blender 3D.
\n\nUses Blender's \"remesh\" modifier in \"voxel\" mode.
\n\nParameters
\n\n\n- mesh (trimesh.Trimesh):\nMesh to remesh.
\n- voxel_size (float):\nSize of individual voxels (edge length).
\n- adaptivity (float):\nReduces final face count where detail is not important.
\n
\n\nReturns
\n\n\n- trimesh.Trimesh: Remeshed mesh.
\n
\n", "signature": "(mesh, voxel_size=50, adaptivity=5):", "funcdef": "def"}, "skeletor.pre.contract": {"fullname": "skeletor.pre.contract", "modulename": "skeletor.pre", "qualname": "contract", "kind": "function", "doc": "Contract mesh.
\n\nIn a nutshell: this function contracts the mesh by applying rounds of\n_constraint_ Laplacian smoothing. This function can be fairly expensive\nand I highly recommend you play around with SL to contract the\nmesh in as few steps as possible. The contraction doesn't have to be perfect\nfor good skeletonization results (<10%, i.e. epsilon<0.1).
\n\nAlso: parameterization matters a lot! Default parameters will get you there\nbut playing around with SL and WH0 might speed things up by an order of\nmagnitude.
\n\nParameters
\n\n\n\nReturns
\n\n\n- trimesh.Trimesh: Contracted copy of original mesh. The final contraction rate\nis attached to the mesh as
.epsilon property. \n
\n\nReferences
\n\n[1] Au OK, Tai CL, Chu HK, Cohen-Or D, Lee TY. Skeleton extraction by mesh\n contraction. ACM Transactions on Graphics (TOG). 2008 Aug 1;27(3):44.
\n", "signature": "(\tmesh,\tepsilon=1e-06,\titer_lim=100,\ttime_lim=None,\tprecision=1e-07,\tSL=2,\tWH0=1,\tWL0='auto',\toperator='cotangent',\tprogress=True,\tvalidate=True):", "funcdef": "def"}, "skeletor.skeletonize": {"fullname": "skeletor.skeletonize", "modulename": "skeletor.skeletonize", "kind": "module", "doc": "The skeletor.skeletonize module contains functions to for skeletonization\nof meshes.
\n\nThere are several approaches to skeletonizing a mesh. Which one to pick depends\n(among other things) on the shape of your mesh and the skeleton quality you want\nto get out of it. In general, unless you mesh already looks like a tube I\nrecommend looking into mesh contraction .
\n\nPlease see the documentation of the individual functions for details but here\nis a quick summary:
\n\n\n\n\n | function | \n speed | \n robust | \n radii | \n mesh map | \n description | \n
\n\n\n\n skeletor.skeletonize.by_wavefront() | \n +++ | \n ++ | \n yes | \n yes | \n works well for tubular meshes | \n
\n\n skeletor.skeletonize.by_vertex_clusters() | \n ++ | \n + | \n no | \n yes | \n best with contracted meshes | \n
\n\n skeletor.skeletonize.by_teasar() | \n + | \n ++ | \n no | \n yes | \n works on mesh surface | \n
\n\n skeletor.skeletonize.by_tangent_ball() | \n ++ | \n 0 | \n yes | \n yes | \n works with mesh normals | \n
\n\n skeletor.skeletonize.by_edge_collapse() | \n - | \n 0 | \n no | \n no | \n published with [1] - never got this to work well | \n
\n\n
\n\nReferences
\n\n[1] Au OK, Tai CL, Chu HK, Cohen-Or D, Lee TY. Skeleton extraction by mesh contraction. ACM Transactions on Graphics (TOG). 2008 Aug 1;27(3):44.
\n\n\n"}, "skeletor.skeletonize.by_teasar": {"fullname": "skeletor.skeletonize.by_teasar", "modulename": "skeletor.skeletonize", "qualname": "by_teasar", "kind": "function", "doc": "Skeletonize a mesh mesh using the TEASAR algorithm [1].
\n\nThis algorithm finds the longest path from a root vertex, invalidates all\nvertices that are within inv_dist. Then picks the second longest (and\nstill valid) path and does the same. Rinse & repeat until all vertices have\nbeen invalidated. It's fast + works very well with tubular meshes, and with\ninv_dist you have control over the level of detail. Note that by its\nnature the skeleton will be exactly on the surface of the mesh.
\n\nBased on the implementation by Sven Dorkenwald, Casey Schneider-Mizell and\nForrest Collman in meshparty (https://github.com/sdorkenw/MeshParty).
\n\nParameters
\n\n\n- mesh (mesh obj):\nThe mesh to be skeletonize. Can an object that has\n
.vertices and .faces properties (e.g. a\ntrimesh.Trimesh) or a tuple (vertices, faces) or a\ndictionary {'vertices': vertices, 'faces': faces}. \n- inv_dist (int | float):\nDistance along the mesh used for invalidation of vertices.\nThis controls how detailed (or noisy) the skeleton will be.
\n- min_length (float, optional):\nIf provided, will skip any branch that is shorter than\n
min_length. Use this to get rid of noise but note that\nit will lead to vertices not being mapped to skeleton nodes.\nSuch vertices will show up with index -1 in\nSkeleton.mesh_map. \n- root (int, optional):\nVertex ID of a root. If not provided will use
0. \n- progress (bool, optional):\nIf True, will show progress bar.
\n
\n\nReturns
\n\n\n- skeletor.Skeleton: Holds results of the skeletonization and enables quick\nvisualization.
\n
\n\nReferences
\n\n[1] Sato, M., Bitter, I., Bender, M. A., Kaufman, A. E., & Nakajima, M.\n (n.d.). TEASAR: tree-structure extraction algorithm for accurate and\n robust skeletons. In Proceedings the Eighth Pacific Conference on\n Computer Graphics and Applications. IEEE Comput. Soc.\n https://doi.org/10.1109/pccga.2000.883951
\n", "signature": "(mesh, inv_dist, min_length=None, root=None, progress=True):", "funcdef": "def"}, "skeletor.skeletonize.by_wavefront": {"fullname": "skeletor.skeletonize.by_wavefront", "modulename": "skeletor.skeletonize", "qualname": "by_wavefront", "kind": "function", "doc": "Skeletonize a mesh using wave fronts.
\n\nThe algorithm tries to find rings of vertices and collapse them to\ntheir center. This is done by propagating a wave across the mesh starting at\na single seed vertex. As the wave travels across the mesh we keep track of\nwhich vertices are are encountered at each step. Groups of connected\nvertices that are \"hit\" by the wave at the same time are considered rings\nand subsequently collapsed. By its nature this works best with tubular meshes.
\n\nParameters
\n\n\n- mesh (mesh obj):\nThe mesh to be skeletonize. Can an object that has\n
.vertices and .faces properties (e.g. a\ntrimesh.Trimesh) or a tuple (vertices, faces) or a\ndictionary {'vertices': vertices, 'faces': faces}. \n- waves (int):\nNumber of waves to run across the mesh. Each wave is\ninitialized at a different vertex which produces slightly\ndifferent rings. The final skeleton is produced from a mean\nacross all waves. More waves produce higher resolution\nskeletons but also introduce more noise.
\n- origins (int | list of ints, optional):\nVertex ID(s) where the wave(s) are initialized. If we run\nout of origins (either because less
origins than waves\nor because no origin for one of the connected components)\nwill fall back to semi-random origin. \n- step_size (int):\nValues greater 1 effectively lead to binning of rings. For\nexample a stepsize of 2 means that two adjacent vertex rings\nwill be collapsed to the same center. This can help reduce\nnoise in the skeleton (and as such counteracts a large\nnumber of waves).
\n- radius_agg (\"mean\" | \"median\" | \"max\" | \"min\" | \"percentile75\" | \"percentile25\"):\nFunction used to aggregate radii over sample (i.e. the\nvertices forming a ring that we collapse to its center).
\n- progress (bool):\nIf True, will show progress bar.
\n
\n\nReturns
\n\n\n- skeletor.Skeleton: Holds results of the skeletonization and enables quick\nvisualization.
\n
\n", "signature": "(\tmesh,\twaves=1,\torigins=None,\tstep_size=1,\tradius_agg='mean',\tprogress=True):", "funcdef": "def"}, "skeletor.skeletonize.by_vertex_clusters": {"fullname": "skeletor.skeletonize.by_vertex_clusters", "modulename": "skeletor.skeletonize", "qualname": "by_vertex_clusters", "kind": "function", "doc": "Skeletonize a (contracted) mesh by clustering vertices.
\n\nThe algorithm traverses the mesh graph and groups vertices together that\nare within a given distance to each other. This uses the geodesic\n(along-the-mesh) distance, not simply the Euclidean distance. Subsequently\nthese groups of vertices are collapsed and re-connected respecting the\ntopology of the input mesh.
\n\nThe graph traversal is fast and scales well, so this method is well suited\nfor meshes with lots of vertices. On the downside: this implementation is\nnot very clever and you might have to play around with the parameters\n(mostly sampling_dist) to get decent results.
\n\nParameters
\n\n\n\nExamples
\n\n\n
>>> import skeletor as sk\n>>> mesh = sk.example_mesh()\n>>> cont = sk.pre.contract(mesh, epsilon=0.1)\n>>> skel = sk.skeletonize.vertex_cluster(cont)\n>>> skel.mesh = mesh\n
\n
Returns
\n\n\n- skeletor.Skeleton: Holds results of the skeletonization and enables quick\nvisualization.
\n
\n", "signature": "(mesh, sampling_dist, cluster_pos='median', progress=True):", "funcdef": "def"}, "skeletor.skeletonize.by_edge_collapse": {"fullname": "skeletor.skeletonize.by_edge_collapse", "modulename": "skeletor.skeletonize", "qualname": "by_edge_collapse", "kind": "function", "doc": "Skeletonize a (contracted) mesh by iteratively collapsing edges.
\n\nThis algorithm (described in [1]) iteratively collapses edges that are part\nof a face until no more faces are left. Edges are chosen based on a cost\nfunction that penalizes collapses that would change the shape of the object\nor would introduce long edges.
\n\nThis is somewhat sensitive to the dimensions of the input mesh: too large\nand you might experience slow-downs or numpy OverflowErrors; too low and\nyou might get skeletons that don't quite match the mesh (e.g. too few nodes).\nIf you experience either, try down- or up-scaling your mesh, respectively.
\n\nParameters
\n\n\n- mesh (mesh obj):\nThe mesh to be skeletonize. Can an object that has\n
.vertices and .faces properties (e.g. a\ntrimesh.Trimesh) or a tuple (vertices, faces) or a\ndictionary {'vertices': vertices, 'faces': faces}. \n- shape_weight (float, optional):\nWeight for shape costs which penalize collapsing edges that\nwould drastically change the shape of the object.
\n- sample_weight (float, optional):\nWeight for sampling costs which penalize collapses that\nwould generate prohibitively long edges.
\n- progress (bool):\nIf True, will show progress bar.
\n
\n\nReturns
\n\n\n- skeletor.Skeleton: Holds results of the skeletonization and enables quick\nvisualization.
\n
\n\nReferences
\n\n[1] Au OK, Tai CL, Chu HK, Cohen-Or D, Lee TY. Skeleton extraction by mesh\n contraction. ACM Transactions on Graphics (TOG). 2008 Aug 1;27(3):44.
\n", "signature": "(mesh, shape_weight=1, sample_weight=0.1, progress=True):", "funcdef": "def"}, "skeletor.skeletonize.by_tangent_ball": {"fullname": "skeletor.skeletonize.by_tangent_ball", "modulename": "skeletor.skeletonize", "qualname": "by_tangent_ball", "kind": "function", "doc": "Skeletonize a mesh by finding the maximal tangent ball.
\n\nThis algorithm casts a ray from every mesh vertex along its inverse normals\n(requires ncollpyde). It then creates a sphere that is tangent to the\nvertex and to where the ray hit the inside of a face on the opposite side.\nNext it drops spheres that overlap with another, larger sphere. Modified\nfrom [1].
\n\nThe method works best on smooth meshes and is rather sensitive to errors in\nthe mesh such as incorrect normals (see skeletor.pre.fix_mesh), internal\nfaces, noisy surface (try smoothing or downsampling) or holes in the mesh.
\n\nParameters
\n\n\n- mesh (mesh obj):\nThe mesh to be skeletonize. Can an object that has\n
.vertices and .faces properties (e.g. a\ntrimesh.Trimesh) or a tuple (vertices, faces) or a\ndictionary {'vertices': vertices, 'faces': faces}. \n
\n\nReturns
\n\n\n- skeletor.Skeleton: Holds results of the skeletonization and enables quick\nvisualization.
\n
\n\nExamples
\n\n\n
>>> import skeletor as sk\n>>> mesh = sk.example_mesh()\n>>> fixed = sk.pre.fix_mesh(mesh, fix_normals=True, remove_disconnected=10)\n>>> skel = sk.skeletonize.by_tangent_ball(fixed)\n
\n
References
\n\n[1] Ma, J., Bae, S.W. & Choi, S. 3D medial axis point approximation using\n nearest neighbors and the normal field. Vis Comput 28, 7\u201319 (2012).\n https://doi.org/10.1007/s00371-011-0594-7
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// mirrored in build-search-index.js (part 1)
// Also split on html tags. this is a cheap heuristic, but good enough.
diff --git a/docs/skeletor.html b/docs/skeletor.html
index 6d61cb3..7173df1 100644
--- a/docs/skeletor.html
+++ b/docs/skeletor.html
@@ -3,14 +3,14 @@
-
+
skeletor API documentation
-
+