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perrette/concave_hull_and_smoothed_outline.ipynb

Created May 27, 2016 18:27
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Draw concave hull of an outline with scipy and shapely. Also explore smoothing methods.
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concave_hull_and_smoothed_outline.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Methods to smooth an outline"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Using matplotlib backend: TkAgg\n",
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"source": [
"%pylab\n",
"%matplotlib inline\n",
"\n",
"%config InlineBackend.figure_format = 'png'\n",
"#matplotlib.rcParams['figure.figsize'] = [8,6]\n",
"import matplotlib as mpl\n",
"mpl.rc(\"savefig\", dpi=150)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from shapely.geometry import LineString, Point, LinearRing"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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],
"text/plain": [
"<shapely.geometry.linestring.LineString at 0x7f0afc048790>"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import json\n",
"line = json.load(open('catchment_daugaard-jensen_pf.json'))['outlines'][0]\n",
"outl = LineString(line)\n",
"outl"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Approach 1: concave hull with alpha-shape approach\n",
"\n",
"- Line simplification\n",
"- Delaunay triangulation of contour line\n",
"- Outlier analysis of circum-circle radii"
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from scipy.spatial import Delaunay\n",
"import numpy as np\n",
"import math, warnings\n",
"from shapely.geometry import MultiLineString, Polygon, Point, MultiPoint, MultiPolygon\n",
"from shapely.ops import cascaded_union, polygonize\n",
"\n",
"def _get_radii(points, tri_vertices):\n",
" \"\"\"Compute circum-circle radii of triangles\n",
" \n",
" points : array-like (n, 2) : collection of points\n",
" tri_vertices : array-like of shape (m, 3) : Delaunay triangle vertices (indices for points)\n",
" returns: array-like (m)\n",
" \n",
" inspired from: https://sgillies.net/2012/10/13/the-fading-shape-of-alpha.html\n",
" \"\"\"\n",
" radii = np.empty(len(tri_vertices))\n",
" radii.fill(np.inf)\n",
"\n",
" # loop over triangles:\n",
" # ia, ib, ic = indices of corner points of the triangle\n",
" for i, v in enumerate(tri_vertices):\n",
" ia, ib, ic = v\n",
" pa = points[ia]\n",
" pb = points[ib]\n",
" pc = points[ic]\n",
"\n",
" # Lengths of sides of triangle\n",
" a = math.sqrt((pa[0]-pb[0])**2 + (pa[1]-pb[1])**2)\n",
" b = math.sqrt((pb[0]-pc[0])**2 + (pb[1]-pc[1])**2)\n",
" c = math.sqrt((pc[0]-pa[0])**2 + (pc[1]-pa[1])**2)\n",
"\n",
" # Semiperimeter of triangle\n",
" s = (a + b + c)/2.0\n",
"\n",
" # Area of triangle by Heron's formula\n",
" if s*(s-a)*(s-b)*(s-c) < 0 : continue\n",
" area = math.sqrt(s*(s-a)*(s-b)*(s-c))\n",
" if area == 0: continue\n",
"\n",
" circum_r = a*b*c/(4.0*area)\n",
" radii[i] = circum_r\n",
" \n",
" return radii\n",
" \n",
" \n",
"def is_outlier(x, thresh=3.5):\n",
" \"\"\"\n",
" Returns a boolean array with True if x are outliers and False \n",
" otherwise.\n",
"\n",
" Parameters:\n",
" -----------\n",
" x : An numobservations by numdimensions array of observations\n",
" thresh : The modified z-score to use as a threshold. Observations with\n",
" a modified z-score (based on the median absolute deviation) greater\n",
" than this value will be classified as outliers.\n",
"\n",
" Returns:\n",
" --------\n",
" mask : A numobservations-length boolean array.\n",
"\n",
" References:\n",
" ----------\n",
" Boris Iglewicz and David Hoaglin (1993), \"Volume 16: How to Detect and\n",
" Handle Outliers\", The ASQC Basic References in Quality Control:\n",
" Statistical Techniques, Edward F. Mykytka, Ph.D., Editor. \n",
"\n",
" Found there:\n",
" http://stackoverflow.com/a/22357811/2192272\n",
" \"\"\"\n",
" if len(x.shape) == 1:\n",
" x = x[:,None]\n",
" median = np.median(x, axis=0)\n",
" diff = np.sum((x - median)**2, axis=-1)\n",
" diff = np.sqrt(diff)\n",
" med_abs_deviation = np.median(diff)\n",
"\n",
" modified_z_score = 0.6745 * diff / med_abs_deviation\n",
"\n",
" return modified_z_score > thresh\n",
"\n",
"\n",
"def _make_polygon(points, tri_vertices):\n",
" \"\"\"Make polygon out of edges (e.g. from a Delaunay triangulation)\n",
" \n",
" Return: Shapely Polygon or MultiPolygon\n",
" \n",
" inspired from: https://sgillies.net/2012/10/13/the-fading-shape-of-alpha.html\n",
" \"\"\"\n",
" edge_points = []\n",
"\n",
" def _add_edge(i, j):\n",
" \"\"\"Add a line between the i-th and j-th points\"\"\"\n",
" edge_points.append(points[ [i, j] ])\n",
"\n",
" # loop over triangles: \n",
" # ia, ib, ic = indices of corner points of the triangle\n",
" for ia, ib, ic in tri_vertices:\n",
" _add_edge(ia, ib)\n",
" _add_edge(ib, ic)\n",
" _add_edge(ic, ia)\n",
"\n",
" m = MultiLineString(edge_points)\n",
" subpoly = list(polygonize(m))\n",
" poly = cascaded_union(subpoly)\n",
" return poly\n",
"\n",
"\n",
"def get_concave_hull(points, thres=3.5):\n",
" \"\"\"\n",
" Parameters\n",
" ----------\n",
" points: shapely line or (n, 2) array of points\n",
" thresh : passed to is_outlier \n",
" \n",
" Returns\n",
" -------\n",
" shapely's Polygon or MultiPolygon (if disjoint polygons)\n",
" if a MultiPolygon is returned, this is a problem...\n",
" Simplify geometry in the first place, or use a higher threshold.\n",
" \"\"\"\n",
" points = np.asarray(points)\n",
" tri = Delaunay(points)\n",
" radii = _get_radii(points, tri.vertices)\n",
" outliers = is_outlier(radii, thres)\n",
" poly = _make_polygon(points, tri.vertices[~outliers])\n",
" if isinstance(poly, MultiPolygon):\n",
" warnings.warn('disjoint polygons: use higher threshold (hint: simplify geometry)')\n",
" return poly.boundary"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": false
},
"outputs": [
{
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"text/plain": [
"<shapely.geometry.linestring.LineString at 0x7f0ae150e210>"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# simply geometry without tolerance\n",
"# speed up things (otherwise final polygons might be disjoint)\n",
"tol = 2e3\n",
"outl2 = outl.simplify(tol)\n",
"outl2"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {
"collapsed": false
},
"outputs": [
{
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],
"text/plain": [
"<shapely.geometry.collection.GeometryCollection at 0x7f0ae11bc610>"
]
},
"execution_count": 59,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"hull = get_concave_hull(outl2)\n",
"import shapely\n",
"shapely.geometry.collection.GeometryCollection([Polygon(outl), hull])"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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