{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# The HFM library - A fast marching solver with adaptive stencils\n", "\n", "## Part : Isotropic and anisotropic metrics\n", "## Chapter : Rander metrics\n", "\n", "In this notebook, we demonstrate anisotropic fast marching with Rander metrics, in two dimensions. \n", "\n", "Rander metrics are a generalization of Riemannian metrics, featuring an additional linear term. \n", "They are also a special case of non-symmetric Finslerian metrics.\n", "A Rander metric measures vectors according to the formula:\n", "$$\n", " F_x(v) := \\|v\\|_{M(x)} + <\\omega(x), v>\n", "$$\n", "where $M$ is a field of symmetric positive definite tensors, and $\\omega$ is a vector field.\n", "Applications of Rander metrics include:\n", "* *Zermelo's navigation problem*: find the shortest path for a boat subject to a drift due to ocean current.\n", "* *Chan-Vese segmentation model*: find a sub-domain in an image minimizing an energy comprised of a region term and a boundary term.\n", "\n", "The HFM software computes the distance associated to a given Rander metric, and the corresponding minimal paths, by solving a variant of the eikonal PDE. Namely for all $x$ within a domain $\\Omega$\n", "$$\n", " \\|\\nabla u(x)\\|_{D(x)} + <\\eta(x),\\nabla u(x)> = 1,\n", "% \\|\\nabla u(x) - \\omega(x)\\|_{M(x)^{-1}} = 1.\n", "$$\n", "where $(D,\\eta)$ is the dual metric. Some algebraic formulas allow to express the dual metric in terms of $(M,\\omega)$, the primal metric, see the first two references below.\n", "\n", "\n", "**References** The experiments presented in this notebook, or close variants, are presented in the following publications.\n", "\n", "* On Zermelo's navigation problem\n", "\n", "Mirebeau, J.-M. (2014). Efficient fast marching with Finsler metrics. Numerische Mathematik, 126(3), 515–557. [link](https://hal.archives-ouvertes.fr/hal-00736431)\n", "\n", "Mirebeau, J.-M. (2017, April 12). Riemannian fast-marching on cartesian grids using Voronoi's first reduction of quadratic forms. HAL (Preprint). [link](https://hal.archives-ouvertes.fr/hal-01507334)\n", "\n", "* On the segmentation problem:\n", "\n", "Mirebeau, J.-M., Cohen, L. D., Chen, D., & Mirebeau, J.-M. (2016). Finsler Geodesics Evolution Model for Region based Active Contours. In E. R. H. Richard C Wilson & W. A. P. Smith (Eds.), (pp. 22.1–22.12). Presented at the Proceedings of the British Machine Vision Conference (BMVC), BMVA Press. http://doi.org/10.5244/C.30.22" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[**Summary**](Summary.ipynb) of volume Fast Marching Methods, this series of notebooks.\n", "\n", "[**Main summary**](../Summary.ipynb) of the Adaptive Grid Discretizations \n", "\tbook of notebooks, including the other volumes.\n", "\n", "# Table of contents\n", " * [1. Zermelo's navigation problem](#1.-Zermelo's-navigation-problem)\n", " * [2. The Chan-Vese model](#2.-The-Chan-Vese-model)\n", " * [2.1 A synthetic instance](#2.1-A-synthetic-instance)\n", "\n", "\n", "\n", "This Python® notebook is intended as documentation and testing for the [HamiltonFastMarching (HFM) library](https://github.com/mirebeau/HamiltonFastMarching), which also has interfaces to the Matlab® and Mathematica® languages. \n", "More information on the HFM library in the manuscript:\n", "* Jean-Marie Mirebeau, Jorg Portegies, \"Hamiltonian Fast Marching: A numerical solver for anisotropic and non-holonomic eikonal PDEs\", 2019 [(link)](https://hal.archives-ouvertes.fr/hal-01778322)\n", "\n", "Copyright Jean-Marie Mirebeau, University Paris-Sud, CNRS, University Paris-Saclay" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 0. Importing the required libraries" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:57:21.600324Z", "iopub.status.busy": "2024-04-30T08:57:21.599843Z", "iopub.status.idle": "2024-04-30T08:57:21.614973Z", "shell.execute_reply": "2024-04-30T08:57:21.614403Z" } }, "outputs": [], "source": [ "import sys; sys.path.insert(0,\"..\") # Allow import of agd from parent directory (useless if conda package installed)\n", "#from Miscellaneous import TocTools; print(TocTools.displayTOC('Rander','FMM'))" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:57:21.618202Z", "iopub.status.busy": "2024-04-30T08:57:21.617922Z", "iopub.status.idle": "2024-04-30T08:57:21.877359Z", "shell.execute_reply": "2024-04-30T08:57:21.876921Z" } }, "outputs": [], "source": [ "from agd import Eikonal\n", "from agd.Plotting import savefig, quiver; #savefig.dirName = 'Figures/Rander'\n", "from agd.Metrics import Rander" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:57:21.879125Z", "iopub.status.busy": "2024-04-30T08:57:21.878992Z", "iopub.status.idle": "2024-04-30T08:57:21.884410Z", "shell.execute_reply": "2024-04-30T08:57:21.884137Z" } }, "outputs": [], "source": [ "import numpy as np; xp=np\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 0.1 Optional configuration\n", "Uncomment the following line use the GPU eikonal solver. (Comment it for the CPU eikonal solver.)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:57:21.885899Z", "iopub.status.busy": "2024-04-30T08:57:21.885815Z", "iopub.status.idle": "2024-04-30T08:57:21.887494Z", "shell.execute_reply": "2024-04-30T08:57:21.887266Z" }, "tags": [ "EikonalGPU_config" ] }, "outputs": [], "source": [ "#import agd.AutomaticDifferentiation as ad; xp,quiver,plt,Eikonal = map(ad.cupy_friendly,(xp,quiver,plt,Eikonal))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Zermelo's navigation problem\n", "\n", "We compute the travel time and shortest path for a vehicle with unit velocity in all directions, but suject to a drift. In order words, the vehicle trajectory $\\gamma$ obeys at all times \n", "$$\n", " \\| \\gamma'(t) - V(\\gamma(t)) \\|_{D(\\gamma(t))^{-1}} = 1,\n", "$$\n", "where $\\eta$ is the given drift, e.g. ocean current. The positive definite tensor field $D$ is chosen here equal to the identity, but could be modified to account for similar problems posed on manifolds.\n", "\n", "Zermelo's navigation is locally controllable iff for all $x$ within the domain $\\Omega$ one has\n", "$$\n", " \\|V(x)\\|_{D(x)^{-1}} < 1.\n", "$$\n", "This condition is a pre-requisite for our eikonal solver to function." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:57:21.888865Z", "iopub.status.busy": "2024-04-30T08:57:21.888784Z", "iopub.status.idle": "2024-04-30T08:57:21.891083Z", "shell.execute_reply": "2024-04-30T08:57:21.890835Z" } }, "outputs": [], "source": [ "hfmIn = Eikonal.dictIn({\n", " 'model':'Rander2',\n", " 'exportValues':1,\n", " 'seed':[0.,0.],\n", "})\n", "\n", "# Define the domain\n", "n=201\n", "hfmIn.SetRect(sides=[[-0.5,0.5],[-0.5,0.5]],dimx=n)\n", "hfmIn.SetUniformTips((6,6))" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:57:21.892440Z", "iopub.status.busy": "2024-04-30T08:57:21.892361Z", "iopub.status.idle": "2024-04-30T08:57:21.895376Z", "shell.execute_reply": "2024-04-30T08:57:21.895067Z" } }, "outputs": [], "source": [ "X = hfmIn.Grid()\n", "R = np.linalg.norm(X,axis=0)\n", "driftMult = 0.9*np.sin(4*np.pi*X[0])*np.sin(4.*np.pi*X[1])\n", "drift = (driftMult/R) * X" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The drift, illustrated in the next figure, increases or decreases the vehicle motion depending on its position and orientation. In particular, we see that close to the image center, the drift field\n", "* *increases* velocity along directions $\\pm (1,1)$.\n", "* *decreases* velocity along directions $\\pm (1,-1)$. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:57:21.896824Z", "iopub.status.busy": "2024-04-30T08:57:21.896740Z", "iopub.status.idle": "2024-04-30T08:57:21.971813Z", "shell.execute_reply": "2024-04-30T08:57:21.971524Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=[4,4]); plt.axis('equal'); \n", "plt.title('Drift vector field');\n", "quiver(*X,*drift,subsampling=(5,5));\n", "savefig(fig,\"DriftVectorField.png\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Rander metric associated to Zermelo's problem is not completely trivial.\n", "The dual metric of Zermelo's navigation problem is $(D,-V)$, whereas the primal metric has a more complex expression, for which we refer to the papers cited in the introduction. In any case, the relevant formulas are implemented in the Rander class." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:57:21.973706Z", "iopub.status.busy": "2024-04-30T08:57:21.973486Z", "iopub.status.idle": "2024-04-30T08:57:22.783719Z", "shell.execute_reply": "2024-04-30T08:57:22.783319Z" } }, "outputs": [], "source": [ "hfmIn['metric'] = Rander.from_Zermelo(xp.eye(2),drift) # Riemannian metric, and drift" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:57:22.785507Z", "iopub.status.busy": "2024-04-30T08:57:22.785398Z", "iopub.status.idle": "2024-04-30T08:57:22.868613Z", "shell.execute_reply": "2024-04-30T08:57:22.868277Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field cosAngleMin defaults to 0.5\n", "Field refineStencilAtWallBoundary defaults to 0\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.025412 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 8.45\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:57:22.870193Z", "iopub.status.busy": "2024-04-30T08:57:22.870084Z", "iopub.status.idle": "2024-04-30T08:57:22.951443Z", "shell.execute_reply": "2024-04-30T08:57:22.951160Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=[4,4]); plt.axis('equal'); \n", "plt.title('Distance map, Zermelo\\'s navigation problem');\n", "plt.contourf(*X,hfmOut['values']);\n", "savefig(fig,\"ZermeloDistance.png\")" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:57:22.953079Z", "iopub.status.busy": "2024-04-30T08:57:22.952969Z", "iopub.status.idle": "2024-04-30T08:57:23.015202Z", "shell.execute_reply": "2024-04-30T08:57:23.014944Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=[4,4]); plt.axis('equal'); \n", "plt.title('Minimal geodesics, Zermelo\\'s navigation problem');\n", "for geo in hfmOut['geodesics']: plt.plot(*geo) \n", "savefig(fig,\"ZermeloPaths.png\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. The Chan-Vese model\n", "\n", "Variational image segmentation methods define image sub-domains by minimizing an energy, comprised of region terms and a boundary terms. The most well known model, the Mumford-Shah model, is also among the most complex and will not be addressed here (unkown number of regions, whose energy contribution is determined by a PDE, cracks, etc ...). \n", "\n", "In the case of binary image segmentation, one is minimizing\n", "$$\n", " E(U) = F(U) + G(\\partial U)\n", "$$\n", "among all sub-domains $U \\subset \\Omega$, the second region being $\\Omega \\setminus U$.\n", "\n", "In the *Chan-Vese model*, the region term is linear and defined by a function $f$, while the boundary term is a measure of length, possibly defined by a Riemannian metric $M$.\n", "$$\n", "\\begin{aligned}\n", " F(U) &= \\int_U f, &\n", " G(\\partial U) &= \\mathrm{len}_M(\\partial U) \n", "\\end{aligned}\n", "$$\n", " \n", "Assume that $\\partial U$ is parametrized counter-clockwise by a path $\\gamma : [0,1] \\to \\Omega$, and that $f = \\mathrm{div} V$ in the neighborhood of $\\gamma$ (more on the computation of $V$ below). Then the energy rewrites, using Stokes theorem for the region term,\n", "$$\n", " E(U) = \\int_0^1 \\| \\gamma'(t) \\|_{M(\\gamma(t))} + < \\gamma'(t), V(t)^\\perp> \\mathrm{d}t.\n", "$$\n", "In other words, $U$ is optimal if and only iff its boundary is a minimal path w.r.t. the Rander metric of parameters $(M,V^\\perp)$. \n", "\n", "\n", "**Application examples.** Due to lack of time, only a synthetic problem is presented in this notebook. See the reference in the introduction for application examples.\n", "\n", "**An iterative or non-iterative method ?** In ideal conditions, the above characterization allows to extract the optimal sub-domain $U$ in a single run of the fast marching algorithm, with the suitable Rander metric. In practice, an iterative approach is nevertheless required for the following reasons:\n", "* *Placement of the endpoints.* Two endpoints lying exactly on the boundary of the optimal $\\partial U$ would be needed to extract $\\partial U$ between them. These endpoints are usually not known initially.\n", "* *Positivity of the Rander metric* The above approach is only valid if $(M,V^\\perp)$ do define a positive Rander metric, in other words if $\\|V(x)^\\perp\\|_{M(x)^{-1}}$ at each point $x$. Such a vector $V$ is obtained by a convolution, or by solving a poisson equation. In order to meet the smallness requirement, these computations are often limited to a small band around some current guess of the boundary.\n", "* *Non-linear region functional* An iterative approach is required if the region term in the energy is non-linear.\n", "\n", "**Note on numerical experiments**\n", "We content ourselves with a purely synthetic instance, and refer to the reference cited in the introduction for application inspired examples." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.1 A synthetic instance\n", "\n", "We check the soundness of the approach on a completely analytic instance.\n", "Contour length is measured using the Euclidean metric $M = \\mathrm{Id}$.\n", "On the other hand, the region term is defined by the integral of \n", "$$\n", "\\begin{aligned}\n", " f(x) = 4(\\|x\\|^2-1) e^{-\\|x\\|^2}.\n", "\\end{aligned}\n", "$$\n", "This function is chosen so that $f=\\mathrm{div} V$ with \n", "$$\n", "\\begin{aligned}\n", " V(x) = - 2 x e^{-\\|x\\|^2}.\n", "\\end{aligned}\n", "$$\n", "\n", "In view of the problem symmetries, the energy is maximized on some disk centered at the origin.\n", "The energy of a disk of radius $r$ is \n", "$$\n", "R(D_r) = 2 \\pi \\int_0^r f(r) r \\mathrm{d}r + 2 \\pi r.\n", "$$\n", "This energy is extremal when $1+r f(r)=0$, which occurs for $r=0.64..$ (minimum), and $r=0.30..$ (local maximum).\n", "\n", "" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:57:23.016725Z", "iopub.status.busy": "2024-04-30T08:57:23.016620Z", "iopub.status.idle": "2024-04-30T08:57:23.065462Z", "shell.execute_reply": "2024-04-30T08:57:23.065173Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Roots of 1+r f(r)\n", "r=xp.linspace(0,1)\n", "def f(r): \n", " return 4*(r**2-1)*np.exp(-r**2)\n", "plt.plot(r,1+r*f(r),\n", " r,0.*r);" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:57:23.067230Z", "iopub.status.busy": "2024-04-30T08:57:23.067120Z", "iopub.status.idle": "2024-04-30T08:57:23.070835Z", "shell.execute_reply": "2024-04-30T08:57:23.070582Z" } }, "outputs": [], "source": [ "hfmIn = Eikonal.dictIn({\n", " 'model':'Rander2',\n", " 'exportValues':1,\n", " \n", " # Ideal case : the seed and tip are \n", " # already on the optimal region boundary\n", " 'seed':[0.64,0.],\n", " 'tip': [-0.64,0.],\n", "})\n", "\n", "# Define the domain\n", "n=201\n", "hfmIn.SetRect(sides=[[-1,1],[-1,1]],dimx=n)\n", "\n", "X = hfmIn.Grid()\n", "R = np.linalg.norm(X,axis=0)\n", "v = -2*X*np.exp(-R**2)\n", "\n", "hfmIn['metric'] = Rander(xp.eye(2),[v[1],-v[0]])" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:57:23.072621Z", "iopub.status.busy": "2024-04-30T08:57:23.072539Z", "iopub.status.idle": "2024-04-30T08:57:23.164305Z", "shell.execute_reply": "2024-04-30T08:57:23.163977Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field cosAngleMin defaults to 0.5\n", "Field refineStencilAtWallBoundary defaults to 0\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.032072 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 8.45\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:57:23.165904Z", "iopub.status.busy": "2024-04-30T08:57:23.165788Z", "iopub.status.idle": "2024-04-30T08:57:23.225800Z", "shell.execute_reply": "2024-04-30T08:57:23.225535Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=[4,4]); plt.title('Distance map, Isoperimetric problem'); plt.axis('equal'); \n", "plt.contourf(*X,hfmOut['values']);" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:57:23.227237Z", "iopub.status.busy": "2024-04-30T08:57:23.227155Z", "iopub.status.idle": "2024-04-30T08:57:23.280203Z", "shell.execute_reply": "2024-04-30T08:57:23.279936Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# As expected, the extracted boundary is an arc of circle.\n", "fig = plt.figure(figsize=[4,4]); plt.title('Minimal geodesic, Isoperimetric problem'); plt.axis('equal'); \n", "plt.plot(*hfmOut['geodesic']);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Extracting the second half of the boundary**\n", "\n", "By exchanging the roles of the seeds and tips, we extract the second half of the boundary." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:57:23.281720Z", "iopub.status.busy": "2024-04-30T08:57:23.281632Z", "iopub.status.idle": "2024-04-30T08:57:23.283507Z", "shell.execute_reply": "2024-04-30T08:57:23.283265Z" } }, "outputs": [], "source": [ "hfmIn['seed'],hfmIn['tip'] = hfmIn['tip'],hfmIn['seed'] " ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:57:23.284867Z", "iopub.status.busy": "2024-04-30T08:57:23.284786Z", "iopub.status.idle": "2024-04-30T08:57:23.381279Z", "shell.execute_reply": "2024-04-30T08:57:23.380896Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field cosAngleMin defaults to 0.5\n", "Field refineStencilAtWallBoundary defaults to 0\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.034914 s.\n", "Field geodesicSolver defaults to Discrete\n", "Field geodesicStep defaults to 0.25\n", "Field geodesicWeightThreshold defaults to 0.001\n", "Field geodesicVolumeBound defaults to 8.45\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:57:23.383210Z", "iopub.status.busy": "2024-04-30T08:57:23.383058Z", "iopub.status.idle": "2024-04-30T08:57:23.449830Z", "shell.execute_reply": "2024-04-30T08:57:23.449531Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=[4,4]); plt.title('Distance map, Isoperimetric problem'); plt.axis('equal'); \n", "plt.contourf(*X,hfmOut['values']);" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:57:23.451517Z", "iopub.status.busy": "2024-04-30T08:57:23.451393Z", "iopub.status.idle": "2024-04-30T08:57:23.509960Z", "shell.execute_reply": "2024-04-30T08:57:23.509685Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# As expected, the extracted boundary is an arc of circle.\n", "fig = plt.figure(figsize=[4,4]); plt.title('Minimal geodesics, Isoperimetric problem'); plt.axis('equal'); \n", "plt.plot(*hfmOut['geodesic']);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Format de la Cellule Texte Brut", "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.8" } }, "nbformat": 4, "nbformat_minor": 2 }