{ "cells": [ { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# The HFM library - A fast marching solver with adaptive stencils\n", "\n", "## Part : Isotropic and anisotropic metrics\n", "## Chapter : Riemannian metrics\n", "\n", "In this notebook, we demonstrate anisotropic Riemannian fast marching, in two and three dimensions. The implementation and the numerical examples are based on the paper:\n", "* [Mir17] J.-M. Mirebeau, “Anisotropic fast-marching on cartesian grids using Voronoi's first reduction of quadratic forms,” SINUM, 2019. [link](https://hal.archives-ouvertes.fr/hal-01507334)\n", "\n", "More formally, we numerically solve Riemannian eikonal equations, and backtrack the corresponding minimal geodesics. In order to describe this mathematical problem we need to introduce some notation. Let $\\Omega \\subset \\mathbb R^d$ be a domain, let $D : \\Omega \\to S^{++}(\\mathbb R^d)$ be a field of positive definite tensors, and let $\\sigma : \\partial \\Omega \\to ]-\\infty,\\infty]$ denote some boundary data. \n", "We seek the viscosity solution $u : \\overline \\Omega \\to ]-\\infty,\\infty]$ to the partial differential equation\n", "\\begin{align*}\n", " \\forall x \\in \\Omega, \\|\\nabla u(x)\\|_{D(x)} &= 1 &\n", " \\forall x \\in \\partial \\Omega, u(x) &= \\sigma(x).\n", "\\end{align*}\n", "We denoted by $\\|v\\|_D := \\sqrt{v^T\\cdot D \\cdot v}$ the anisotropic norm of a vectors $v \\in \\mathbb R^d$ defined by a positive definite tensor $D\\in S^{++}(\\mathbb R^d)$.\n", "\n", "\n", "The solution value $u(x)$, for $x\\in \\Omega$, is known to be the minimal Riemannian length (plus the initial penalization $\\sigma$) of a path $\\gamma : [0,1] \\to \\overline \\Omega$ from $\\partial \\Omega$ to $x$. \n", "\\begin{equation*}\n", " u(x) = \\inf_{\\substack{\\gamma(0) \\in \\partial \\Omega\\\\ \\gamma(1)=x}} \\sigma(\\gamma(0)) + \\int_0^1 \\| \\gamma'(t) \\|_{M(\\gamma(t))} \\, \\mathrm d t.\n", "\\end{equation*}\n", "In the last equation, path length is measured using the Riemannian metric $M : \\Omega \\to S^{++}(\\mathbb R^d)$ defined as the inverse $M = D^{-1}$ of the tensor fields appearing in the eikonal PDE.\n", "\n", "\n", "**Anisotropy of a Riemannian metric.**\n", "Denote by $\\mu(M)$ the anisotropy of a positive definite tensor, which is also the square root of its condition number:\n", "$$\n", " \\mu(M) := \\max_{|v|=|w|=1} \\frac {\\|v\\|_M}{\\|w\\|_M} = \\sqrt{\\frac{\\lambda_{\\max}(M)}{\\lambda_{\\min}(M)}},\n", "$$\n", "where $\\lambda_{\\min}(M)$ and $\\lambda_{\\max}(M)$ denote respectively the smallest and largest eigenvalue of $M$.\n", "\n", "The algorithms implemented in the HFM library use adaptive stencils, depending on the metric tensor anisotropy, which work best when $\\mu(M(x)) \\lesssim 10$ for all $x \\in \\Omega$. Some test cases satisfying $\\mu(M(x)) = 100$ for some $x \\in \\Omega$, are also passed successfully, but there is a risk of accuracy loss for such strong anisotropies. \n" ] }, { "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. Two dimensional examples](#1.-Two-dimensional-examples)\n", " * [1.1 Geodesic distance on a surface defined by a height map](#1.1-Geodesic-distance-on--a-surface-defined-by-a-height-map)\n", " * [1.2 Defining a metric by its eigenvectors and eigenvalues](#1.2-Defining-a-metric-by-its-eigenvectors-and-eigenvalues)\n", " * [1.3 A discontinuous and extremely anisotropic Riemannian metric](#1.3-A-discontinuous-and-extremely-anisotropic-Riemannian-metric)\n", " * [1.4 Axis dependent grid scale](#1.4-Axis-dependent-grid-scale)\n", " * [2. Three dimensional examples](#2.-Three-dimensional-examples)\n", " * [2.1 A smooth Riemannian metric](#2.1-A-smooth-Riemannian-metric)\n", " * [2.2 A discontinuous and strongly anisotropic Riemannian metric](#2.2-A-discontinuous-and-strongly-anisotropic-Riemannian-metric)\n", " * [3. Sensitivity analysis](#3.-Sensitivity-analysis)\n", " * [3.1 Backward differentiation](#3.1-Backward-differentiation)\n", " * [3.2 Forward differentiation](#3.2-Forward-differentiation)\n", " * [4. Voronoi regions](#4.-Voronoi-regions)\n", " * [5. Contruction of the Riemannian tensors](#5.-Contruction-of-the-Riemannian-tensors)\n", " * [5.1 Dimension lifting](#5.1-Dimension-lifting)\n", " * [5.2 Mapping the eigenvalues of a given tensor field.](#5.2-Mapping-the-eigenvalues-of-a-given-tensor-field.)\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": "2024-04-30T08:59:15.655551Z", "iopub.status.busy": "2024-04-30T08:59:15.655095Z", "iopub.status.idle": "2024-04-30T08:59:15.671582Z", "shell.execute_reply": "2024-04-30T08:59:15.670946Z" } }, "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('Riemannian','FMM'))" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:15.675348Z", "iopub.status.busy": "2024-04-30T08:59:15.675030Z", "iopub.status.idle": "2024-04-30T08:59:15.938284Z", "shell.execute_reply": "2024-04-30T08:59:15.937946Z" } }, "outputs": [], "source": [ "from agd import Eikonal\n", "from agd.Metrics import Riemann\n", "from agd.Plotting import savefig, quiver; #savefig.dirName = 'Figures/Riemannian'\n", "from agd import LinearParallel as lp\n", "from agd import AutomaticDifferentiation as ad\n", "norm_infinity = ad.Optimization.norm_infinity" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:15.940393Z", "iopub.status.busy": "2024-04-30T08:59:15.940197Z", "iopub.status.idle": "2024-04-30T08:59:15.946340Z", "shell.execute_reply": "2024-04-30T08:59:15.946090Z" } }, "outputs": [], "source": [ "import numpy as np; xp=np\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "\n", "# Required for 3D plotting\n", "from mpl_toolkits.mplot3d import Axes3D # Plots geodesics\n", "useMayavi = False\n", "if useMayavi:\n", " from mayavi import mlab # Plots implicit surfaces" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 0.1 Optional configuration\n", "Uncomment the following line to use the GPU eikonal solver. (Comment it for the CPU eikonal solver.)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:15.947846Z", "iopub.status.busy": "2024-04-30T08:59:15.947763Z", "iopub.status.idle": "2024-04-30T08:59:15.949416Z", "shell.execute_reply": "2024-04-30T08:59:15.949206Z" }, "tags": [ "EikonalGPU_config" ] }, "outputs": [], "source": [ "#xp,plt,quiver,Eikonal = map(ad.cupy_friendly,(xp,plt,quiver,Eikonal))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Two dimensional examples\n", "\n", "\n", "Our first step is to define the domain $\\Omega$, which is chosen as the unit square $]-0.5,0.5[^2$. A seed point is introduced in the center." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:15.950781Z", "iopub.status.busy": "2024-04-30T08:59:15.950702Z", "iopub.status.idle": "2024-04-30T08:59:15.952770Z", "shell.execute_reply": "2024-04-30T08:59:15.952524Z" } }, "outputs": [], "source": [ "hfmIn = Eikonal.dictIn({\n", " 'model':'Riemann2', # Two-dimensional Riemannian eikonal equation\n", " 'seed':[0.,0.], # Using a single seed point in this example.\n", " 'seedValue':0, # Can be omitted, since this is the default.\n", "})\n", "hfmIn.SetRect(sides=[[-0.5,0.5],[-0.5,0.5]],dimx=101)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We choose to use a formally second order accurate scheme, so as to improve accuracy. As discussed in [[1]](#cite_Mirebeau_2017_Voronoi) second order convergence rates can indeed be achieved in certain cases, but only in the average sense, and with boundary data less singular than the single seeds considered here." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:15.954193Z", "iopub.status.busy": "2024-04-30T08:59:15.954106Z", "iopub.status.idle": "2024-04-30T08:59:15.955740Z", "shell.execute_reply": "2024-04-30T08:59:15.955505Z" } }, "outputs": [], "source": [ "hfmIn['order'] = 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We next introduce a coordinate system $X,Y$ in the domain $\\Omega = ]0.5,0.5[^2$, which will be used to define the Riemannian metrics. The HFM library uses the convention that discretization points are centered in the corresponding voxels, hence we need to introduce an adequate variant of the np.linspace function." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.1 Geodesic distance on a surface defined by a height map\n", "\n", "Our first objective is to compute minimal geodesics along a parametrized surface, defined by the following height map\n", "\\begin{align*}\n", " z(x,y) &:= (3/4) sin(3 \\pi x) sin(3 \\pi y), &\n", " \\text{ where } (x,y) \\in ]-0.5,0.5[^2.\n", "\\end{align*}\n", "" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:15.957162Z", "iopub.status.busy": "2024-04-30T08:59:15.957084Z", "iopub.status.idle": "2024-04-30T08:59:15.959340Z", "shell.execute_reply": "2024-04-30T08:59:15.959120Z" } }, "outputs": [], "source": [ "def Elevation(x,y):\n", " return (3/4.)*np.sin(3*np.pi*x)*np.sin(3*np.pi*y)\n", "X,Y = hfmIn.Grid()\n", "Z = Elevation(X,Y)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:15.960634Z", "iopub.status.busy": "2024-04-30T08:59:15.960557Z", "iopub.status.idle": "2024-04-30T08:59:15.962336Z", "shell.execute_reply": "2024-04-30T08:59:15.962085Z" } }, "outputs": [], "source": [ "if useMayavi:\n", " mlab.surf(Y,X,Z)\n", " mlab.view(azimuth=-60,distance=4,elevation=30)\n", " mlab.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This should be displayed in the Mayavi window.\n", "![Embedded surface](https://dl.dropbox.com/s/25epuya62r90ouh/EmbeddedManifold.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By standard arguments of differential geometry, it is equivalent to compute geodesics on the parametrization domain $]-0.5,0.5[^2$, with respect to the metric defined by \n", "\\begin{equation*}\n", " M(x,y) := 1+\\nabla z(x,y) \\cdot \\nabla z(x,y)^T = \n", " \\begin{pmatrix}\n", " 1+ (\\partial_x z)^2 & (\\partial_x z) (\\partial_y z) \\\\\n", " (\\partial_x z) (\\partial_y z) & 1+ (\\partial_y z)^2\n", " \\end{pmatrix}\n", "\\end{equation*}\n", "where we denoted $\\partial_x z := \\frac{\\partial z}{\\partial x}(x,y)$ and likewise $\\partial_y z := \\frac{\\partial z}{\\partial y}(x,y)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The HFM library requires two-dimensional symmetric matrices\n", "$\n", "\\begin{pmatrix}\n", "a & b \\\\\n", "b & c\n", "\\end{pmatrix}\n", "$\n", "to be described as a triplet $(a,b,c)$.\n", "The Riemannian metric of the problem of interest is thus represented numerically as follows.\n", "\n", "**Three dimensional case.**\n", "In general, a Riemannian metric in dimension $d$ can be specified as `Riemann(m)` where `m` is an array of shape $(d,d,n_1,\\cdots,n_d)$, which is symmetric w.r.t the first two indices. The code presented below thus extends in a straightforward manner to three dimensions. " ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:15.963736Z", "iopub.status.busy": "2024-04-30T08:59:15.963657Z", "iopub.status.idle": "2024-04-30T08:59:15.965824Z", "shell.execute_reply": "2024-04-30T08:59:15.965571Z" } }, "outputs": [], "source": [ "try: DxZ,DyZ = np.gradient(Z,hfmIn['gridScale'],axis=(0,1)) # Warning : numpy's default is axis=(1,0) !\n", "except TypeError: # cupy does not implement 'gradient'. We rely on automatic differentiation instead.\n", " DxZ,DyZ = Elevation(*ad.Dense.identity(constant=(X,Y),shape_free=(2,))).gradient()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:15.967109Z", "iopub.status.busy": "2024-04-30T08:59:15.967033Z", "iopub.status.idle": "2024-04-30T08:59:15.968962Z", "shell.execute_reply": "2024-04-30T08:59:15.968742Z" } }, "outputs": [], "source": [ "hfmIn['metric'] = Riemann([[1+DxZ**2,DxZ*DyZ],[DxZ*DyZ,1+DyZ**2]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Internally, the HFM software will invert the metric tensors. The inverse tensor may be provided directly, instead of the primal tensors, via key 'dualMetric'." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we indicate which outputs are required (some backtraced geodesics, the PDE solution, the geodesic flow direction), and call the HFM software." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:15.970350Z", "iopub.status.busy": "2024-04-30T08:59:15.970265Z", "iopub.status.idle": "2024-04-30T08:59:15.972070Z", "shell.execute_reply": "2024-04-30T08:59:15.971825Z" } }, "outputs": [], "source": [ "hfmIn.SetUniformTips((6,6)) # Uniformly sampled tips in the domain.\n", "hfmIn['exportValues'] = 1\n", "hfmIn['exportGeodesicFlow'] = 1" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:15.973498Z", "iopub.status.busy": "2024-04-30T08:59:15.973422Z", "iopub.status.idle": "2024-04-30T08:59:15.996475Z", "shell.execute_reply": "2024-04-30T08:59:15.996189Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.004575 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": 13, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:15.998100Z", "iopub.status.busy": "2024-04-30T08:59:15.997981Z", "iopub.status.idle": "2024-04-30T08:59:16.065750Z", "shell.execute_reply": "2024-04-30T08:59:16.065466Z" } }, "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, on a parametrized manifold'); plt.axis('equal'); \n", "plt.contourf(X,Y,hfmOut['values']);" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:16.067340Z", "iopub.status.busy": "2024-04-30T08:59:16.067230Z", "iopub.status.idle": "2024-04-30T08:59:16.131668Z", "shell.execute_reply": "2024-04-30T08:59:16.131393Z" } }, "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.title('Minimal geodesics, on a parametrized manifold'); plt.axis('equal'); \n", "for geo in hfmOut['geodesics']: plt.plot(*geo) \n", "savefig(fig,'ParametrizedGeodesics.png')" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:16.133201Z", "iopub.status.busy": "2024-04-30T08:59:16.133097Z", "iopub.status.idle": "2024-04-30T08:59:16.135342Z", "shell.execute_reply": "2024-04-30T08:59:16.135108Z" } }, "outputs": [], "source": [ "if useMayavi:\n", " for geo in hfmOut['geodesics']:\n", " mlab.plot3d(geo[0],geo[1],np.array([Elevation(x,y) for (x,y) in geo]),tube_radius=0.01)\n", " mlab.surf(X,Y,Z)\n", " mlab.view(azimuth=-60,distance=4,elevation=30)\n", " mlab.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This should be displayed in the Mayavi window.\n", "![Embedded surface and geodesics](https://dl.dropbox.com/s/b7jpocelfo1y6s0/EmbeddedGeodesics.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similar to the isotropic case, the minimal Riemannian geodesic $\\gamma$ from $\\partial \\Omega$ to a point $x \\in \\Omega$ obeys an Ordinary Differential Equation (ODE). This equation is solved backwards in time and involves a *terminal* boundary condition, at the final time $T = u(x)$, and reads:\n", "\\begin{align*}\n", " \\forall t \\leq T, \\gamma'(t) &= V(\\gamma(t)), &\n", " \\gamma(T) &=x\n", "\\end{align*}\n", "The vector field $V : \\Omega \\to {\\mathbb R}^2$ is referred to as the geodesic flow direction, and is related with the solution $u$ of the eikonal PDE by the relation\n", "\\begin{equation*}\n", " V(x) := D(x) \\nabla u(x).\n", "\\end{equation*}\n", "The geodesic flow returned by the HFM sofware is computed in an upwind manner, taking advantage of the properties of the numerical scheme. This approach is expected to be more stable than the naive approach, namely approximating of $\\nabla u(x)$ using finite differences and post-multplying by $D(x)$.\n", "\n", "Note that what we call the 'geodesic flow' is referred to as the 'Riemannian gradient of $u$' by mathematical geometers." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:16.136762Z", "iopub.status.busy": "2024-04-30T08:59:16.136662Z", "iopub.status.idle": "2024-04-30T08:59:16.217279Z", "shell.execute_reply": "2024-04-30T08:59:16.217004Z" } }, "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('Geodesic flow vector field'); plt.axis('equal'); \n", "quiver(X,Y,*hfmOut['flow'],subsampling=(5,5));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The geodesic flow has unit norm w.r.t. the Riemannian metric. Let us check this property formally: recalling that $D(x) = M(x)^{-1}$ is the inverse metric tensor\n", "\\begin{equation*}\n", "\\| V(x)\\|_{M(x)}^2 = V(x)^T \\cdot M(x) \\cdot V(x) = \\nabla u(x)^T D(x) M(x) D(x) \\nabla u(x) = \\nabla u(x)^T D(x) \\nabla u(x) = \\|\\nabla u(x)\\|^2_{D(x)}.\n", "\\end{equation*}\n", "Numerically, this identity does approximately hold, except at the seed point." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:16.218919Z", "iopub.status.busy": "2024-04-30T08:59:16.218805Z", "iopub.status.idle": "2024-04-30T08:59:16.299962Z", "shell.execute_reply": "2024-04-30T08:59:16.299697Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=[5,4]); plt.title('Riemannian norm of the geodesic flow'); plt.axis('equal')\n", "flowNorms = hfmIn['metric'].norm(hfmOut['flow'])\n", "plt.contourf(X,Y,flowNorms); plt.colorbar();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Contrary to the isotropic case, and to what the previous figure suggests, the flow norm is not exactly one. This is due to the discretization error, and illustrated in the following figure." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:16.301559Z", "iopub.status.busy": "2024-04-30T08:59:16.301440Z", "iopub.status.idle": "2024-04-30T08:59:16.397729Z", "shell.execute_reply": "2024-04-30T08:59:16.397413Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.contourf(X,Y,flowNorms, levels = np.linspace(0.90,1.05,20))\n", "plt.colorbar(); # TODO : tighter level lines around 1" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:16.399291Z", "iopub.status.busy": "2024-04-30T08:59:16.399180Z", "iopub.status.idle": "2024-04-30T08:59:16.400905Z", "shell.execute_reply": "2024-04-30T08:59:16.400661Z" } }, "outputs": [], "source": [ "hfmIn.pop('metric',None);\n", "hfmIn.pop('dualMetric',None);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.2 Defining a metric by its eigenvectors and eigenvalues\n", "\n", "In this second experiment, inspired by seismic imaging, we consider a metric $M$ with two eigenvalues $\\alpha^{-2}$ and $\\beta^{-2}$. The first one is associated with some eigenvector $v$, assumed to be of unit norm, and the second one with the orthogonal direction $v^\\perp$.\n", "\\begin{equation*}\n", " M(x,y) = \\alpha(x,y)^{-2} v(x,y)\\cdot v(x,y)^\\perp + \\beta(x,y)^{-2} v^\\perp(x,y)\\cdot v^\\perp(x,y)^T.\n", "\\end{equation*}\n", "The coefficient field $\\alpha: \\Omega \\to ]0,\\infty[$ should be regarder as the maximum speed allowed locally in the direction of the vector field $v : \\Omega \\to \\mathbb R^2$. The coefficient $\\beta$ is likewise the maximum allowed speed in the orthogonal direction. In contrast, the isotropic metrics considered in the previous notebooks only have one speed function (the speed function is the inverse $s=1/c$ of the cost function).\n", "\n", "The inverse tensor field $D=M^{-1}$ admits an expression similar to the metric\n", "\\begin{equation*}\n", " D(x,y) = \\alpha(x,y)^2 v(x,y)\\cdot v(x,y)^T + \\beta(x,y)^{2} v^\\perp(x,y)\\cdot v^\\perp(x,y)^T.\n", "\\end{equation*}\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We choose the parameters $\\alpha=0.8$, $\\beta=0.2$, and $V=(1,(\\pi/2)\\cos(4 \\pi x))$, so as to reproduce a classical test case. Note that $\\alpha$ and $\\beta$ could equally well be position dependent." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:16.402287Z", "iopub.status.busy": "2024-04-30T08:59:16.402185Z", "iopub.status.idle": "2024-04-30T08:59:16.613569Z", "shell.execute_reply": "2024-04-30T08:59:16.613275Z" } }, "outputs": [], "source": [ "alpha,beta = 0.8,0.2\n", "V = xp.ones(X.shape),(np.pi/2)*np.cos(4*np.pi*X)\n", "hfmIn['metric'] = Riemann.needle(V,alpha,beta).dual()\n", "hfmIn['exportGeodesicFlow']=0 # The geodesic flow is not used in this example" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The metric anisotropy is the ratio $\\alpha/\\beta$ of the square root of its eigenvalues." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:16.615227Z", "iopub.status.busy": "2024-04-30T08:59:16.615126Z", "iopub.status.idle": "2024-04-30T08:59:16.618421Z", "shell.execute_reply": "2024-04-30T08:59:16.618187Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Metric max anisotropy = 4.000000000000005. (alpha/beta = 4.0)\n" ] } ], "source": [ "print(f\"Metric max anisotropy = {np.max(hfmIn['metric'].anisotropy())}. (alpha/beta = {alpha/beta})\")" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:16.619818Z", "iopub.status.busy": "2024-04-30T08:59:16.619740Z", "iopub.status.idle": "2024-04-30T08:59:16.641251Z", "shell.execute_reply": "2024-04-30T08:59:16.640947Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.003592 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": 23, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:16.642893Z", "iopub.status.busy": "2024-04-30T08:59:16.642716Z", "iopub.status.idle": "2024-04-30T08:59:16.697755Z", "shell.execute_reply": "2024-04-30T08:59:16.697501Z" } }, "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'); plt.axis('equal'); \n", "plt.contourf(X,Y,hfmOut['values']);" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:16.699221Z", "iopub.status.busy": "2024-04-30T08:59:16.699140Z", "iopub.status.idle": "2024-04-30T08:59:16.760863Z", "shell.execute_reply": "2024-04-30T08:59:16.760565Z" } }, "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('Minimal paths'); plt.axis('equal'); \n", "for geo in hfmOut['geodesics']: plt.plot(*geo);" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:16.762451Z", "iopub.status.busy": "2024-04-30T08:59:16.762346Z", "iopub.status.idle": "2024-04-30T08:59:16.764074Z", "shell.execute_reply": "2024-04-30T08:59:16.763835Z" } }, "outputs": [], "source": [ "hfmIn.pop('metric',None);\n", "hfmIn.pop('dualMetric',None);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.3 A discontinuous and extremely anisotropic Riemannian metric\n", "\n", "We illustrate the robustness of the HFM library by considering a hard test case, related with medical image processing, and in particular with tubular structure segmentation. The condition number $100^2$ of the metric tensors exceeds what we would typically recommend, namely $10^2$ at most. The the discontinuities of the metric fall outside the scope of the mathematical convergence analysis of our numerical method. Nevertheles, the HFM software yields results that are usable and behave as expected qualitatively.\n", "\n", "We define a Riemannian metric $M : \\Omega \\to S^++(\\mathbb R^2)$ which strongly favors paths remaining close and tangent to a given curve $\\Gamma$.\n", "More precisely, yhe metric tensor $M(p)$, at a point $p\\in ]0.5,0.5[^2$, is defined as the identity matrix,\n", "except on a neighborhood of width $0.01$ of the spiraling curve parametrized by\n", "\\begin{equation*}\n", "\\Gamma(t) = t (\\cos(\\omega t), \\sin(\\omega t)),\n", "\\end{equation*}\n", "where $t\\in [0,0.43]$, and $\\omega=12 \\pi$. On this, extremely thin, neighborhood of the curve $\\Gamma$, the metric tensor has an extremely small eigenvalue $0.01^2$ associated with the eigenvector $\\Gamma'(t)$. The second eigenvalue is $1$. " ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:16.765566Z", "iopub.status.busy": "2024-04-30T08:59:16.765462Z", "iopub.status.idle": "2024-04-30T08:59:16.767443Z", "shell.execute_reply": "2024-04-30T08:59:16.767208Z" } }, "outputs": [], "source": [ "# For better results, we slightly increase the resolution of the domain.\n", "hfmIn.SetRect(sides=[[-0.5,0.5],[-0.5,0.5]],dimx=201)\n", "X,Y = hfmIn.Grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A short mathematical analysis, not presented here, allows to deduce the following expressions of the curve neighborhood and tangent." ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:16.768843Z", "iopub.status.busy": "2024-04-30T08:59:16.768739Z", "iopub.status.idle": "2024-04-30T08:59:16.772469Z", "shell.execute_reply": "2024-04-30T08:59:16.772222Z" } }, "outputs": [], "source": [ "omega = 12*np.pi\n", "curveNeighborhoodWidth = 0.01\n", "inverseAnisotropy = 0.01\n", "\n", "R=np.sqrt(X**2+Y**2)\n", "Theta=np.arctan2(Y,X)\n", "\n", "CurveNeighborhood = np.logical_and(np.remainder(R*omega - Theta,2.*np.pi) <= omega*curveNeighborhoodWidth, R<=0.43)\n", "CurveTangentx = -R*omega*np.sin(Theta)+np.cos(Theta)\n", "CurveTangenty = R*omega*np.cos(Theta)+np.sin(Theta)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:16.773793Z", "iopub.status.busy": "2024-04-30T08:59:16.773713Z", "iopub.status.idle": "2024-04-30T08:59:16.832605Z", "shell.execute_reply": "2024-04-30T08:59:16.832299Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=[4,4]); plt.title('Target curve neighborhood'); plt.axis('equal'); \n", "plt.contourf(X,Y,CurveNeighborhood);" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:16.834157Z", "iopub.status.busy": "2024-04-30T08:59:16.834050Z", "iopub.status.idle": "2024-04-30T08:59:16.892532Z", "shell.execute_reply": "2024-04-30T08:59:16.892269Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=[4,4]); plt.title('Target curve tangent (extended to the domain)'); plt.axis('equal'); \n", "quiver(X,Y,CurveTangentx,CurveTangenty,subsampling=(10,10));" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:16.894068Z", "iopub.status.busy": "2024-04-30T08:59:16.893963Z", "iopub.status.idle": "2024-04-30T08:59:16.898057Z", "shell.execute_reply": "2024-04-30T08:59:16.897791Z" } }, "outputs": [], "source": [ "hfmIn['metric'] = Riemann.needle([CurveTangentx,CurveTangenty],xp.where(CurveNeighborhood,inverseAnisotropy,1.),1.)" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "TODO", "GPU_geodesic_solver_does_not_converge" ] }, "source": [ "This metric has an extremely strong anisotropy, at the limit of what the HFM library can handle." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:16.899535Z", "iopub.status.busy": "2024-04-30T08:59:16.899450Z", "iopub.status.idle": "2024-04-30T08:59:16.906620Z", "shell.execute_reply": "2024-04-30T08:59:16.906370Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Max metric anisotropy : 100.00000000019524. (1/inverseAnisotropy = 100.0)\n" ] } ], "source": [ "print(f\"Max metric anisotropy : {np.max(hfmIn['metric'].anisotropy())}. (1/inverseAnisotropy = {1/inverseAnisotropy})\")" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:16.908078Z", "iopub.status.busy": "2024-04-30T08:59:16.907992Z", "iopub.status.idle": "2024-04-30T08:59:16.948332Z", "shell.execute_reply": "2024-04-30T08:59:16.948014Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.009693 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": "markdown", "metadata": {}, "source": [ "We observe numerically, as was desired from the thoretical standpoint, that the shortest path from an arbitrary point to the domain center is the concatenation of the following two parts\n", "* First: reach for the curve $\\Gamma$, in straight line.\n", "* Second: follow the curve $\\Gamma$, up to its origin. " ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:16.949965Z", "iopub.status.busy": "2024-04-30T08:59:16.949853Z", "iopub.status.idle": "2024-04-30T08:59:17.011137Z", "shell.execute_reply": "2024-04-30T08:59:17.010846Z" } }, "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, tubular segmentation test'); plt.axis('equal'); \n", "plt.contourf(X,Y,hfmOut['values'],10);" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:17.012691Z", "iopub.status.busy": "2024-04-30T08:59:17.012580Z", "iopub.status.idle": "2024-04-30T08:59:17.079652Z", "shell.execute_reply": "2024-04-30T08:59:17.079335Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=[4,4]); plt.title('Minimal paths, tubular segmentation test'); plt.axis('equal'); \n", "for geo in hfmOut['geodesics']: plt.plot(*geo)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:17.081443Z", "iopub.status.busy": "2024-04-30T08:59:17.081290Z", "iopub.status.idle": "2024-04-30T08:59:17.083369Z", "shell.execute_reply": "2024-04-30T08:59:17.083109Z" } }, "outputs": [], "source": [ "hfmIn.pop('metric',None);\n", "hfmIn.pop('dualMetric',None);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.4 Axis dependent grid scale\n", "\n", "The grid scale, along each axis, can be specified independently. We reproduce one of the above examples with this feature on. (This is also possible with the isotropic model.)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:17.084859Z", "iopub.status.busy": "2024-04-30T08:59:17.084748Z", "iopub.status.idle": "2024-04-30T08:59:17.192132Z", "shell.execute_reply": "2024-04-30T08:59:17.191880Z" } }, "outputs": [], "source": [ "#Square domain, axis dependent grid scale\n", "hfmIn = Eikonal.dictIn({\n", " 'model' : 'Riemann2',\n", " 'seeds' : [[0.,0.]],\n", " 'exportValues':1,\n", "})\n", "hfmIn.SetRect(sides=[[-0.5,0.5],[-0.5,0.5]],gridScales=[0.01,0.02]) \n", "X,Y = hfmIn.Grid()\n", "hfmIn['metric'] = Riemann.needle([xp.ones(X.shape),(np.pi/2)*np.cos(4*np.pi*X)],0.8,0.2).dual()" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:17.193644Z", "iopub.status.busy": "2024-04-30T08:59:17.193556Z", "iopub.status.idle": "2024-04-30T08:59:17.195416Z", "shell.execute_reply": "2024-04-30T08:59:17.195182Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of points along the horizontal and vertical axes: [100. 50.]\n" ] } ], "source": [ "print(\"Number of points along the horizontal and vertical axes:\",hfmIn['dims'])" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:17.196830Z", "iopub.status.busy": "2024-04-30T08:59:17.196728Z", "iopub.status.idle": "2024-04-30T08:59:17.210347Z", "shell.execute_reply": "2024-04-30T08:59:17.210041Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.001449 s.\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:17.211937Z", "iopub.status.busy": "2024-04-30T08:59:17.211823Z", "iopub.status.idle": "2024-04-30T08:59:17.276507Z", "shell.execute_reply": "2024-04-30T08:59:17.276202Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.axis('equal'); plt.title(\"Seismic test case, axis dependent grid scale\")\n", "plt.contourf(X,Y,hfmOut['values']); " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Three dimensional examples" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We conclude this notebook with by solving some three dimensional minimal path problems, with respect to anisotropic Riemannian metrics. Two test cases are considered, generalizing the two dimensional ones. More precisely, we illustrate:\n", "* the accuracy of our discretization with a test involving a smooth Riemannian metric.\n", "* the robustness of our method with a second test case involving a strongly an anisotropic and discontinuous metric.\n", "\n", "At the time of writing, generic Riemannian metrics in dimension four and above are not handled by the HFM software." ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:17.278173Z", "iopub.status.busy": "2024-04-30T08:59:17.278067Z", "iopub.status.idle": "2024-04-30T08:59:17.283270Z", "shell.execute_reply": "2024-04-30T08:59:17.282965Z" } }, "outputs": [], "source": [ "hfmIn = Eikonal.dictIn({\n", " 'model':'Riemann3', # Three-dimensional Riemannian eikonal equation\n", " 'exportValues':1,\n", " 'seed':[0.,0.,0.],\n", "})\n", "\n", "# Define the domain and get a coordinate system\n", "hfmIn.SetRect(sides=[[-0.5,0.5],[-0.5,0.5],[-0.5,0.5]],dimx=101)\n", "X,Y,Z = hfmIn.Grid()\n", "\n", "hfmIn.SetUniformTips((4,4,4))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.1 A smooth Riemannian metric\n", "\n", "We generalize to three dimensions the test case 1.b, inspired by seismic imaging. Our Riemannian metric tensors again has two eigenvalues $\\alpha^{-2}$ and $\\beta^{-2}$. The former is associated with a field $v$ of unit vectors, and later with the orthogonal plane. For any $p =(x,y,z)\\in \\mathbb R^3$, we let $M(p) \\in S^++(\\mathbb R^3)$ be defined by \n", "\\begin{equation*}\n", "M(p) = \\alpha(p)^{-2} v(p)\\cdot v(p)^T + \\beta(p)^{-2} ( \\mathrm{Id}_3 - v(p)\\cdot v(p)^T).\n", "\\end{equation*}\n", "We denoted by $\\mathrm{Id}_3$ the $3\\times 3$ identity matrix. \n", "As in the two dimensional case, the dual metric $D = M^{-1}$ is obtained by reciprocating the coefficients $\\alpha,\\beta : \\Omega \\to ]0,\\infty[$\n", "\\begin{equation*}\n", "D(p) = \\alpha(p)^{2} v(p)\\cdot v(p)^T + \\beta(p)^{2} ( \\mathrm{Id}_3 - v(p)\\cdot v(p)^T).\n", "\\end{equation*}\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Reproducing the example in [[Mir17]](#cite_Mirebeau_2017_Voronoi), we choose the eigenvalues $0.2^{-2}$ and $0.8^{-2}$, and let the field of eigenvectors be $(\\cos (3 \\pi (x+y)), \\sin (3 \\pi (2 x-y)), 0.5)$." ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:17.284831Z", "iopub.status.busy": "2024-04-30T08:59:17.284748Z", "iopub.status.idle": "2024-04-30T08:59:38.303475Z", "shell.execute_reply": "2024-04-30T08:59:38.303020Z" } }, "outputs": [], "source": [ "hfmIn['metric'] = Riemann.needle([np.cos(3*np.pi*(X+Y)), np.sin(3*np.pi*(2*X-Y)), 0.5*xp.ones(X.shape)],0.2,0.8).dual()" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:38.305182Z", "iopub.status.busy": "2024-04-30T08:59:38.305067Z", "iopub.status.idle": "2024-04-30T08:59:41.345672Z", "shell.execute_reply": "2024-04-30T08:59:41.345306Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 1.4464 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 10.985\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:41.347370Z", "iopub.status.busy": "2024-04-30T08:59:41.347249Z", "iopub.status.idle": "2024-04-30T08:59:41.443863Z", "shell.execute_reply": "2024-04-30T08:59:41.443548Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = plt.axes(projection='3d')\n", "ax.text2D(0.5,0.95,\"Minimal geodesics for a smooth 3d Riemannian metric\",transform=ax.transAxes,horizontalalignment='center')\n", "for geodesic in hfmOut['geodesics']: plt.plot(*geodesic)" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:41.445878Z", "iopub.status.busy": "2024-04-30T08:59:41.445727Z", "iopub.status.idle": "2024-04-30T08:59:41.447861Z", "shell.execute_reply": "2024-04-30T08:59:41.447575Z" } }, "outputs": [], "source": [ "if useMayavi: # Show the solution level set\n", " mlab.contour3d(hfmOutput['values'], contours=[0.3])\n", " mlab.view(azimuth=120, elevation=30)\n", " mlab.show() # Displays in an external window. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is what the previous command should display (with an appropriate viewpoint).\n", "\n", "![Solution level set](https://dl.dropbox.com/s/jjsaya4foffiu1c/2_Riemannian_Contour3D.png?dl=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.2 A discontinuous and strongly anisotropic Riemannian metric" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our second example involves discontinuous and strongly anisotropic three dimensional Riemannian metric, which favors paths remaining close and tangent to the curve $\\Gamma : [0,3] \\to {\\mathbb R}^3$ of parametrization\n", "\\begin{equation*}\n", "\\Gamma(t) := (\\cos \\omega t, \\sin \\omega t, t),\n", "\\end{equation*}\n", "where $\\omega := \\frac 5 2 \\pi$.\n", "More precisely, the metric tensors are equal to the identity matrix, except on a tube of radius 0.02 around the curve $\\Gamma$, where they have eigenvalues $(0.02^2,1,1)$, the former being associated with the tangent vector $\\Gamma'(t)$.\n", "\n", "This test case is inspired by applications to tubular structure segmentation.\n", "The condition number $50^2$ of these metric tensors, significantly exceeds what we would advise, namely $10^2$ at most. In addition, it falls outside the scope of our mathematical convergence analysis, due to its discontinuities. Nevertheless, the obtained numerical results are qualitatively satisfying, illustrating the robustness of our numerical method." ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:41.449404Z", "iopub.status.busy": "2024-04-30T08:59:41.449292Z", "iopub.status.idle": "2024-04-30T08:59:41.833771Z", "shell.execute_reply": "2024-04-30T08:59:41.833361Z" } }, "outputs": [], "source": [ "omega = (5/2)*np.pi\n", "delta = 0.02\n", "r = 0.02\n", "n=200 # We double the resolution for this test case.\n", "\n", "hfmIn.SetRect(sides=[[-1.1,1.1],[-1.1,1.1],[0,3]],dimx=n)\n", "\n", "X,Y,Z = hfmIn.Grid()\n", "Theta = np.arctan2(Y,X)\n", "\n", "def symmetricRemainder(x,n): return x - np.round(x/n)*n\n", "curveNeighborhood = symmetricRemainder(Z-Theta/omega,2.*np.pi/omega)**2+ \\\n", " (X-np.cos(Theta))**2+(Y-np.sin(Theta))**2 <= (r/2)**2\n", "curveTangentX,curveTangentY,curveTangentZ = -omega*np.sin(omega*Z), omega*np.cos(omega*Z), xp.ones(Z.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The neighborhood of the curve $\\Gamma$, where the metric tensors are distinct from the identity matrix, is only a few pixels thick as shown in the following visualization." ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:41.835530Z", "iopub.status.busy": "2024-04-30T08:59:41.835427Z", "iopub.status.idle": "2024-04-30T08:59:41.837127Z", "shell.execute_reply": "2024-04-30T08:59:41.836869Z" } }, "outputs": [], "source": [ "if useMayavi:\n", " mlab.contour3d(curveNeighborhood.astype(float), contours=[0.7])\n", " mlab.show() # Displays in an external window. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is what the mayavi window should display.\n", "![Curve neighborhood](https://dl.dropbox.com/s/4yvgdgq2k1f2ykj/2_Riemannian_TubularSupport.png?dl=0)\n", "We next gather the problem input description, and call the HFM sofware." ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:41.838581Z", "iopub.status.busy": "2024-04-30T08:59:41.838474Z", "iopub.status.idle": "2024-04-30T08:59:42.962426Z", "shell.execute_reply": "2024-04-30T08:59:42.962130Z" } }, "outputs": [], "source": [ "hfmIn.update({\n", " 'metric':Riemann.needle([curveTangentX,curveTangentY,curveTangentZ],xp.where(curveNeighborhood,delta,1.),1.),\n", " 'seed':[0.,0.,0.01],\n", " 'tip':[0.,0.,2.99],\n", "})" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T08:59:42.964115Z", "iopub.status.busy": "2024-04-30T08:59:42.964022Z", "iopub.status.idle": "2024-04-30T09:00:05.063414Z", "shell.execute_reply": "2024-04-30T09:00:05.063037Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field order defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 11.5075 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 10.985\n" ] } ], "source": [ "# Computations may take up to a minute for this rather large scale instance\n", "hfmOut = hfmIn.Run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A contour plot illustrates, as expected, the that the front propagation goes extremely fast along the spiraling curve $\\Gamma$." ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.065192Z", "iopub.status.busy": "2024-04-30T09:00:05.065060Z", "iopub.status.idle": "2024-04-30T09:00:05.067221Z", "shell.execute_reply": "2024-04-30T09:00:05.066984Z" } }, "outputs": [], "source": [ "if useMayavi:\n", " mlab.contour3d(hfmOutput['values'], contours=[0.7,1.6])\n", " mlab.show() # Displays in an external window. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is what the mayavi window should display.\n", "![Solution level set](https://dl.dropbox.com/s/ofvmbx6bol33c7x/2_Riemannian_TubularContour.png?dl=0)" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "TODO", "GPU_geodesic_does_not_reach_tip" ] }, "source": [ "The minimal geodesic from $(0,0,0)$ to $(0,0,3)$, illustrated below, is qualitatively the concatenation of three parts:\n", "* a straight line from the seed to the neighborhood of the curve $\\Gamma$\n", "* a part close and tangent to the curve $\\gamma$.\n", "* a straight line from the curve $\\gamma$ to the geodesic tip.\n", "\n", "" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.068812Z", "iopub.status.busy": "2024-04-30T09:00:05.068701Z", "iopub.status.idle": "2024-04-30T09:00:05.127347Z", "shell.execute_reply": "2024-04-30T09:00:05.127099Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = plt.axes(projection='3d')\n", "ax.text2D(0.5,0.95,\"Geodesic for a discontinuous and highly anisotropic metric\",transform=ax.transAxes,horizontalalignment='center')\n", "plt.plot(*hfmOut['geodesic']);" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.129029Z", "iopub.status.busy": "2024-04-30T09:00:05.128918Z", "iopub.status.idle": "2024-04-30T09:00:05.130661Z", "shell.execute_reply": "2024-04-30T09:00:05.130435Z" } }, "outputs": [], "source": [ "if hfmIn.mode=='gpu': \n", " raise ad.DeliberateNotebookError(\"Avanced stopping criteria and automatic differentiation not implemented on GPU\")" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## 3. Sensitivity analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sensitivity analysis, also referred to as forward and backward differentation, is described in the [previous notebook](http://nbviewer.jupyter.org/urls/rawgithub.com/Mirebeau/HFM_Python_Notebooks/master/1_Sensitivity.ipynb), in the context of isotropic metrics. This feature is also available for anisotropic Riemannian metrics.\n", "More precisely, we consider perturbations of the eikonal equation of the form \n", "\\begin{align*}\n", " \\forall x \\in \\Omega, \\| \\nabla_\\varepsilon u(x)\\|_{D(x)} &= 1+\\varepsilon\\xi(x), &\n", " \\forall x \\in \\partial \\Omega, u_\\varepsilon(x) &= \\sigma(x)+\\varepsilon \\zeta(x). \n", "\\end{align*}\n", "The calling procedure is similar to the isotropic case.\n", "\n", "One may also be interested in more general sensitivity analysis, w.r.t. generic changes in the (inverse) metric tensors, as follows\n", "\\begin{equation*}\n", "D_\\varepsilon(x) = D(x)+\\varepsilon \\Xi(x).\n", "\\end{equation*}\n", "This currently exists as well in the HFM software, but only as an experimental and undocumented feature so far. Please contact the author in case of interest.\n", "\n", "Our first step is to define the optimal control problem to be studied." ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.132064Z", "iopub.status.busy": "2024-04-30T09:00:05.131959Z", "iopub.status.idle": "2024-04-30T09:00:05.349334Z", "shell.execute_reply": "2024-04-30T09:00:05.349046Z" } }, "outputs": [], "source": [ "hfmIn = Eikonal.dictIn({\n", " 'model':'Riemann2',\n", " 'exportValues':1,\n", " 'order':1,\n", " 'seed':[0,0],\n", "})\n", "\n", "# Define the domain, here ]-0.5,0.5[^2\n", "hfmIn.SetRect(sides=[[-0.5,0.5],[-0.5,0.5]],dimx=101)\n", "X,Y = hfmIn.Grid()\n", "\n", "# Problem parameters, here similar to section 1.b\n", "hfmIn['metric'] = Riemann.needle([xp.ones(X.shape),(np.pi/2)*np.cos(4*np.pi*X)],0.8,0.2).dual()\n", "hfmIn.SetUniformTips((6,6))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.1 Backward differentiation\n", "\n", "Let us first consider backward differentiation, aka reverse mode sensitivity analysis. Denote by $u_\\varepsilon : \\overline \\Omega \\to \\mathbb R$ the solution to the eikonal equation \n", "\\begin{align*}\n", "\\forall x \\in \\Omega, \\|\\nabla u_\\varepsilon(x)\\|_{D(x)} &= 1+\\varepsilon \\xi(x) & \n", "\\forall x \\in \\partial \\Omega, u_\\varepsilon(x) &= \\sigma(x)+\\varepsilon \\zeta(x).\n", "\\end{align*}\n", "\n", "Let also $x_*\\in \\Omega$. Then, formally, similarly to the isotropic case, there exists fields $\\rho : \\Omega \\to \\mathbb R$ and $\\pi : \\partial \\Omega \\to \\mathbb R$ such that for any perturbations $\\xi, \\zeta$\n", "\\begin{equation*}\n", "u_\\varepsilon(x_*) = u(x_*)+ \\varepsilon \\left(\\int_\\Omega \\rho\\xi + \\int_{\\partial_\\Omega} \\pi \\zeta\\right) + o(\\varepsilon).\n", "\\end{equation*}" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.350935Z", "iopub.status.busy": "2024-04-30T09:00:05.350843Z", "iopub.status.idle": "2024-04-30T09:00:05.352678Z", "shell.execute_reply": "2024-04-30T09:00:05.352442Z" } }, "outputs": [], "source": [ "hfmIn['inspectSensitivity']=hfmIn['tips'][0:10] # Inspect the sensitivity of the solution at some of the tips" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.354038Z", "iopub.status.busy": "2024-04-30T09:00:05.353960Z", "iopub.status.idle": "2024-04-30T09:00:05.389389Z", "shell.execute_reply": "2024-04-30T09:00:05.389028Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.003005 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": "markdown", "metadata": {}, "source": [ "The cost sensitivity field $\\xi$ can be regarded as a diffuse representation of the geodesic from $x_*$ to the closest seed. This property, illustrated in the following visualization, is at the foundation of one of our backtracking methods. \n", "\n", "We here display the geodesic, and the sensitivity, associated with the sixth tip." ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.390982Z", "iopub.status.busy": "2024-04-30T09:00:05.390865Z", "iopub.status.idle": "2024-04-30T09:00:05.445854Z", "shell.execute_reply": "2024-04-30T09:00:05.445592Z" } }, "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('Sensitivity and minimal geodesic'); plt.axis('equal'); \n", "plt.plot(*hfmOut['geodesics'][1]);\n", "plt.contourf(X,Y,hfmOut['costSensitivity_1'],levels=np.linspace(0,0.005,10));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The sensitivity $\\pi : \\partial \\Omega \\to \\mathbb R$ to the boundary conditions is rather trivial: it is a Dirac mass, of weight $1$, located at the unique seed $(0,0)$." ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.447411Z", "iopub.status.busy": "2024-04-30T09:00:05.447305Z", "iopub.status.idle": "2024-04-30T09:00:05.449555Z", "shell.execute_reply": "2024-04-30T09:00:05.449301Z" } }, "outputs": [ { "data": { "text/plain": [ "array([[0., 0., 1.]])" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hfmOut['seedSensitivity_1']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We discuss a consistency test based on Euler's identity for homogeneous functions. Assume that the cost perturbation is $\\xi = 1$, and observe that we the boundary conditions were chosen null. Then, by a basic rescaling argument, one obtains \n", "$\n", " u_\\varepsilon = (1+\\varepsilon) u \n", "$ on all of $\\Omega$, for any $\\varepsilon \\in ]-1,\\infty[$.\n", "\n", "Comparing this with the [Taylor expansion](#Taylor_Solution) of the solution, we conclude that \n", "\\begin{equation*}\n", "u(x_*) = \\int_\\Omega \\rho.\n", "\\end{equation*}\n", "This equality is checked numerically in the next line." ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.450951Z", "iopub.status.busy": "2024-04-30T09:00:05.450853Z", "iopub.status.idle": "2024-04-30T09:00:05.452702Z", "shell.execute_reply": "2024-04-30T09:00:05.452480Z" } }, "outputs": [], "source": [ "index_1,_ = hfmIn.IndexFromPoint(hfmIn['inspectSensitivity'][1])\n", "assert np.abs(hfmOut['costSensitivity_1'].sum() - hfmOut['values'][tuple(index_1)]) < 1e-15" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.2 Forward differentiation\n", "\n", "In forward differentiation mode, one explicitly provides the variation $\\xi$ in the cost, and $\\zeta$ in the boundary conditions (here null by default). The first order term $\\mu : \\Omega \\to \\mathbb R$ in the Taylor expansion of the solution is recovered, such that \n", "\\begin{equation*}\n", " u_\\varepsilon(x) = u(x)+\\varepsilon \\mu(x) + o(\\varepsilon).\n", "\\end{equation*}\n", "Two cases are considered: a uniform variation $\\xi=1$ of the cost for a consistency check, and a generic variation $\\xi=x+y^2$. No variation is imposed on the boundary conditions." ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.454100Z", "iopub.status.busy": "2024-04-30T09:00:05.454000Z", "iopub.status.idle": "2024-04-30T09:00:05.455859Z", "shell.execute_reply": "2024-04-30T09:00:05.455612Z" } }, "outputs": [], "source": [ "hfmIn['costVariation'] = np.stack([1.+0.*X, X+Y**2],axis=2) # Fist order perturbation of the cost (problem r.h.s)" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.457211Z", "iopub.status.busy": "2024-04-30T09:00:05.457113Z", "iopub.status.idle": "2024-04-30T09:00:05.485955Z", "shell.execute_reply": "2024-04-30T09:00:05.485458Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.003025 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": "markdown", "metadata": {}, "source": [ "By Euler's identity for homogeneous functions, one gets $\\mu = u$ in the case $\\xi=1$ of the uniform variation." ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.487902Z", "iopub.status.busy": "2024-04-30T09:00:05.487772Z", "iopub.status.idle": "2024-04-30T09:00:05.490076Z", "shell.execute_reply": "2024-04-30T09:00:05.489816Z" } }, "outputs": [], "source": [ "values = hfmOut['values'] # First order dense automatic-differentiation variable\n", "assert np.max(np.abs(values.gradient(0) - values.value)) < 1e-14" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We next compare the forward differentiation with backward sensitivity analysis, for consistency again.\n", "More precisely, with the above notations, we check that \n", "\\begin{equation*}\n", "\\nu(x_*) = \\int_\\Omega \\rho \\xi \n", "\\end{equation*}" ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.491549Z", "iopub.status.busy": "2024-04-30T09:00:05.491461Z", "iopub.status.idle": "2024-04-30T09:00:05.493476Z", "shell.execute_reply": "2024-04-30T09:00:05.493224Z" } }, "outputs": [], "source": [ "assert np.abs(hfmOut['values'][tuple(index_1)].gradient(1) - \n", " (hfmOut['costSensitivity_1']*hfmIn['costVariation'][:,:,1]).sum()) < 1e-15" ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.494823Z", "iopub.status.busy": "2024-04-30T09:00:05.494742Z", "iopub.status.idle": "2024-04-30T09:00:05.496518Z", "shell.execute_reply": "2024-04-30T09:00:05.496291Z" } }, "outputs": [], "source": [ "# Restore input\n", "hfmIn.pop('costVariation',None);\n", "hfmIn.pop('inspectSensitivity',None);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4. Voronoi regions\n", "\n", "We illustrate the Voronoi diagram associated with a family of seeds. A similar experiment, with isotropic metrics instead of anisotropic Riemannian metrics, is presented in the [first notebook](http://nbviewer.jupyter.org/urls/rawgithub.com/Mirebeau/HFM_Python_Notebooks/master/0_Isotropic.ipynb)." ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.497885Z", "iopub.status.busy": "2024-04-30T09:00:05.497799Z", "iopub.status.idle": "2024-04-30T09:00:05.499631Z", "shell.execute_reply": "2024-04-30T09:00:05.499402Z" } }, "outputs": [], "source": [ "hfmIn['seeds']=[[0.,0.2],[-0.2,-0.1],[0.2,-0.1]]\n", "hfmIn['seedFlags']=[0,1,2]" ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.500988Z", "iopub.status.busy": "2024-04-30T09:00:05.500900Z", "iopub.status.idle": "2024-04-30T09:00:05.522896Z", "shell.execute_reply": "2024-04-30T09:00:05.522574Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field seedRadius defaults to 0\n", "Field voronoiStoppingCriterion defaults to None\n", "Fast marching solver completed in 0.003954 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", "Field exportVoronoiFlags defaults to 1\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The computation of Voronoi diagrams is more challenging with anisotropic metrics, such as Riemannian metrics, than with isotropic ones. Indeed, the numerical scheme relies on wide adaptive stencils, which risks blurring the lines between the regions. \n", "\n", "Qualitatively convincing results are obtained though, largerly because the stencils of the FM-VR1 numerical scheme used in the HFM software remain rather compact." ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.524525Z", "iopub.status.busy": "2024-04-30T09:00:05.524407Z", "iopub.status.idle": "2024-04-30T09:00:05.527163Z", "shell.execute_reply": "2024-04-30T09:00:05.526930Z" } }, "outputs": [ { "data": { "text/plain": [ "3" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "int(hfmOut['MaxStencilWidth']) # Returns the size of the widest stencil used in the discretization." ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.528519Z", "iopub.status.busy": "2024-04-30T09:00:05.528442Z", "iopub.status.idle": "2024-04-30T09:00:05.581776Z", "shell.execute_reply": "2024-04-30T09:00:05.581530Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=[4,4]); plt.title('Riemannian Voronoi regions'); plt.axis('equal'); \n", "plt.contourf(X,Y,hfmOut['voronoiFlags']);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the next experiment, we stop the front propagation as soon as two of the regions meet, and display the minimal paths from the meeting point. They can be concatenated into a minimal geodesic joining the two closest seeds." ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.583265Z", "iopub.status.busy": "2024-04-30T09:00:05.583185Z", "iopub.status.idle": "2024-04-30T09:00:05.584974Z", "shell.execute_reply": "2024-04-30T09:00:05.584766Z" } }, "outputs": [], "source": [ "hfmIn['voronoiStoppingCriterion']='RegionsMeeting'" ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.586498Z", "iopub.status.busy": "2024-04-30T09:00:05.586412Z", "iopub.status.idle": "2024-04-30T09:00:05.604863Z", "shell.execute_reply": "2024-04-30T09:00:05.604446Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.001097 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", "Field exportVoronoiFlags defaults to 1\n", "Field voronoiDiagram_exportGeodesicFromMeetingPoint defaults to 1\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.606590Z", "iopub.status.busy": "2024-04-30T09:00:05.606493Z", "iopub.status.idle": "2024-04-30T09:00:05.700186Z", "shell.execute_reply": "2024-04-30T09:00:05.699909Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=[4,4]); plt.title('Termination when two Voronoi regions meet'); plt.axis('equal'); \n", "plt.contourf(X,Y,hfmOut['voronoiFlags']) # Display the Voronoi regions.\n", "for geo in hfmOut['geodesics_voronoiDiagram']: plt.plot(*geo) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The same flag can be attributed to several seeds. As a result, the corresponding Voronoi regions are regarded as a single, unique region." ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.701807Z", "iopub.status.busy": "2024-04-30T09:00:05.701687Z", "iopub.status.idle": "2024-04-30T09:00:05.703465Z", "shell.execute_reply": "2024-04-30T09:00:05.703220Z" } }, "outputs": [], "source": [ "hfmIn['seedFlags']=[0,0,1]" ] }, { "cell_type": "code", "execution_count": 71, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.704846Z", "iopub.status.busy": "2024-04-30T09:00:05.704752Z", "iopub.status.idle": "2024-04-30T09:00:05.722944Z", "shell.execute_reply": "2024-04-30T09:00:05.722641Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field verbosity defaults to 1\n", "Field seedRadius defaults to 0\n", "Fast marching solver completed in 0.00122 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", "Field exportVoronoiFlags defaults to 1\n", "Field voronoiDiagram_exportGeodesicFromMeetingPoint defaults to 1\n" ] } ], "source": [ "hfmOut = hfmIn.Run()" ] }, { "cell_type": "code", "execution_count": 72, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.724510Z", "iopub.status.busy": "2024-04-30T09:00:05.724403Z", "iopub.status.idle": "2024-04-30T09:00:05.782222Z", "shell.execute_reply": "2024-04-30T09:00:05.781943Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=[4,4]); plt.title('Aggregation of several Voronoi regions'); plt.axis('equal'); \n", "plt.contourf(X,Y,hfmOut['voronoiFlags']) # Display the Voronoi regions.\n", "for geo in hfmOut['geodesics_voronoiDiagram']: plt.plot(*geo) " ] }, { "cell_type": "code", "execution_count": 73, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.783789Z", "iopub.status.busy": "2024-04-30T09:00:05.783679Z", "iopub.status.idle": "2024-04-30T09:00:05.785432Z", "shell.execute_reply": "2024-04-30T09:00:05.785201Z" } }, "outputs": [], "source": [ "hfmIn.pop('voronoiStoppingCriterion',None);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5. Contruction of the Riemannian tensors\n", "\n", "In applications, the construction of the Riemannian metric tensors is often the key difficulty, requiring expert knowledge of the problem at hand. A few classical constructions are illustrated in this series of notebooks." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.1 Dimension lifting\n", "\n", "The HFM software implements Riemannian models in dimension $d+1$, where $d \\in \\{2,3\\}$, and the tensor structure is block diagonal. They take the form\n", "\\begin{equation*}\n", "\\mathcal D(p)=\n", "\\begin{pmatrix}\n", "D(p) & \\\\\n", "& \\lambda(p)\n", "\\end{pmatrix}\n", "\\end{equation*}\n", "where $D(p)$ is a $d\\times d$ symmetric positive definite matrix, and $\\lambda(p)>0$.\n", "These tensor structures are common in image processing, where usually $d$ is the input image dimension, and the last coordinate is an abstract parameter. Usually it accounts for a feature of the objects represented in the image, expected to vary regularly along them, such as the radius, orientation, or gray level of some tubular structures.\n", "\n", "Such models are discussed in the [notebook on tubular structures extraction](Tubular.ipynb). A related construction allows to penalize curvature, see the notebooks on [curvature](Curvature.ipynb) and [distorted curvature](DeviationHorizontality.ipynb)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.2 Mapping the eigenvalues of a given tensor field.\n", "\n", "Another approach is to extract direction information from an image in the form of a symmetric matrix field $A$. To this end, one may consider the hessian, the structure tensor, the oriented flux of L. Cohen, or some other filter.\n", "At each discretization point $x$, the eigen decomposition of $A$ reads:\n", "$$\n", " A(x) = \\sum_{1 \\leq i \\leq d} \\lambda_i(x) e_i(x) e_i(x)^T.\n", "$$\n", "\n", "The eigenvectors $(e_i)$ of the previous tensor typically indicate well the directions of interest in the image, e.g. the directions of the tubular structures or the objects contours. However the eigenvalues $\\lambda_i$ are usually not adequate for minimal path computation: they may have a negative sign, an excessive magnitude, etc. \n", "\n", "A typical construction is to construct a Riemannian metric tensor which has the same eigenvectors $e_i$ as the filtered tensor, but eigenvalues $\\mu_i$ mapped in an arbitrary way. \n", "$$\n", " M(x) = \\sum_{1 \\leq i \\leq d} \\mu_i(x) e_i(x) e_i(x)^T\n", "$$\n", "where\n", "$$\n", " (\\mu_1(x),\\mu_2(x),\\mu_3(x)) = f(\\lambda_1(x),\\lambda_2(x),\\lambda_3(x))\n", "$$\n", "for some given function $f$. For convenience, one expects that $\\lambda_1(x) \\leq \\lambda_2(x) \\leq \\lambda_3(x)$: the eigenvalues are sorted by increasing value.\n", "\n", "We provide a helper function for applying this strategy, documented below. We do not illustrate it on real data, but only test it on a random example for correctness.\n", "\n", "**Anisotropy of the metric.**\n", "The largest value of $\\mu_{\\max} := \\sqrt{\\mu_i(x)/\\mu_j(x)}$, for $i,j\\in \\{1,2,3\\}$ and $x\\in \\Omega$, is the anisotropy of the produced metric. For best results, please ensure that $\\mu_{\\max} \\lesssim 10$, or at the very least $\\mu_{\\max} \\lesssim 100$.\n" ] }, { "cell_type": "code", "execution_count": 74, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.787056Z", "iopub.status.busy": "2024-04-30T09:00:05.786950Z", "iopub.status.idle": "2024-04-30T09:00:05.789211Z", "shell.execute_reply": "2024-04-30T09:00:05.788979Z" } }, "outputs": [], "source": [ "# Construct a symmetric tensor describing an image's features (hessian, structure tensor, etc)\n", "# Here, we content ourselves with random data\n", "image_dim = 3\n", "image_shape = (5,6,7)\n", "\n", "np.random.seed(0) # Reproducibility\n", "A = np.random.normal( size=(image_dim,image_dim)+image_shape)\n", "A = A+lp.transpose(A) # Make symmetric" ] }, { "cell_type": "code", "execution_count": 75, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.790678Z", "iopub.status.busy": "2024-04-30T09:00:05.790571Z", "iopub.status.idle": "2024-04-30T09:00:05.800669Z", "shell.execute_reply": "2024-04-30T09:00:05.800422Z" } }, "outputs": [], "source": [ "# Construct a function for mapping the eigenvalues. \n", "# Important : in practical applications, mu0,mu1,mu2 must all be positive\n", "def f(eigenvalues):\n", " lambda0,lambda1,lambda2 = eigenvalues\n", " mu0,mu1,mu2 = lambda0,lambda1+1,lambda2+2\n", " return mu0,mu1,mu2\n", "\n", "# The Riemannian metric\n", "M = Riemann.from_mapped_eigenvalues(A,f)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We check below some of the properties of proposed construction." ] }, { "cell_type": "code", "execution_count": 76, "metadata": { "execution": { "iopub.execute_input": "2024-04-30T09:00:05.802408Z", "iopub.status.busy": "2024-04-30T09:00:05.802296Z", "iopub.status.idle": "2024-04-30T09:00:05.816197Z", "shell.execute_reply": "2024-04-30T09:00:05.815875Z" } }, "outputs": [], "source": [ "def f_inv(x):\n", " x0,x1,x2 = x\n", " # Test that the eigenvalues are sorted as expected.\n", " assert np.all(x0<=x1) and np.all(x1<=x2)\n", " return x0,x1-1,x2-2\n", "\n", "# Test that composing f and f_inv yields identity\n", "assert norm_infinity(Riemann.from_mapped_eigenvalues(M.m,f_inv).m - A) < 1e-13\n", "\n", "# Test that the mapping lambda->1/lambda yields the inverse matrix\n", "A_inv = Riemann.from_mapped_eigenvalues(A,lambda t:1/t).m\n", "Id = np.eye(image_dim).reshape( (image_dim,image_dim)+image_dim*(1,) )\n", "assert norm_infinity(lp.dot_AA(A_inv,A) - Id)<1e-12" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Format de la Cellule Texte Brut", "kernelspec": { "display_name": "Python 3 (ipykernel)", "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" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autocomplete": false, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 1 }