torch-fit-plane.ipynb

!RANSAC-based plane fitting - A rough batched PyTorch implementation.md

A simple PyTorch implementation of plane fitting with RANSAC. Some ideas are taken from: https://github.com/leomariga/pyRANSAC-3D.

In each (batched-)RANSAC iteration, a batch of triplets is sampled and assessed in parallel. A cross-product is used to get plane equations from triplets. The refinement, post identification of inliers, is done with an eigen decomposition of P.T @ P where P is the matrix of points in homogeneous coordinates. Classicially, an SVD decomposition of P is used but this can be slow and memory intensive with large number of points. We thus opted for the eigen decomposition approach despite it being less numerically stable.

torch-fit-plane.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyPVEFGSh4AjTBgfivZS7hwk",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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    "language_info": {
      "name": "python"
    },
    "accelerator": "GPU",
    "gpuClass": "standard"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/tvercaut/d210ed103f64ebb24606eb032b38de0a/torch-fit-plane.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import torch\n",
        "print(f'Running PyTorch version: {torch.__version__}')\n",
        "\n",
        "torchdevice = torch.device('cpu')\n",
        "if torch.cuda.is_available():\n",
        "  torchdevice = torch.device('cuda')\n",
        "  print('Default GPU is ' + torch.cuda.get_device_name(torch.device('cuda')))\n",
        "print('Running on ' + str(torchdevice))\n",
        "\n",
        "import numpy as np"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JmLeblLAb_eG",
        "outputId": "88604f7d-d66f-433b-e48c-beebd0cca180"
      },
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Running PyTorch version: 1.12.1+cu113\n",
            "Default GPU is Tesla T4\n",
            "Running on cuda\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def fit_plane_batch_crossprod(points, normalize=False):\n",
        "  # points: BxNx3 batched groups of N=3 3d points\n",
        "  # return: Bx4 where for each input in the batch we get [a, b, c, d] such that\n",
        "  # ax+by+cz+d = 0 is the equation of teh corresponding plane\n",
        "  # No care is taken about colinear inputs\n",
        "  num_batch = points.shape[0]\n",
        "  num_points = points.shape[1]\n",
        "  dim = points.shape[2]\n",
        "\n",
        "  if dim != 3:\n",
        "    raise ValueError(f\"Only 3D points are supported, got dim={dim}\")\n",
        "\n",
        "  if num_points != 3:\n",
        "    raise ValueError(f\"Only groups of 3 points are supported, got num_points={num_points}\")\n",
        "\n",
        "  # We have to find the plane equation described by those 3 points\n",
        "  # We find first 2 vectors that are part of this plane\n",
        "  # V10 = pt1 - pt0\n",
        "  # V20 = pt2 - pt0\n",
        "  vec10 = points[:,1,:] - points[:,0,:]\n",
        "  vec20 = points[:,2,:] - points[:,0,:]\n",
        "\n",
        "  # Now we compute the cross product of vec10 and vec20 to get vecN which is normal to the plane\n",
        "  vecN = torch.linalg.cross(vec10, vec20)\n",
        "  \n",
        "  # The plane equation will be vecN[0]*x + vecN[1]*y + vecN[0]*z = -d\n",
        "  # We use any of the points to find k\n",
        "  d = -torch.einsum('bd,bd->b', vecN, points[:,0,:].squeeze(dim=1))\n",
        "  plane_params = torch.cat((vecN,d.unsqueeze(1)),1)\n",
        "\n",
        "  # We can normalise for better interpretability but this would lead to issues\n",
        "  # if the points are co-linear\n",
        "  if normalize:\n",
        "    plane_params /= torch.linalg.norm(plane_params,dim=1,keepdim=True)\n",
        "  return plane_params\n",
        "\n",
        "def plane_batch_dist(points, plane_params, signeddist=False):\n",
        "  # plane_params: Bx4 B plane equations ax+by+cz+d = 0 given as [a, b, c, d] \n",
        "  # points: Nx3 N 3d points\n",
        "  # return: BxN distances\n",
        "  # No care is taken in case [a,b,c] has a zero norm\n",
        "  num_batch = plane_params.shape[0]\n",
        "  num_points = points.shape[0]\n",
        "  dim = points.shape[1]\n",
        "\n",
        "  if dim != 3:\n",
        "    raise ValueError(f\"Only 3D points are supported, got dim={dim}\")\n",
        "\n",
        "  # Distance from a point to a plane\n",
        "  # https://mathworld.wolfram.com/Point-PlaneDistance.html\n",
        "  # ax+by+cz+d / norm([a,b,c])\n",
        "  denoms = torch.linalg.norm(plane_params[:,0:3],dim=1,keepdim=True)\n",
        "  point_h = torch.cat((points, torch.ones((num_points,1),device=points.device)),1)\n",
        "  dists = torch.einsum('bd,nd->bn', plane_params, point_h) / denoms\n",
        "  if not signeddist:\n",
        "    dists = torch.abs( dists )\n",
        "  return dists\n",
        "\n",
        "def fit_plane_batch_eigh(points):\n",
        "  # points: BxNx3 batched groups of N 3d points\n",
        "  # return: Bx4 where for each input in the batch we get [a, b, c, d] such that\n",
        "  # ax+by+cz+d = 0 is the equation of teh corresponding plane\n",
        "  # No care is taken about colinear inputs\n",
        "  num_batch = points.shape[0]\n",
        "  num_points = points.shape[1]\n",
        "  dim = points.shape[2]\n",
        "\n",
        "  if dim != 3:\n",
        "    raise ValueError(f\"Only 3D points are supported, got dim={dim}\")\n",
        "\n",
        "  points_h = torch.cat((points, torch.ones((num_batch,num_points,1),device=points.device)),2)\n",
        "  smat = torch.matmul( torch.transpose(points_h,1,2), points_h )\n",
        "  w, v = torch.linalg.eigh(smat)\n",
        "  return v[:, :, 0]\n",
        "\n",
        "def fit_plane_ransac(points, inlierthresh=0.05, batch=1000, numbatchiter=100, verbose=False):\n",
        "  # points: Nx3 N 3d points\n",
        "  # inlierthresh: Threshold distance from the plane which is considered inlier.\n",
        "  # batch: Number of triplets considered in parallel during each batched RANSAC\n",
        "  # iteration\n",
        "  # numbatchiter: Number of maximum iteration which RANSAC will loop over.\n",
        "  # return: [a, b, c, d] such that ax+by+cz+d = 0 is the equation of the\n",
        "  # corresponding plane\n",
        "  num_points = points.shape[0]\n",
        "  dim = points.shape[1]\n",
        "\n",
        "  if dim != 3:\n",
        "    raise ValueError(f\"Only 3D points are supported, got dim={dim}\")\n",
        "\n",
        "  best_num_inliers = 0\n",
        "  best_inliers = None\n",
        "  best_plane = None\n",
        "\n",
        "  for iter in range(numbatchiter):\n",
        "    if verbose:\n",
        "      print(f\"iteration: {iter}\")\n",
        "    # Get random triplets. Ideally, we would draw without replacement in each\n",
        "    # triplet and also ensure we don't use duplicate triplets.\n",
        "    randidx = torch.randint(0, num_points, (batch,3))\n",
        "    triplets = points[randidx.flatten(),:].reshape(batch,3,3)\n",
        "\n",
        "    # Get planes going through triplets\n",
        "    planes = fit_plane_batch_crossprod(triplets)\n",
        "\n",
        "    # Estimate quality of each plane\n",
        "    dists = plane_batch_dist(points, planes)\n",
        "    inliers = (dists < inlierthresh)\n",
        "    num_inliers = torch.sum(inliers, dim=1)\n",
        "\n",
        "    batch_best_idx = torch.argmax(num_inliers)\n",
        "    batch_best_num_inliers = num_inliers[batch_best_idx]\n",
        "    if verbose:\n",
        "      print(f'  best batch plane: {planes[batch_best_idx,:] / torch.linalg.norm(planes[batch_best_idx,:])} - ({batch_best_num_inliers}/{num_points})')\n",
        "    if batch_best_num_inliers > best_num_inliers:\n",
        "      best_num_inliers = batch_best_num_inliers\n",
        "      best_inliers = inliers[batch_best_idx,:]\n",
        "      best_plane = planes[batch_best_idx,:]\n",
        "      if verbose:\n",
        "        print(f'best new plane: {best_plane / torch.linalg.norm(best_plane)} - ({best_num_inliers}/{num_points})')\n",
        "\n",
        "  # Refine plane equation based on inliers\n",
        "  inlier_points = points[best_inliers,:]\n",
        "  best_plane = fit_plane_batch_eigh(inlier_points.unsqueeze(0))\n",
        "  if verbose:\n",
        "    print(f'refined_plane {best_plane}')\n",
        "  return best_plane, best_inliers"
      ],
      "metadata": {
        "id": "tq3hVG1IFA0Q"
      },
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import urllib.request\n",
        "\n",
        "# Download an example point cloud\n",
        "url=\"https://github.com/leomariga/pyRANSAC-3D/raw/master/tests/dataset/caixa.ply\"\n",
        "urllib.request.urlretrieve(url, \"caixa.ply\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fpfZzTHx0Tnd",
        "outputId": "111b430e-6222-4494-db58-ed56c358b2c0"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "('caixa.ply', <http.client.HTTPMessage at 0x7f6edb863290>)"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hS7kX7MJhn9k",
        "outputId": "eb397e03-b1cd-4eab-c40d-dd871ad5bd76"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
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            "Requirement already satisfied: mistune<2,>=0.8.1 in /usr/local/lib/python3.7/dist-packages (from nbconvert<6.0->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets>=7.6.0->open3d) (0.8.4)\n",
            "Requirement already satisfied: entrypoints>=0.2.2 in /usr/local/lib/python3.7/dist-packages (from nbconvert<6.0->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets>=7.6.0->open3d) (0.4)\n",
            "Requirement already satisfied: bleach in /usr/local/lib/python3.7/dist-packages (from nbconvert<6.0->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets>=7.6.0->open3d) (5.0.1)\n",
            "Requirement already satisfied: pandocfilters>=1.4.1 in /usr/local/lib/python3.7/dist-packages (from nbconvert<6.0->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets>=7.6.0->open3d) (1.5.0)\n",
            "Requirement already satisfied: testpath in /usr/local/lib/python3.7/dist-packages (from nbconvert<6.0->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets>=7.6.0->open3d) (0.6.0)\n",
            "Requirement already satisfied: ptyprocess in /usr/local/lib/python3.7/dist-packages (from terminado>=0.8.1->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets>=7.6.0->open3d) (0.7.0)\n",
            "Requirement already satisfied: webencodings in /usr/local/lib/python3.7/dist-packages (from bleach->nbconvert<6.0->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets>=7.6.0->open3d) (0.5.1)\n"
          ]
        }
      ],
      "source": [
        "# Get open3d for IO and visualisation purposes\n",
        "!pip install open3d\n",
        "import open3d as o3d"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Load point cloud and visualize it\n",
        "pcd_load = o3d.io.read_point_cloud(\"caixa.ply\")\n",
        "points = np.asarray(pcd_load.points)\n",
        "o3d.visualization.draw_plotly([pcd_load])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 417
        },
        "id": "fg0AVRQejLjL",
        "outputId": "d4d4c123-8632-4dc4-a425-8c1dafb5f55c"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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