Refactor find_extrinsic_object.py: update object points parquet file name, enhance type annotations with MarkerFace TypedDict for diamond ArUco markers, and improve code organization.

Refactor Jupyter notebooks for marker processing: deleted boom.ipynb and compute_3d_maybe.ipynb, added calculate_box_coord_naive.ipynb, calculate_box_face_coord_naive.ipynb, estimate_extrinstic.ipynb, find_aruco_points_with_image.ipynb, find_aruco_points.py, and find_extrinsic_object.py. Updated .gitignore to include new output files.
Update execution counts in find_cute_box_with_image.ipynb and adjust coordinate transformations for OpenGL to Blender compatibility.
2025-04-30 11:45:41 +08:00 · 2025-04-30 11:43:59 +08:00 · 2025-04-24 14:23:56 +08:00 · 2025-04-24 12:56:34 +08:00 · 2025-04-24 12:13:50 +08:00 · 2025-04-23 19:13:04 +08:00
20 changed files with 1425 additions and 2906 deletions
--- a/.gitattributes
+++ b/.gitattributes
@ -1,2 +1,3 @@
 *.parquet filter=lfs diff=lfs merge=lfs -text
 *.pdf filter=lfs diff=lfs merge=lfs -text
+*.glb filter=lfs diff=lfs merge=lfs -text
--- a/.gitignore
+++ b/.gitignore
@ -165,6 +165,7 @@ cython_debug/
 #  option (not recommended) you can uncomment the following to ignore the entire idea folder.
 #.idea/
 .DS_Store
-output/svg
 *.mp4
-output
+output/*.json
+~output/standard_box_markers.parquet
+~output/object_points.parquet
--- a/boom.ipynb
+++ b/boom.ipynb
--- a/calculate_box_coord_naive.ipynb
+++ b/calculate_box_coord_naive.ipynb
@ -0,0 +1,497 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from dataclasses import dataclass\n",
+    "import numpy as np\n",
+    "from matplotlib import pyplot as plt\n",
+    "\n",
+    "NDArray = np.ndarray\n",
+    "\n",
+    "# Order of detection result\n",
+    "# 0,   1,     2,    3\n",
+    "# TL,  TR,    BR,   BL\n",
+    "# RED, GREEN, BLUE, YELLOW\n",
+    "\n",
+    "\n",
+    "@dataclass\n",
+    "class DiamondBoardParameter:\n",
+    "    marker_leghth: float\n",
+    "    \"\"\"\n",
+    "    the ArUco marker length in meter\n",
+    "    \"\"\"\n",
+    "    chess_length: float\n",
+    "    \"\"\"\n",
+    "    the length of the chess board in meter\n",
+    "    \"\"\"\n",
+    "    border_length: float = 0.01\n",
+    "    \"\"\"\n",
+    "    border_length in m, default is 1cm\n",
+    "    \"\"\"\n",
+    "\n",
+    "    @property\n",
+    "    def marker_border_length(self):\n",
+    "        assert self.chess_length > self.marker_leghth\n",
+    "        return (self.chess_length - self.marker_leghth) / 2\n",
+    "\n",
+    "    @property\n",
+    "    def total_side_length(self):\n",
+    "        assert self.chess_length > self.marker_leghth\n",
+    "        return self.marker_border_length * 2 + self.chess_length * 3\n",
+    "\n",
+    "\n",
+    "# 9mm + 127mm + 127mm (97mm marker) + 127mm + 10mm\n",
+    "# i.e. marker boarder = 127mm - 97mm = 30mm (15mm each side)\n",
+    "Point2D = tuple[float, float]\n",
+    "Quad2D = tuple[Point2D, Point2D, Point2D, Point2D]\n",
+    "\n",
+    "\n",
+    "@dataclass\n",
+    "class ArUcoMarker2D:\n",
+    "    id: int\n",
+    "    corners: Quad2D\n",
+    "    params: DiamondBoardParameter\n",
+    "\n",
+    "    @property\n",
+    "    def np_corners(self):\n",
+    "        \"\"\"\n",
+    "        returns corners in numpy array\n",
+    "        (4, 2) shape\n",
+    "        \"\"\"\n",
+    "        return np.array(self.corners, dtype=np.float32)\n",
+    "\n",
+    "\n",
+    "# let's let TL be the origin\n",
+    "def generate_diamond_corners(\n",
+    "    ids: tuple[int, int, int, int], params: DiamondBoardParameter\n",
+    "):\n",
+    "    \"\"\"\n",
+    "    A diamond chess board, which could be count as a kind of ChArUco board\n",
+    "\n",
+    "    C | 0 | C\n",
+    "    ---------\n",
+    "    1 | C | 2\n",
+    "    ---------\n",
+    "    C | 3 | C\n",
+    "\n",
+    "    where C is the chess box, and 0, 1, 2, 3 are the markers (whose ids are passed in order)\n",
+    "\n",
+    "    Args:\n",
+    "        ids: a tuple of 4 ids of the markers\n",
+    "        params: DiamondBoardParameter\n",
+    "    \"\"\"\n",
+    "\n",
+    "    def tl_to_square(tl_x: float, tl_y: float, side_length: float) -> Quad2D:\n",
+    "        return (\n",
+    "            (tl_x, tl_y),\n",
+    "            (tl_x + side_length, tl_y),\n",
+    "            (tl_x + side_length, tl_y + side_length),\n",
+    "            (tl_x, tl_y + side_length),\n",
+    "        )\n",
+    "\n",
+    "    tl_0_x = params.border_length + params.chess_length + params.marker_border_length\n",
+    "    tl_0_y = params.border_length + params.marker_border_length\n",
+    "\n",
+    "    tl_1_x = params.border_length + params.marker_border_length\n",
+    "    tl_1_y = params.border_length + params.chess_length + params.marker_border_length\n",
+    "\n",
+    "    tl_2_x = (\n",
+    "        params.border_length + params.chess_length * 2 + params.marker_border_length\n",
+    "    )\n",
+    "    tl_2_y = tl_1_y\n",
+    "\n",
+    "    tl_3_x = params.border_length + params.chess_length + params.marker_border_length\n",
+    "    tl_3_y = (\n",
+    "        params.border_length + params.chess_length * 2 + params.marker_border_length\n",
+    "    )\n",
+    "    return (\n",
+    "        ArUcoMarker2D(ids[0], tl_to_square(tl_0_x, tl_0_y, params.marker_leghth), params),\n",
+    "        ArUcoMarker2D(ids[1], tl_to_square(tl_1_x, tl_1_y, params.marker_leghth), params),\n",
+    "        ArUcoMarker2D(ids[2], tl_to_square(tl_2_x, tl_2_y, params.marker_leghth), params),\n",
+    "        ArUcoMarker2D(ids[3], tl_to_square(tl_3_x, tl_3_y, params.marker_leghth), params),\n",
+    "    )\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "params = DiamondBoardParameter(0.097, 0.127)\n",
+    "markers = generate_diamond_corners((16, 17, 18, 19), params)\n",
+    "\n",
+    "fig = plt.figure()\n",
+    "ax = fig.gca()\n",
+    "ax.set_xlim((0, params.total_side_length))\n",
+    "ax.set_ylim((0, params.total_side_length)) # type: ignore\n",
+    "ax.set_aspect(\"equal\")\n",
+    "# set origin to top-left (from bottom-left)\n",
+    "ax.invert_yaxis()\n",
+    "ax.xaxis.set_ticks_position('top')\n",
+    "\n",
+    "for marker in markers:\n",
+    "    plt.plot(*marker.np_corners.T, \"o-\", label=str(marker.id))\n",
+    "    for i, (x, y) in enumerate(marker.corners):\n",
+    "        ax.text(x, y, str(i))\n",
+    "plt.legend()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from typing import Sequence\n",
+    "import plotly.graph_objects as go\n",
+    "import awkward as ak\n",
+    "import cv2\n",
+    "from cv2.typing import MatLike\n",
+    "\n",
+    "\n",
+    "def transform_point(matrix: MatLike, point: MatLike):\n",
+    "    assert matrix.shape == (4, 4)\n",
+    "    assert point.shape == (3,)\n",
+    "\n",
+    "    # Lift point to 4D\n",
+    "    homogeneous_point = np.array([point[0], point[1], point[2], 1])\n",
+    "    # Apply transformation\n",
+    "    transformed = matrix @ homogeneous_point\n",
+    "    # Project back to 3D if w != 1\n",
+    "    if transformed[3] != 1:\n",
+    "        transformed = transformed / transformed[3]\n",
+    "    return transformed[:3]\n",
+    "\n",
+    "\n",
+    "class DiamondPlane3D:\n",
+    "    _ids: NDArray\n",
+    "    \"\"\"\n",
+    "    (n,)\n",
+    "    \"\"\"\n",
+    "    _corners: NDArray\n",
+    "    \"\"\"\n",
+    "    (n, 4, 3)\n",
+    "    \"\"\"\n",
+    "    _transform_matrix: NDArray\n",
+    "    \"\"\"\n",
+    "    4x4 transformation matrix\n",
+    "    \"\"\"\n",
+    "    _normal_vector: NDArray\n",
+    "    \"\"\"\n",
+    "    (2, 3)\n",
+    "    start (the center of the plane) and end (the normal vector), length 1\n",
+    "    \"\"\"\n",
+    "\n",
+    "    def __init__(self, items: Sequence[ArUcoMarker2D]):\n",
+    "        self._ids = np.array([item.id for item in items])\n",
+    "        # (n, 4, 2)\n",
+    "        corners_2d = np.array([item.np_corners for item in items])\n",
+    "        # (n, 4, 3)\n",
+    "        self._corners = np.concatenate(\n",
+    "            [corners_2d, np.zeros((corners_2d.shape[0], 4, 1))], axis=-1\n",
+    "        )\n",
+    "        self._transform_matrix = np.eye(4)\n",
+    "\n",
+    "        def center(items: Sequence[ArUcoMarker2D]):\n",
+    "            return np.mean([item.np_corners for item in items], axis=(0, 1))\n",
+    "\n",
+    "        c = center(items)\n",
+    "        assert c.shape == (2,)\n",
+    "        self._normal_vector = np.array([(c[0], c[1], 0), (c[0], c[1], 0.1)])\n",
+    "\n",
+    "    @property\n",
+    "    def ids(self):\n",
+    "        return self._ids\n",
+    "\n",
+    "    @property\n",
+    "    def corners(self):\n",
+    "        return self._corners\n",
+    "\n",
+    "    @property\n",
+    "    def transform_matrix(self):\n",
+    "        return self._transform_matrix\n",
+    "\n",
+    "    @property\n",
+    "    def transformed_corners(self):\n",
+    "        def g():\n",
+    "            for corner in self.corners:\n",
+    "                yield np.array(\n",
+    "                    [transform_point(self.transform_matrix, c) for c in corner]\n",
+    "                )\n",
+    "\n",
+    "        return np.array(list(g()))\n",
+    "\n",
+    "    @property\n",
+    "    def transformed_normal_vector(self):\n",
+    "        def g():\n",
+    "            for v in self._normal_vector:\n",
+    "                yield transform_point(self.transform_matrix, v)\n",
+    "\n",
+    "        return np.array(list(g()))\n",
+    "\n",
+    "    @property\n",
+    "    def transformed_geometry_center(self):\n",
+    "        return np.mean(self.transformed_corners, axis=(0, 1))\n",
+    "\n",
+    "    def local_rotate(self, angle: float, axis: NDArray):\n",
+    "        \"\"\"\n",
+    "        rotate the plane by angle (in radian) around local center\n",
+    "\n",
+    "        Args:\n",
+    "            angle: in radian\n",
+    "            axis: (3,)\n",
+    "\n",
+    "        change basis to local basis, rotate, then change back\n",
+    "        \"\"\"\n",
+    "        raise NotImplementedError\n",
+    "\n",
+    "    def rotate(self, angle: float, axis: NDArray):\n",
+    "        \"\"\"\n",
+    "        rotate the plane by angle (in radian) around the axis\n",
+    "        \"\"\"\n",
+    "        assert axis.shape == (3,)\n",
+    "        rot_mat = cv2.Rodrigues(axis * angle)[0]\n",
+    "        self._transform_matrix[:3, :3] = np.dot(rot_mat, self._transform_matrix[:3, :3])\n",
+    "\n",
+    "    def translate(self, vec: NDArray):\n",
+    "        \"\"\"\n",
+    "        translate the plane by vec\n",
+    "        \"\"\"\n",
+    "        assert vec.shape == (3,)\n",
+    "        self._transform_matrix[:3, 3] += vec\n",
+    "\n",
+    "    def set_transform_matrix(self, mat: NDArray):\n",
+    "        assert mat.shape == (4, 4)\n",
+    "        self._transform_matrix = mat"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "plane_a = DiamondPlane3D(markers)\n",
+    "\n",
+    "OFFSET = 0.000\n",
+    "markers_b = generate_diamond_corners((20, 21, 22, 23), params)\n",
+    "plane_b = DiamondPlane3D(markers_b)\n",
+    "# plane_b.translate(np.array([0, 0, 0.1]))\n",
+    "plane_b.rotate(np.pi/2, np.array([1, 0, 0]))\n",
+    "plane_b.rotate(np.pi, np.array([0, 0, 1]))\n",
+    "tmp_c = plane_b.transformed_geometry_center\n",
+    "plane_b.translate(-tmp_c)\n",
+    "plane_b.rotate(np.pi, np.array([0, 1, 0]))\n",
+    "plane_b.translate(tmp_c)\n",
+    "plane_b.translate(np.array([0, 0, params.total_side_length]))\n",
+    "plane_b.translate(np.array([0, 0, -OFFSET]))\n",
+    "# OFFSET for plane_b\n",
+    "# plane_b.translate(np.array([0, 0.001, 0]))\n",
+    "\n",
+    "markers_c = generate_diamond_corners((24, 25, 26, 27), params)\n",
+    "plane_c = DiamondPlane3D(markers_c)\n",
+    "tmp = plane_c.transformed_geometry_center\n",
+    "plane_c.translate(-tmp)\n",
+    "plane_c.rotate(-np.pi/2, np.array([0, 0, 1]))\n",
+    "plane_c.translate(tmp)\n",
+    "plane_c.translate(np.array([0, params.total_side_length-params.border_length, 0]))\n",
+    "plane_c.rotate(np.pi/2, np.array([0, 1, 0]))\n",
+    "plane_c.translate(np.array([0, 0, params.total_side_length]))\n",
+    "plane_c.translate(np.array([0, 0, -OFFSET]))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "fig = go.Figure()\n",
+    "t_corners_a = plane_a.transformed_corners\n",
+    "for i, corners in enumerate(t_corners_a):\n",
+    "    fig.add_trace(\n",
+    "        go.Scatter3d(\n",
+    "            x=corners[:, 0],\n",
+    "            y=corners[:, 1],\n",
+    "            z=corners[:, 2],\n",
+    "            mode=\"markers+lines+text\",\n",
+    "            text=list(map(lambda x: f\"{plane_a.ids[i]}:{x}\", range(4))),\n",
+    "            textposition=\"middle center\",\n",
+    "            name=str(plane_a.ids[i]),\n",
+    "            marker=dict(size=1),\n",
+    "        )\n",
+    "    )\n",
+    "\n",
+    "# normal vector\n",
+    "fig.add_trace(\n",
+    "    go.Scatter3d(\n",
+    "        x=plane_a.transformed_normal_vector[:, 0],\n",
+    "        y=plane_a.transformed_normal_vector[:, 1],\n",
+    "        z=plane_a.transformed_normal_vector[:, 2],\n",
+    "        mode=\"markers+lines\",\n",
+    "        name=\"normal_a\",\n",
+    "        marker=dict(size=2),\n",
+    "    )\n",
+    ")\n",
+    "\n",
+    "t_corners_b = plane_b.transformed_corners\n",
+    "for i, corners in enumerate(t_corners_b):\n",
+    "    fig.add_trace(\n",
+    "        go.Scatter3d(\n",
+    "            x=corners[:, 0],\n",
+    "            y=corners[:, 1],\n",
+    "            z=corners[:, 2],\n",
+    "            mode=\"markers+lines+text\",\n",
+    "            text=list(map(lambda x: f\"{plane_b.ids[i]}:{x}\", range(4))),\n",
+    "            textposition=\"middle center\",\n",
+    "            name=str(plane_b.ids[i]),\n",
+    "            marker=dict(size=1),\n",
+    "        )\n",
+    "    )\n",
+    "fig.add_trace(\n",
+    "    go.Scatter3d(\n",
+    "        x=plane_b.transformed_normal_vector[:, 0],\n",
+    "        y=plane_b.transformed_normal_vector[:, 1],\n",
+    "        z=plane_b.transformed_normal_vector[:, 2],\n",
+    "        mode=\"markers+lines\",\n",
+    "        name=\"normal_b\",\n",
+    "        marker=dict(size=2),\n",
+    "    )\n",
+    ")\n",
+    "\n",
+    "t_corners_c = plane_c.transformed_corners\n",
+    "for i, corners in enumerate(t_corners_c):\n",
+    "    fig.add_trace(\n",
+    "        go.Scatter3d(\n",
+    "            x=corners[:, 0],\n",
+    "            y=corners[:, 1],\n",
+    "            z=corners[:, 2],\n",
+    "            mode=\"markers+lines+text\",\n",
+    "            text=list(map(lambda x: f\"{plane_c.ids[i]}:{x}\", range(4))),\n",
+    "            name=str(plane_c.ids[i]),\n",
+    "            marker=dict(size=1),\n",
+    "        )\n",
+    "    )\n",
+    "fig.add_trace(\n",
+    "    go.Scatter3d(\n",
+    "        x=plane_c.transformed_normal_vector[:, 0],\n",
+    "        y=plane_c.transformed_normal_vector[:, 1],\n",
+    "        z=plane_c.transformed_normal_vector[:, 2],\n",
+    "        mode=\"markers+lines\",\n",
+    "        textposition=\"middle center\",\n",
+    "        name=\"normal_c\",\n",
+    "        marker=dict(size=2),\n",
+    "    )\n",
+    ")\n",
+    "\n",
+    "# fig.update_layout(\n",
+    "#     scene=dict(\n",
+    "#         aspectmode=\"cube\",\n",
+    "#         yaxis_autorange=\"reversed\",\n",
+    "#     )\n",
+    "# )\n",
+    "\n",
+    "fig.update_layout(\n",
+    "    scene=dict(\n",
+    "        aspectmode='cube',\n",
+    "        xaxis=dict(range=[-0.1, params.total_side_length]),\n",
+    "        yaxis=dict(range=[params.total_side_length, -0.1]),\n",
+    "        zaxis=dict(range=[-0.1, params.total_side_length]),\n",
+    "    )\n",
+    ")\n",
+    "fig.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import awkward as ak\n",
+    "from awkward import Record as AwkwardRecord, Array as AwkwardArray\n",
+    "\n",
+    "coords = AwkwardArray(\n",
+    "    [\n",
+    "        {\n",
+    "            \"name\": \"a\",\n",
+    "            \"ids\": plane_a.ids,\n",
+    "            \"corners\": t_corners_a,\n",
+    "        },\n",
+    "        {\n",
+    "            \"name\": \"b\",\n",
+    "            \"ids\": plane_b.ids,\n",
+    "            \"corners\": t_corners_b,\n",
+    "        },\n",
+    "        {\n",
+    "            \"name\": \"c\",\n",
+    "            \"ids\": plane_c.ids,\n",
+    "            \"corners\": t_corners_c,\n",
+    "        },\n",
+    "    ]\n",
+    ")\n",
+    "display(coords)\n",
+    "_ = ak.to_parquet(coords, \"output/object_points.parquet\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from typing import cast\n",
+    "total_ids = cast(NDArray, ak.to_numpy(coords[\"ids\"])).flatten()\n",
+    "total_corners = cast(NDArray, ak.to_numpy(coords[\"corners\"])).reshape(-1, 4, 3)\n",
+    "#display(total_ids, total_corners)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "dict(zip(total_ids, total_corners))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "total_ids = np.concatenate([plane_a.ids, plane_b.ids, plane_c.ids])\n",
+    "total_corners = np.concatenate([t_corners_a, t_corners_b, t_corners_c])\n",
+    "id_corner_map: dict[int, NDArray] = dict(zip(total_ids, total_corners))"
+   ]
+  }
+ ],
+ "metadata": {
+  "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": "3.12.10"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
--- a/calculate_box_face_coord_naive.ipynb
+++ b/calculate_box_face_coord_naive.ipynb
--- a/compute_3d_maybe.ipynb
+++ b/compute_3d_maybe.ipynb
@ -1,157 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import awkward as ak\n",
-    "from awkward import Array as AwakwardArray, Record as AwkwardRecord\n",
-    "from typing import cast\n",
-    "import numpy as np"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<pre>[{prediction: None, trackings: [], frame_num: 0, ...},\n",
-       " {prediction: None, trackings: [], frame_num: 1, ...},\n",
-       " {prediction: None, trackings: [], frame_num: 2, ...},\n",
-       " {prediction: None, trackings: [], frame_num: 3, ...},\n",
-       " {prediction: None, trackings: [], frame_num: 4, ...},\n",
-       " {prediction: None, trackings: [], frame_num: 5, ...},\n",
-       " {prediction: None, trackings: [], frame_num: 6, ...},\n",
-       " {prediction: None, trackings: [], frame_num: 7, ...},\n",
-       " {prediction: None, trackings: [], frame_num: 8, ...},\n",
-       " {prediction: {Akeypoints: [[...]], ...}, trackings: [{...}], ...},\n",
-       " ...,\n",
-       " {prediction: {Akeypoints: [[...]], ...}, trackings: [{...}], ...},\n",
-       " {prediction: {Akeypoints: [[...]], ...}, trackings: [{...}], ...},\n",
-       " {prediction: {Akeypoints: [[...]], ...}, trackings: [{...}], ...},\n",
-       " {prediction: {Akeypoints: [[...]], ...}, trackings: [{...}], ...},\n",
-       " {prediction: {Akeypoints: [[...]], ...}, trackings: [{...}], ...},\n",
-       " {prediction: {Akeypoints: [[...]], ...}, trackings: [{...}], ...},\n",
-       " {prediction: {Akeypoints: [[...]], ...}, trackings: [{...}], ...},\n",
-       " {prediction: {Akeypoints: [[...]], ...}, trackings: [{...}], ...},\n",
-       " {prediction: {Akeypoints: [[...]], ...}, trackings: [{...}], ...}]\n",
-       "-------------------------------------------------------------------\n",
-       "type: 808 * {\n",
-       "    prediction: ?{\n",
-       "        Akeypoints: var * var * var * float64,\n",
-       "        bboxes: var * var * float64,\n",
-       "        scores: var * var * var * float64,\n",
-       "        frame_number: int64,\n",
-       "        reference_frame_size: {\n",
-       "            &quot;0&quot;: int64,\n",
-       "            &quot;1&quot;: int64\n",
-       "        }\n",
-       "    },\n",
-       "    trackings: var * {\n",
-       "        id: int64,\n",
-       "        bounding_boxes: var * var * float64\n",
-       "    },\n",
-       "    frame_num: int64,\n",
-       "    reference_frame_size: {\n",
-       "        height: int64,\n",
-       "        width: int64\n",
-       "    }\n",
-       "}</pre>"
-      ],
-      "text/plain": [
-       "<Array [{prediction: None, ...}, ..., {...}] type='808 * {prediction: ?{Ake...'>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "a_ak = ak.from_parquet(\"pose/a.parquet\")\n",
-    "b_ak = ak.from_parquet(\"pose/b.parquet\")\n",
-    "# display(a_ak)\n",
-    "display(b_ak)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<pre>{Akeypoints: [[[893, 417], [898, 408], [...], ..., [782, 596], [785, 599]]],\n",
-       " bboxes: [[756, 341, 940, 597]],\n",
-       " scores: [[[0.907], [0.896], [0.916], [0.341], ..., [0.811], [0.835], [0.802]]],\n",
-       " frame_number: 5,\n",
-       " reference_frame_size: {&#x27;0&#x27;: 1080, &#x27;1&#x27;: 1920}}\n",
-       "--------------------------------------------------------------------------------\n",
-       "type: {\n",
-       "    Akeypoints: var * var * var * float64,\n",
-       "    bboxes: var * var * float64,\n",
-       "    scores: var * var * var * float64,\n",
-       "    frame_number: int64,\n",
-       "    reference_frame_size: {\n",
-       "        &quot;0&quot;: int64,\n",
-       "        &quot;1&quot;: int64\n",
-       "    }\n",
-       "}</pre>"
-      ],
-      "text/plain": [
-       "<Record {Akeypoints: [[...]], bboxes: ..., ...} type='{Akeypoints: var * va...'>"
-      ]
-     },
-     "execution_count": 24,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "a_ak[\"prediction\"][5]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "unique_tracking_ids_a = np.unique(ak.to_numpy(ak.flatten(cast(AwakwardArray, a_ak[\"trackings\"][\"id\"]))))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "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": "3.12.8"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
--- a/draw.ipynb
+++ b/draw.ipynb
--- a/draw_uv.ipynb
+++ b/draw_uv.ipynb
@ -0,0 +1,131 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from PIL import Image, ImageOps\n",
+    "from pathlib import Path\n",
+    "from typing import Optional\n",
+    "from matplotlib import pyplot as plt\n",
+    "import logging"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "TILE_SIZE = 1650 # in pixels\n",
+    "BORDER_SIZE = 200  # in pixels\n",
+    "BORDER_COLOR = (255, 255, 255)\n",
+    "BACKGROUND_COLOR = (255, 255, 255)\n",
+    "IMAGE_DIR = Path(\"board\")\n",
+    "\n",
+    "# Define the layout grid (rows of indices, None for empty)\n",
+    "# fmt: off\n",
+    "layout:list[list[Optional[int]]] = [\n",
+    "    [None, None, 0, None, None],\n",
+    "    [None, None, 1, None, None],\n",
+    "    [None,    5, 2,    4, None],\n",
+    "    [None, None, 3, None, None],\n",
+    "]\n",
+    "# fmt: on\n",
+    "\n",
+    "\n",
+    "\n",
+    "# charuco_410x410_3x3_s133_m105_face3_no_12_DICT_7X7_1000\n",
+    "# xxxxxxx_<phy_size>_<grid_size>_<checker_size>_<marker_space>_face<face_idx>_no_<no_idx>_DICT_<dict_size>\n",
+    "# 0        1          2           3              4              5             6   7             8\n",
+    "def parse_filename_to_face_idx(filename: str):\n",
+    "    parts = filename.split(\"_\")\n",
+    "    return int(parts[5][len(\"face\") :])\n",
+    "\n",
+    "\n",
+    "image_pathes = list(IMAGE_DIR.glob(\"*.png\"))\n",
+    "image_indice = map(lambda p: parse_filename_to_face_idx(p.stem), image_pathes)\n",
+    "images = {k: v for k, v in zip(image_indice, image_pathes)}\n",
+    "display(images)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Create blank canvas\n",
+    "rows = len(layout)\n",
+    "cols = len(layout[0])\n",
+    "canvas = Image.new(\"RGB\", (cols * TILE_SIZE, rows * TILE_SIZE), BACKGROUND_COLOR)\n",
+    "\n",
+    "# Paste tiles\n",
+    "for y, row in enumerate(layout):\n",
+    "    for x, idx in enumerate(row):\n",
+    "        if idx is not None:\n",
+    "            path = images.get(idx)\n",
+    "            if path is not None:\n",
+    "                tile = Image.open(path)\n",
+    "                # for the face index 4, rotate the tile 180 degrees\n",
+    "                if idx == 4:\n",
+    "                    tile = tile.rotate(180)\n",
+    "                canvas.paste(tile, (x * TILE_SIZE, y * TILE_SIZE))\n",
+    "            else:\n",
+    "                logging.warning(f\"Missing: {idx}\")\n",
+    "\n",
+    "# Calculate canvas size (before border)\n",
+    "canvas_width = cols * TILE_SIZE\n",
+    "canvas_height = rows * TILE_SIZE\n",
+    "\n",
+    "# Determine target size to make it square after padding\n",
+    "target_size = max(canvas_width, canvas_height)\n",
+    "extra_padding = target_size - canvas_height\n",
+    "top_pad = extra_padding // 2\n",
+    "bottom_pad = extra_padding - top_pad\n",
+    "\n",
+    "# First add vertical padding to center the layout\n",
+    "canvas_with_border = ImageOps.expand(\n",
+    "    canvas,\n",
+    "    border=(0, top_pad, 0, bottom_pad),  # (left, top, right, bottom)\n",
+    "    fill=BACKGROUND_COLOR,\n",
+    ")\n",
+    "\n",
+    "plt.imshow(canvas_with_border)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "canvas_with_border.save(\"merged_uv_layout.png\")"
+   ]
+  }
+ ],
+ "metadata": {
+  "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": "3.12.10"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
--- a/estimate_extrinstic.ipynb
+++ b/estimate_extrinstic.ipynb
@ -0,0 +1,230 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import cv2\n",
+    "import cv2.aruco as aruco\n",
+    "from typing import Sequence, cast\n",
+    "import awkward as ak\n",
+    "from pathlib import Path\n",
+    "import numpy as np\n",
+    "from typing import Final\n",
+    "from matplotlib import pyplot as plt\n",
+    "from cv2.typing import MatLike"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "A_PATH = Path(\"output/af_03.parquet\")\n",
+    "B_PATH = Path(\"output/ae_08.parquet\")\n",
+    "\n",
+    "a_params = ak.from_parquet(A_PATH)[0]\n",
+    "b_params = ak.from_parquet(B_PATH)[0]\n",
+    "display(a_params)\n",
+    "display(b_params)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def create_new_aruco_marker_origin(marker_length: float):\n",
+    "    \"\"\"\n",
+    "    Create a new ArUco marker origin with the given length.\n",
+    "\n",
+    "    0 -> x\n",
+    "    |\n",
+    "    v\n",
+    "    y\n",
+    "\n",
+    "    0---1\n",
+    "    |   |\n",
+    "    3---2\n",
+    "\n",
+    "    So that the center of the marker is the origin for this PnP problem.\n",
+    "\n",
+    "    Args:\n",
+    "        marker_length: The length of the marker.\n",
+    "    \"\"\"\n",
+    "    return np.array(\n",
+    "        [\n",
+    "            [-marker_length / 2, marker_length / 2, 0],\n",
+    "            [marker_length / 2, marker_length / 2, 0],\n",
+    "            [marker_length / 2, -marker_length / 2, 0],\n",
+    "            [-marker_length / 2, -marker_length / 2, 0],\n",
+    "        ]\n",
+    "    ).astype(np.float32)\n",
+    "\n",
+    "\n",
+    "DICTIONARY: Final[int] = aruco.DICT_4X4_50\n",
+    "# 400mm\n",
+    "MARKER_LENGTH: Final[float] = 0.4\n",
+    "aruco_dict = aruco.getPredefinedDictionary(DICTIONARY)\n",
+    "detector = aruco.ArucoDetector(\n",
+    "    dictionary=aruco_dict, detectorParams=aruco.DetectorParameters()\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "a_img = cv2.imread(str(Path(\"dumped/marker/video-20241205-152716-board.png\")))\n",
+    "a_mtx = ak.to_numpy(a_params[\"camera_matrix\"])\n",
+    "a_dist = ak.to_numpy(a_params[\"distortion_coefficients\"])\n",
+    "\n",
+    "b_img = cv2.imread(str(Path(\"dumped/marker/video-20241205-152721-board.png\")))\n",
+    "b_mtx =  ak.to_numpy(b_params[\"camera_matrix\"])\n",
+    "b_dist = ak.to_numpy(b_params[\"distortion_coefficients\"])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "a_corners, a_ids, _a_rejected = detector.detectMarkers(a_img)\n",
+    "b_corners, b_ids, _b_rejected = detector.detectMarkers(b_img)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "a_corners"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "ok, a_rvec, a_tvec = cv2.solvePnP(create_new_aruco_marker_origin(MARKER_LENGTH), a_corners[0], a_mtx, a_dist)\n",
+    "if not ok:\n",
+    "    raise ValueError(\"Failed to solve PnP for A\")\n",
+    "a_img_output =  cv2.drawFrameAxes(a_img, a_mtx, a_dist, a_rvec, a_tvec, MARKER_LENGTH)\n",
+    "plt.imshow(cv2.cvtColor(a_img_output, cv2.COLOR_BGR2RGB))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "ok, b_rvec, b_tvec = cv2.solvePnP(create_new_aruco_marker_origin(MARKER_LENGTH), b_corners[0], b_mtx, b_dist)\n",
+    "if not ok:\n",
+    "    raise ValueError(\"Failed to solve PnP for B\")\n",
+    "b_img_output =  cv2.drawFrameAxes(b_img, b_mtx, b_dist, b_rvec, b_tvec, MARKER_LENGTH)\n",
+    "plt.imshow(cv2.cvtColor(b_img_output, cv2.COLOR_BGR2RGB))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from typing import TypeVar, Union\n",
+    "\n",
+    "\n",
+    "T = TypeVar(\"T\")\n",
+    "\n",
+    "\n",
+    "def create_transform_matrix(rvec: MatLike, tvec: MatLike, dtype: type = np.float32):\n",
+    "    assert rvec.shape == (3, 1)\n",
+    "    assert tvec.shape == (3, 1)\n",
+    "    R, _ = cv2.Rodrigues(rvec)\n",
+    "    transform = np.eye(4, dtype=dtype)\n",
+    "    transform[:3, :3] = R\n",
+    "    transform[:3, 3] = tvec.flatten()\n",
+    "    return transform\n",
+    "\n",
+    "\n",
+    "def extract_translation(transform: MatLike):\n",
+    "    assert transform.shape == (4, 4)\n",
+    "    return transform[:3, 3]\n",
+    "\n",
+    "\n",
+    "def extract_rotation(transform: MatLike):\n",
+    "    assert transform.shape == (4, 4)\n",
+    "    return transform[:3, :3]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "a_trans = create_transform_matrix(a_rvec, a_tvec)\n",
+    "display(a_trans)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "np.linalg.inv(a_trans)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Converts a rotation matrix to a rotation vector or vice versa\n",
+    "a_rmtx, _ = cv2.Rodrigues(a_rvec)\n",
+    "b_rmtx, _ = cv2.Rodrigues(b_rvec)\n",
+    "a_camera_coord = -(a_rmtx.T@ a_tvec)\n",
+    "b_camera_coord = -(b_rmtx.T @ b_tvec)\n",
+    "distance = np.linalg.norm(a_camera_coord - b_camera_coord)\n",
+    "a_distance = np.linalg.norm(a_camera_coord)\n",
+    "b_distance = np.linalg.norm(b_camera_coord)\n",
+    "display(\"d_ab={:.4}m a={:.4}m b={:.4}m\".format(distance, a_distance, b_distance))\n",
+    "display(\"a_coord={}\".format(a_camera_coord.T))\n",
+    "display(\"b_coord={}\".format(b_camera_coord.T))"
+   ]
+  }
+ ],
+ "metadata": {
+  "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": "3.12.10"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
--- a/find_aruco_points.py
+++ b/find_aruco_points.py
--- a/find_aruco_points_with_image.ipynb
+++ b/find_aruco_points_with_image.ipynb
@ -0,0 +1,442 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from datetime import datetime\n",
+    "from pathlib import Path\n",
+    "from typing import Any, Final, Optional, TypeAlias, TypedDict, Union, cast\n",
+    "from dataclasses import dataclass\n",
+    "\n",
+    "import cv2\n",
+    "import numpy as np\n",
+    "import orjson\n",
+    "import trimesh\n",
+    "from beartype import beartype\n",
+    "from cv2 import aruco\n",
+    "from cv2.typing import MatLike\n",
+    "from jaxtyping import Float, Int, Num, jaxtyped\n",
+    "from loguru import logger\n",
+    "from matplotlib import pyplot as plt\n",
+    "from numpy.typing import ArrayLike\n",
+    "from numpy.typing import NDArray as NDArrayT\n",
+    "\n",
+    "NDArray: TypeAlias = np.ndarray"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "INPUT_IMAGE = Path(\"merged_uv_layout.png\")\n",
+    "# 7x7\n",
+    "DICTIONARY: Final[int] = aruco.DICT_7X7_1000\n",
+    "# 400mm\n",
+    "MARKER_LENGTH: Final[float] = 0.4"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "aruco_dict = aruco.getPredefinedDictionary(DICTIONARY)\n",
+    "detector = aruco.ArucoDetector(\n",
+    "    dictionary=aruco_dict, detectorParams=aruco.DetectorParameters()\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "frame = cv2.imread(str(INPUT_IMAGE))\n",
+    "grey = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)\n",
+    "# pylint: disable-next=unpacking-non-sequence\n",
+    "markers, ids, rejected = detector.detectMarkers(grey)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Note: BGR\n",
+    "RED = (0, 0, 255)\n",
+    "GREEN = (0, 255, 0)\n",
+    "BLUE = (255, 0, 0)\n",
+    "YELLOW = (0, 255, 255)\n",
+    "GREY = (128, 128, 128)\n",
+    "CYAN = (255, 255, 0)\n",
+    "MAGENTA = (255, 0, 255)\n",
+    "ORANGE = (0, 165, 255)\n",
+    "PINK = (147, 20, 255)\n",
+    "\n",
+    "UI_SCALE = 10\n",
+    "UI_SCALE_FONT = 8\n",
+    "UI_SCALE_FONT_WEIGHT = 20"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "out = frame.copy()\n",
+    "# `markers` is [N, 1, 4, 2]\n",
+    "# `ids` is [N, 1]\n",
+    "if ids is not None:\n",
+    "    markers = np.reshape(markers, (-1, 4, 2))\n",
+    "    ids = np.reshape(ids, (-1, 1))\n",
+    "    # logger.info(\"markers={}, ids={}\", np.array(markers).shape, np.array(ids).shape)\n",
+    "    for m, i in zip(markers, ids):\n",
+    "        # logger.info(\"id={}, center={}\", i, center)\n",
+    "        center = np.mean(m, axis=0).astype(int) # type: ignore\n",
+    "        # BGR\n",
+    "        color_map = [RED, GREEN, BLUE, YELLOW]\n",
+    "        for color, corners in zip(color_map, m):\n",
+    "            corners = corners.astype(int)\n",
+    "            out = cv2.circle(out, corners, 5*UI_SCALE, color, -1)\n",
+    "        cv2.circle(out, tuple(center), 5*UI_SCALE, CYAN, -1)\n",
+    "        cv2.putText(\n",
+    "            out,\n",
+    "            str(i),\n",
+    "            tuple(center),\n",
+    "            cv2.FONT_HERSHEY_SIMPLEX,\n",
+    "            1*UI_SCALE_FONT,\n",
+    "            MAGENTA,\n",
+    "            UI_SCALE_FONT_WEIGHT,\n",
+    "        )"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "@jaxtyped(typechecker=beartype)\n",
+    "@dataclass\n",
+    "class Marker:\n",
+    "    id: int\n",
+    "    center: Num[NDArray, \"2\"]\n",
+    "    corners: Num[NDArray, \"4 2\"]\n",
+    "\n",
+    "\n",
+    "output_markers: list[Marker] = []\n",
+    "if ids is not None:\n",
+    "    IMAGE_WIDTH = frame.shape[1]\n",
+    "    IMAGE_HEIGHT = frame.shape[0]\n",
+    "\n",
+    "    def normalize_point(point: NDArrayT[Any]) -> NDArrayT[np.float64]:\n",
+    "        \"\"\"\n",
+    "        input could be: [N, 2] or [2]\n",
+    "        \"\"\"\n",
+    "        if point.ndim == 1:\n",
+    "            return point / np.array([IMAGE_WIDTH, IMAGE_HEIGHT])\n",
+    "        elif point.ndim == 2:\n",
+    "            return point / np.array([IMAGE_WIDTH, IMAGE_HEIGHT])\n",
+    "        else:\n",
+    "            raise ValueError(f\"Invalid shape: {point.shape}\")\n",
+    "\n",
+    "    def flip_y(point: NDArrayT[Any], y_max: int) -> NDArrayT[Any]:\n",
+    "        \"\"\"\n",
+    "        flip y axis;\n",
+    "\n",
+    "        Usually OpenCV image y-axis is inverted. (origin at top-left)\n",
+    "        In UV layout, the origin is at bottom-left.\n",
+    "        \"\"\"\n",
+    "        return np.array([point[0], y_max - point[1]])\n",
+    "\n",
+    "    for m, i in zip(markers, ids):\n",
+    "        center = np.mean(m, axis=0).astype(int)  # type: ignore\n",
+    "        output_markers.append(\n",
+    "            Marker(\n",
+    "                id=int(i[0]),\n",
+    "                center=flip_y(normalize_point(center), 1),\n",
+    "                corners=np.array([flip_y(normalize_point(c), 1) for c in m]),\n",
+    "            )\n",
+    "        )\n",
+    "\n",
+    "with open(\"output/aruco_2d_uv_coords_normalized.json\", \"wb\") as f:\n",
+    "    f.write(orjson.dumps(output_markers, option=orjson.OPT_SERIALIZE_NUMPY))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "plt.imshow(cv2.cvtColor(out, cv2.COLOR_BGR2RGB))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "cv2.imwrite(\"merged_uv_layout_with_markers.png\", out)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "@jaxtyped(typechecker=beartype)\n",
+    "def interpolate_uvs_to_3d(\n",
+    "    uv_points: Num[NDArray, \"N 2\"],\n",
+    "    vertices: Num[NDArray, \"V 3\"],\n",
+    "    uvs: Num[NDArray, \"V 2\"],\n",
+    "    faces: Num[NDArray, \"F 3\"],\n",
+    "    epsilon: float = 1e-6,\n",
+    ") -> Num[NDArray, \"N 3\"]:\n",
+    "    \"\"\"\n",
+    "    Map multiple UV points to 3D coordinates using barycentric interpolation.\n",
+    "\n",
+    "    Args:\n",
+    "        uv_points: (N, 2) array of UV coordinates in [0,1]\n",
+    "        vertices: (V, 3) array of mesh vertex positions\n",
+    "        uvs:      (V, 2) array of per-vertex UV coordinates\n",
+    "        faces:    (F, 3) array of triangle vertex indices\n",
+    "        epsilon:  barycentric inside-triangle tolerance\n",
+    "\n",
+    "    Returns:\n",
+    "        (N, 3) array of interpolated 3D coordinates (NaNs if no triangle found)\n",
+    "    \"\"\"\n",
+    "    results = np.full((uv_points.shape[0], 3), np.nan, dtype=np.float64)\n",
+    "\n",
+    "    for pi, uv_point in enumerate(uv_points):\n",
+    "        for face in faces:\n",
+    "            uv_tri = uvs[face]  # (3,2)\n",
+    "            v_tri = vertices[face]  # (3,3)\n",
+    "\n",
+    "            A = np.array(\n",
+    "                [\n",
+    "                    [uv_tri[0, 0] - uv_tri[2, 0], uv_tri[1, 0] - uv_tri[2, 0]],\n",
+    "                    [uv_tri[0, 1] - uv_tri[2, 1], uv_tri[1, 1] - uv_tri[2, 1]],\n",
+    "                ]\n",
+    "            )\n",
+    "            b = uv_point - uv_tri[2]\n",
+    "\n",
+    "            try:\n",
+    "                w0, w1 = np.linalg.solve(A, b)\n",
+    "                w2 = 1.0 - w0 - w1\n",
+    "                if min(w0, w1, w2) >= -epsilon:\n",
+    "                    results[pi] = w0 * v_tri[0] + w1 * v_tri[1] + w2 * v_tri[2]\n",
+    "                    break  # Stop after first matching triangle\n",
+    "            except np.linalg.LinAlgError:\n",
+    "                continue\n",
+    "\n",
+    "    return results\n",
+    "\n",
+    "\n",
+    "@jaxtyped(typechecker=beartype)\n",
+    "def interpolate_uvs_to_3d_trimesh(\n",
+    "    uv_points: Num[NDArray, \"N 2\"],\n",
+    "    mesh: Union[trimesh.Trimesh, trimesh.Scene],\n",
+    "    epsilon: float = 1e-6,\n",
+    ") -> Num[NDArray, \"N 3\"]:\n",
+    "    \"\"\"\n",
+    "    Wrapper for batched UV-to-3D interpolation using a trimesh mesh or scene.\n",
+    "\n",
+    "    Args:\n",
+    "        uv_points: (N, 2) UV coordinates to convert\n",
+    "        mesh: a Trimesh or Scene object\n",
+    "        epsilon: barycentric epsilon tolerance\n",
+    "\n",
+    "    Returns:\n",
+    "        (N, 3) array of 3D positions (NaN if outside mesh)\n",
+    "    \"\"\"\n",
+    "    if isinstance(mesh, trimesh.Scene):\n",
+    "        if len(mesh.geometry) == 0:\n",
+    "            raise ValueError(\"Scene has no geometry.\")\n",
+    "        mesh = list(mesh.geometry.values())[0]\n",
+    "\n",
+    "    if not isinstance(mesh, trimesh.Trimesh):\n",
+    "        raise TypeError(\"Expected a Trimesh or Scene with geometry.\")\n",
+    "\n",
+    "    if mesh.visual is None:\n",
+    "        raise ValueError(\"Mesh does not have visual.\")\n",
+    "\n",
+    "    if mesh.visual.uv is None:\n",
+    "        raise ValueError(\"Mesh does not have UVs.\")\n",
+    "\n",
+    "    return interpolate_uvs_to_3d(\n",
+    "        uv_points=uv_points,\n",
+    "        vertices=mesh.vertices,\n",
+    "        uvs=mesh.visual.uv,\n",
+    "        faces=mesh.faces,\n",
+    "        epsilon=epsilon,\n",
+    "    )"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "m = trimesh.load_mesh(\"sample/standard_box.glb\")\n",
+    "def marker_to_3d_coords(marker: Marker, mesh: trimesh.Trimesh):\n",
+    "    uv_points = marker.corners\n",
+    "    return interpolate_uvs_to_3d_trimesh(uv_points, mesh)\n",
+    "\n",
+    "id_to_3d_coords = {marker.id: marker_to_3d_coords(marker, m) for marker in output_markers}\n",
+    "# note that the glb is Y up\n",
+    "# when visualizing with matplotlib, it's Z up\n",
+    "OPEN_GL_TO_BLENDER = np.array([[1, 0, 0], [0, 0, -1], [0, 1, 0]])\n",
+    "display(np.linalg.inv(OPEN_GL_TO_BLENDER)) # should be the same"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# matplotlib default colors scheme\n",
+    "colors: list[str] = plt.rcParams[\"axes.prop_cycle\"].by_key()[\"color\"]\n",
+    "\n",
+    "def hex_to_rgb(hex_color: str) -> tuple[float, float, float]:\n",
+    "    assert hex_color.startswith(\"#\")\n",
+    "    assert len(hex_color) == 7\n",
+    "    return tuple(int(hex_color[i:i+2], 16) / 255.0 for i in (1, 3, 5)) # type: ignore"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from functools import lru_cache\n",
+    "from typing import Optional, TypedDict\n",
+    "import awkward as ak\n",
+    "\n",
+    "\n",
+    "class MarkerFace(TypedDict):\n",
+    "    name: str\n",
+    "    ids: Int[NDArray, \"N\"]\n",
+    "    \"\"\"\n",
+    "    ArUco marker ids\n",
+    "    \"\"\"\n",
+    "    corners: Num[NDArray, \"N 4 3\"]\n",
+    "    \"\"\"\n",
+    "    Corner coordinates in 3D of rectangle,\n",
+    "    relative to the world origin\n",
+    "    \"\"\"\n",
+    "\n",
+    "\n",
+    "@dataclass\n",
+    "class Face:\n",
+    "    color: tuple[float, float, float]\n",
+    "    marker_ids: list[int]\n",
+    "\n",
+    "\n",
+    "# fmt: off\n",
+    "layout:list[list[Optional[int]]] = [\n",
+    "    [None, None, 0, None, None],\n",
+    "    [None, None, 1, None, None],\n",
+    "    [None,    5, 2,    4, None],\n",
+    "    [None, None, 3, None, None],\n",
+    "]\n",
+    "# fmt: on\n",
+    "\n",
+    "faces = {\n",
+    "    \"bottom\": Face(color=hex_to_rgb(colors[0]), marker_ids=[0, 1, 2, 3]),\n",
+    "    \"back\": Face(color=hex_to_rgb(colors[1]), marker_ids=[4, 5, 6, 7]),\n",
+    "    \"top\": Face(color=hex_to_rgb(colors[2]), marker_ids=[8, 9, 10, 11]),\n",
+    "    \"front\": Face(color=hex_to_rgb(colors[3]), marker_ids=[12, 13, 14, 15]),\n",
+    "    \"right\": Face(color=hex_to_rgb(colors[4]), marker_ids=[16, 17, 18, 19]),\n",
+    "    \"left\": Face(color=hex_to_rgb(colors[5]), marker_ids=[20, 21, 22, 23]),\n",
+    "}\n",
+    "\n",
+    "markers: list[MarkerFace] = []\n",
+    "for name, face in faces.items():\n",
+    "    corners = np.array([id_to_3d_coords[id] for id in face.marker_ids])\n",
+    "    assert corners.shape == (4, 4, 3)\n",
+    "    markers.append(MarkerFace(name=name, ids=np.array(face.marker_ids), corners=corners))\n",
+    "display(markers)\n",
+    "ak.to_parquet(markers, \"output/standard_box_markers.parquet\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "@lru_cache\n",
+    "def get_face_by_marker_id(marker_id: int) -> Optional[Face]:\n",
+    "    for face in faces.values():\n",
+    "        if marker_id in face.marker_ids:\n",
+    "            return face\n",
+    "    return None\n",
+    "\n",
+    "\n",
+    "# 3D Visualization (with flipped and fully valid data)\n",
+    "fig = plt.figure(figsize=(8, 8))\n",
+    "ax = fig.add_subplot(111, projection=\"3d\")\n",
+    "\n",
+    "for tag_id, corners in id_to_3d_coords.items():\n",
+    "    corners = np.array(corners)\n",
+    "    face = get_face_by_marker_id(tag_id)\n",
+    "    assert face is not None\n",
+    "    color = face.color\n",
+    "    for i in range(4):\n",
+    "        p1 = OPEN_GL_TO_BLENDER @ corners[i]\n",
+    "        p2 = OPEN_GL_TO_BLENDER @ corners[(i + 1) % 4]\n",
+    "        ax.plot(*zip(p1, p2), color=color)\n",
+    "    center = OPEN_GL_TO_BLENDER @ corners.mean(axis=0)\n",
+    "    ax.scatter(*center, color=color)\n",
+    "    ax.text(*center, str(tag_id), fontsize=9, color=\"black\")  # type: ignore\n",
+    "\n",
+    "ax.set_box_aspect([1, 1, 1])  # type: ignore\n",
+    "ax.set_title(\"ArUco Corners in 3D\")\n",
+    "ax.set_xlabel(\"X\")\n",
+    "ax.set_ylabel(\"Y\")\n",
+    "ax.set_zlabel(\"Z\")  # type: ignore\n",
+    "\n",
+    "# Set the viewing angle\n",
+    "# ax.view_init(elev=60, azim=35) # type: ignore\n",
+    "\n",
+    "plt.show()"
+   ]
+  }
+ ],
+ "metadata": {
+  "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": "3.12.10"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
--- a/find_cute_box_with_image.ipynb
+++ b/find_cute_box_with_image.ipynb
--- a/find_extrinsic_object.py
+++ b/find_extrinsic_object.py
@ -1,21 +1,44 @@
-import cv2
-from cv2 import aruco
 from datetime import datetime
-from loguru import logger
 from pathlib import Path
-from typing import Optional, cast, Final
+from typing import Final, Optional, TypedDict, cast
+
 import awkward as ak
-from cv2.typing import MatLike
+import cv2
 import numpy as np
+from cv2 import aruco
+from cv2.typing import MatLike
+from jaxtyping import Int, Num
+from loguru import logger

 NDArray = np.ndarray
 CALIBRATION_PARQUET = Path("output") / "usbcam_cal.parquet"
-OBJECT_POINTS_PARQUET = Path("output") / "object_points.parquet"
+# OBJECT_POINTS_PARQUET = Path("output") / "object_points.parquet"
+OBJECT_POINTS_PARQUET = Path("output") / "standard_box_markers.parquet"
 DICTIONARY: Final[int] = aruco.DICT_4X4_50
 # 400mm
 MARKER_LENGTH: Final[float] = 0.4


+class MarkerFace(TypedDict):
+    """
+    for diamond ArUco markers, N is 4
+    """
+
+    name: str
+    """
+    a label for the face
+    """
+    ids: Int[NDArray, "N"]
+    """
+    ArUco marker ids
+    """
+    corners: Num[NDArray, "N 4 3"]
+    """
+    Corner coordinates in 3D of rectangle,
+    relative to the world origin
+    """
+
+
 def gen():
    API = cv2.CAP_AVFOUNDATION
    cap = cv2.VideoCapture(0, API)
--- a/interactive_example.py
+++ b/interactive_example.py
@ -0,0 +1,18 @@
+# %%
+import numpy as np
+
+
+# %%
+
+# %% [markdown]
+# # Extract the 3D coordinates of the ArUco markers from the image
+#
+# 1. Load the image
+# 2. Detect the ArUco markers
+# 3. Get the 3D coordinates of the markers
+# 4. Save the 3D coordinates to a file
+
+
+# %%
+
+# %%
--- a/output/object_points.parquet
+++ b/output/object_points.parquet
--- a/output/standard_box_markers.parquet
+++ b/output/standard_box_markers.parquet
--- a/play.ipynb
+++ b/play.ipynb
--- a/playground.py
+++ b/playground.py
@ -0,0 +1,53 @@
+# ---
+# jupyter:
+#   jupytext:
+#     text_representation:
+#       extension: .py
+#       format_name: percent
+#       format_version: '1.3'
+#       jupytext_version: 1.17.0
+#   kernelspec:
+#     language: python
+#     name: python3
+# ---
+
+
+# %%
+import awkward as ak
+from pathlib import Path
+import numpy as np
+from IPython.display import display
+from typing import TypedDict
+from jaxtyping import Int, Num
+
+NDArray = np.ndarray
+
+
+# %%
+class MarkerFace(TypedDict):
+    """
+    for diamond ArUco markers, N is 4
+    """
+
+    name: str
+    """
+    a label for the face
+    """
+    ids: Int[NDArray, "N"]
+    """
+    ArUco marker ids
+    """
+    corners: Num[NDArray, "N 4 3"]
+    """
+    Corner coordinates in 3D of rectangle,
+    relative to the world origin
+    """
+
+
+# %%
+# OBJECT_POINTS_PARQUET = Path("output") / "object_points.parquet"
+OBJECT_POINTS_PARQUET = Path("output") / "standard_box_markers.parquet"
+ops = ak.from_parquet(OBJECT_POINTS_PARQUET)
+display(ops)
+
+# %%
--- a/preprocess_camera_parameters.ipynb
+++ b/preprocess_camera_parameters.ipynb
@ -181,18 +181,9 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 43,
+   "execution_count": null,
   "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/cj/0zmvpygn7m72m42lh6x_hcgw0000gn/T/ipykernel_79393/542219436.py:22: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
-      "  id = int(id)\n"
-     ]
-    }
-   ],
+   "outputs": [],
   "source": [
    "a_result_img, a_rvec, a_tvec = process(a_img, a_mtx, a_dist)\n",
    "# plt.imshow(cv2.cvtColor(a_result_img, cv2.COLOR_BGR2RGB))"
@ -200,18 +191,9 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 44,
+   "execution_count": null,
   "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/cj/0zmvpygn7m72m42lh6x_hcgw0000gn/T/ipykernel_79393/542219436.py:22: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
-      "  id = int(id)\n"
-     ]
-    }
-   ],
+   "outputs": [],
   "source": [
    "b_result_img, b_rvec, b_tvec = process(b_img, b_mtx, b_dist)\n",
    "# plt.imshow(cv2.cvtColor(b_result_img, cv2.COLOR_BGR2RGB))"
@ -219,18 +201,9 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 45,
+   "execution_count": null,
   "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/cj/0zmvpygn7m72m42lh6x_hcgw0000gn/T/ipykernel_79393/542219436.py:22: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
-      "  id = int(id)\n"
-     ]
-    }
-   ],
+   "outputs": [],
   "source": [
    "c_result_img, c_rvec, c_tvec = process(c_img, c_mtx, c_dist)\n",
    "c_prime_result_img, c_prime_rvec, c_prime_tvec = process(c_prime_img, c_mtx, c_dist)"
@ -238,58 +211,9 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 46,
+   "execution_count": null,
   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'params'"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "text/html": [
-       "<pre>[{name: &#x27;a-ae_08&#x27;, rvec: [[-0.602], ..., [-3.05]], tvec: [...], ...},\n",
-       " {name: &#x27;b-ae_09&#x27;, rvec: [[0.572], ..., [3.02]], tvec: [...], ...},\n",
-       " {name: &#x27;c-af_03&#x27;, rvec: [[-1.98], ..., [-2.4]], tvec: [...], ...},\n",
-       " {name: &#x27;c-prime-af_03&#x27;, rvec: [[-1.99], ...], tvec: [...], ...}]\n",
-       "---------------------------------------------------------------------\n",
-       "type: 4 * {\n",
-       "    name: string,\n",
-       "    rvec: var * var * float64,\n",
-       "    tvec: var * var * float64,\n",
-       "    camera_matrix: var * var * float64,\n",
-       "    distortion_coefficients: var * var * float64\n",
-       "}</pre>"
-      ],
-      "text/plain": [
-       "<Array [{name: 'a-ae_08', rvec: ..., ...}, ...] type='4 * {name: string, rv...'>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "text/plain": [
-       "<pyarrow._parquet.FileMetaData object at 0x311da8900>\n",
-       "  created_by: parquet-cpp-arrow version 14.0.1\n",
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-       "  num_row_groups: 1\n",
-       "  format_version: 2.6\n",
-       "  serialized_size: 0"
-      ]
-     },
-     "execution_count": 46,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
   "source": [
    "params = AwkwardArray(\n",
    "    [\n",
@ -329,20 +253,9 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 47,
+   "execution_count": null,
   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "True"
-      ]
-     },
-     "execution_count": 47,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
   "source": [
    "cv2.imwrite(\"output/a_result_img.png\", a_result_img)\n",
    "cv2.imwrite(\"output/b_result_img.png\", b_result_img)\n",
@ -367,7 +280,7 @@
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
-   "version": "3.12.8"
+   "version": "3.12.10"
  }
 },
 "nbformat": 4,
--- a/sample/standard_box.glb
+++ b/sample/standard_box.glb
Author	SHA1	Message	Date
crosstyan	e593c7b363	Refactor find_extrinsic_object.py: update object points parquet file name, enhance type annotations with MarkerFace TypedDict for diamond ArUco markers, and improve code organization.	2025-04-30 11:45:41 +08:00
crosstyan	c8f4a7ab26	Refactor Jupyter notebooks for marker processing: deleted boom.ipynb and compute_3d_maybe.ipynb, added calculate_box_coord_naive.ipynb, calculate_box_face_coord_naive.ipynb, estimate_extrinstic.ipynb, find_aruco_points_with_image.ipynb, find_aruco_points.py, and find_extrinsic_object.py. Updated .gitignore to include new output files.	2025-04-30 11:43:59 +08:00
crosstyan	733c6f8670	Update execution counts in find_cute_box_with_image.ipynb and adjust coordinate transformations for OpenGL to Blender compatibility.	2025-04-24 14:23:56 +08:00
crosstyan	801485e6d5	Add draw_uv.ipynb for UV layout generation, including image processing and canvas creation. Updated find_cute_box_with_image.ipynb with new functions for 3D coordinate extraction and improved type annotations.	2025-04-24 12:56:34 +08:00
crosstyan	9e1ac3d941	Add support for GLB files in LFS tracking, enhance find_cute_box_with_image.ipynb with new functions for 3D coordinate extraction, and introduce interactive_example.py for marker processing workflow.	2025-04-24 12:13:50 +08:00
crosstyan	aa081f46ec	Refactor find_cute_box_with_image.ipynb to reset execution counts, enhance type annotations, and add new functions for marker processing and UV-to-3D interpolation. Introduced TypedDict for marker representation and improved code organization.	2025-04-23 19:13:04 +08:00
crosstyan	531bc6c29a	Update Jupyter notebooks to reset execution counts and remove output cells. Added padding calculations for canvas in draw.ipynb and simplified output handling in find_cute_box_with_image.ipynb.	2025-04-23 17:07:59 +08:00