{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Computing with shapes of landmarks in Kendall shape spaces" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Lead author: Nina Miolane.\n", "\n", "In this tutorial, we show how to use geomstats to perform a shape data analysis. Specifically, we aim to study the difference between two groups of data:\n", "- optical nerve heads that correspond to normal eyes,\n", "- optical nerve heads that correspond to glaucoma eyes.\n", "\n", "We wish to investigate if there is a difference in these two groups, and if this difference is a difference in sizes of the optical nerve heads, or a difference in shapes (where the size has been quotiented out)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "INFO: Using numpy backend\n" ] } ], "source": [ "import matplotlib.colors as colors\n", "import matplotlib.patches as mpatches\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D # NOQA\n", "from mpl_toolkits.mplot3d.art3d import Poly3DCollection\n", "\n", "import geomstats.backend as gs\n", "import geomstats.datasets.utils as data_utils\n", "from geomstats.geometry.pre_shape import PreShapeSpace\n", "\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We import the dataset of the optical nerve heads from 22 images of Rhesus monkeys’ eyes (11 monkeys), available in [[PE2015]](#References). \n", "\n", "For each monkey, an experimental glaucoma was introduced in one eye, while the second\n", "eye was kept as control. One seeks to observe differences between the glaucoma and the\n", "control eyes. On each image, 5 anatomical landmarks were recorded: \n", "- 1st landmark: superior aspect of the retina, \n", "- 2nd landmark: side of the retina closest to the temporal bone of the skull,\n", "- 3rd landmark: nose side of the retina, \n", "- 4th landmark: inferior point,\n", "- 5th landmark: optical nerve head deepest point.\n", "\n", "Label 0 refers to a normal eye, and Label 1 to an eye with glaucoma." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(22, 5, 3)\n", "[0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1]\n", "[ 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10]\n" ] } ], "source": [ "nerves, labels, monkeys = data_utils.load_optical_nerves()\n", "print(nerves.shape)\n", "print(labels)\n", "print(monkeys)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We extract the landmarks' sets corresponding to the two eyes' nerves of the first monkey, with their corresponding labels." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(2, 5, 3)\n", "[0 1]\n" ] } ], "source": [ "two_nerves = nerves[monkeys == 0]\n", "print(two_nerves.shape)\n", "\n", "two_labels = labels[monkeys == 0]\n", "print(two_labels)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "tags": [ "nbsphinx-thumbnail" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "label_to_str = {0: \"Normal nerve\", 1: \"Glaucoma nerve\"}\n", "label_to_color = {\n", " 0: (102 / 255, 178 / 255, 255 / 255, 1.0),\n", " 1: (255 / 255, 178 / 255, 102 / 255, 1.0),\n", "}\n", "\n", "fig = plt.figure()\n", "ax = plt.axes(projection=\"3d\")\n", "ax.set_xlim((2000, 4000))\n", "ax.set_ylim((1000, 5000))\n", "ax.set_zlim((-600, 200))\n", "\n", "for nerve, label in zip(two_nerves, two_labels):\n", " x = nerve[:, 0]\n", " y = nerve[:, 1]\n", " z = nerve[:, 2]\n", "\n", " verts = [list(zip(x, y, z))]\n", "\n", " poly = Poly3DCollection(verts, alpha=0.5)\n", " color = label_to_color[int(label)]\n", " poly.set_color(colors.rgb2hex(color))\n", " poly.set_edgecolor(\"k\")\n", " ax.add_collection3d(poly)\n", "\n", "patch_0 = mpatches.Patch(color=label_to_color[0], label=label_to_str[0], alpha=0.5)\n", "patch_1 = mpatches.Patch(color=label_to_color[1], label=label_to_str[1], alpha=0.5)\n", "plt.legend(handles=[patch_0, patch_1], prop={\"size\": 14})\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We first try to detect if there are two groups of optical nerve heads, based on the 3D coordinates of the landmarks sets." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from geomstats.geometry.euclidean import Euclidean\n", "\n", "nerves_vec = nerves.reshape(22, -1)\n", "\n", "eucl = Euclidean(dim=nerves_vec.shape[-1])\n", "\n", "eucl_dist = eucl.metric.dist_pairwise(nerves_vec)\n", "\n", "plt.figure()\n", "plt.imshow(eucl_dist);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We do not see any two clear clusters." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We want to investigate if there is a difference between these two groups of shapes - normal nerve versus glaucoma nerve - or if the main difference is merely relative to the global size of the landmarks' sets." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ambient_dim = 3\n", "k_landmarks = 5\n", "\n", "preshape = PreShapeSpace(ambient_dim=ambient_dim, k_landmarks=k_landmarks)\n", "\n", "sizes = preshape.embedding_space.metric.norm(preshape.center(nerves))\n", "\n", "plt.figure(figsize=(6, 4))\n", "for label, col in label_to_color.items():\n", " label_sizes = sizes[labels == label]\n", " plt.hist(label_sizes, color=col, label=label_to_str[label], alpha=0.5, bins=10)\n", " plt.axvline(gs.mean(label_sizes), color=col)\n", "plt.legend(fontsize=14)\n", "plt.title(\"Sizes of optical nerves\", fontsize=14);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The vertical lines represent the sample mean of each group (normal/glaucoma)." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(6, 4))\n", "plt.hist(sizes[labels == 1] - sizes[labels == 0], alpha=0.5)\n", "plt.axvline(0, color=\"black\")\n", "plt.title(\n", " \"Difference in size of optical nerve between glaucoma and normal eyes\", fontsize=14\n", ");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We perform a hypothesis test, testing if the two samples of sizes have the same average. We use the t-test for related samples, since the sample elements are paired: two eyes for each monkey." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "True\n" ] } ], "source": [ "from scipy import stats\n", "\n", "signif_level = 0.05\n", "\n", "tstat, pvalue = stats.ttest_rel(sizes[labels == 0], sizes[labels == 1])\n", "print(pvalue < signif_level)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is a significative difference, in optical nerve eyes' sizes, between the glaucoma and normal eye." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We want to investigate if there is a difference in shapes, where the size component has been quotiented out. \n", "\n", "We project the data to the Kendall pre-shape space, which:\n", "- centers the nerve landmark sets so that they share the same barycenter,\n", "- normalizes the sizes of the landmarks' sets to 1." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(22, 5, 3)\n", "[ True True True True True True True True True True True True\n", " True True True True True True True True True True]\n", "[ True True True True True True True True True True True True\n", " True True True True True True True True True True]\n" ] } ], "source": [ "nerves_preshape = preshape.projection(nerves)\n", "print(nerves_preshape.shape)\n", "print(preshape.belongs(nerves_preshape))\n", "print(gs.isclose(preshape.embedding_space.metric.norm(nerves_preshape), 1.0))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to quotient out the 3D orientation component, we align the landmark sets in the preshape space. " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "preshape.equip_with_group_action(\"rotations\")\n", "preshape.equip_with_quotient()\n", "\n", "base_point = nerves_preshape[0]\n", "\n", "nerves_shape = preshape.fiber_bundle.align(point=nerves_preshape, base_point=base_point)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Kendall metric is a Riemannian metric that takes this alignment into account. It corresponds to the metric of the Kendall shape space, which is the manifold defined as the preshape space quotient by the action of the rotation in `ambient_dim` dimensions, here in 3 dimensions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use it to perform a tangent PCA in the Kendall shape space, and determine if we see a difference in the shapes of the optical nerves." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from geomstats.learning.pca import TangentPCA\n", "\n", "tpca = TangentPCA(preshape.quotient)\n", "tpca.fit(nerves_shape)\n", "\n", "plt.plot(tpca.explained_variance_ratio_)\n", "plt.xlabel(\"Number of principal tangent components\", size=14)\n", "plt.ylabel(\"Fraction of explained variance\", size=14);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Two principal components already describe around 60% of the variance. We plot the data projected in the tangent space defined by these two principal components." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = tpca.transform(nerves_shape)\n", "\n", "plt.figure(figsize=(12, 12))\n", "\n", "for label, col in label_to_color.items():\n", " mask = labels == label\n", " plt.scatter(X[mask, 0], X[mask, 1], color=col, s=100, label=label_to_str[label])\n", "plt.legend(fontsize=14)\n", "\n", "for label, x, y in zip(monkeys, X[:, 0], X[:, 1]):\n", " plt.annotate(\n", " label,\n", " xy=(x, y),\n", " xytext=(-20, 20),\n", " textcoords=\"offset points\",\n", " ha=\"right\",\n", " va=\"bottom\",\n", " bbox=dict(boxstyle=\"round,pad=0.5\", fc=\"white\", alpha=0.5),\n", " arrowprops=dict(arrowstyle=\"->\", connectionstyle=\"arc3,rad=0\"),\n", " )\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The indices represent the monkeys' indices. \n", "\n", "In contrast to the above study focusing on the optical nerves' sizes, visual inspection does not reveal any clusters between the glaucoma and normal optical nerves' shapes. We also do not see any obvious pattern between the two optical nerves of the same monkey.\n", "\n", "This shows that the difference between the optical nerve heads mainly resides in the over sizes of the optical nerves." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(22, 22)\n" ] } ], "source": [ "dist_pairwise = preshape.quotient.metric.dist_pairwise(nerves_shape)\n", "print(dist_pairwise.shape)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.imshow(dist_pairwise);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We try a agglomerative hierarchical clustering to investigate if we can cluster in the Kendall shape space." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "True labels: [0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1]\n", "Predicted labels: [0 1 1 1 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1]\n", "Accuracy: 0.55\n" ] } ], "source": [ "from sklearn.cluster import AgglomerativeClustering\n", "\n", "clustering = AgglomerativeClustering(\n", " metric=\"precomputed\", n_clusters=2, linkage=\"average\"\n", ")\n", "clustering.fit(dist_pairwise)\n", "predicted_labels = clustering.labels_\n", "\n", "print(\"True labels:\", labels)\n", "print(\"Predicted labels:\", predicted_labels)\n", "\n", "accuracy = gs.sum(labels == predicted_labels) / len(labels)\n", "print(f\"Accuracy: {accuracy:.2f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The accuracy is barely above the accuracy of a random classifier, that would assign 0 or 1 with probably 0.5 to each of the shapes. This confirms that the difference that exists between the two groups is mostly due to the landmarks' set size and not their shapes." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", ".. [PE2015] Patrangenaru and L. Ellingson. Nonparametric Statistics on Manifolds and Their Applications to Object Data, 2015. https://doi.org/10.1201/b18969" ] } ], "metadata": { "backends": [ "numpy", "autograd" ], "celltoolbar": "Edit Metadata", "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": "3.11.3" } }, "nbformat": 4, "nbformat_minor": 4 }