{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Basics of the PIV algorithms\n", "\n", "Using open source PIV software, OpenPIV (http://www.openpiv.net) written with the great help of Python, Numpy, Scipy (http://www.scipy.org) and runs online thanks to the great MyBinder project." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What is it about? Particle Image Velocimetry (PIV)\n", "\n", "From Wikipedia: \"Particle image velocimetry (PIV) is an optical method of flow visualization used in education and research. It is used to obtain instantaneous velocity measurements and related properties in fluids. The fluid is seeded with tracer particles which, for sufficiently small particles, are assumed to faithfully follow the flow dynamics (the degree to which the particles faithfully follow the flow is represented by the Stokes number). The fluid with entrained particles is illuminated so that particles are visible. The motion of the seeding particles is used to calculate speed and direction (the velocity field) of the flow being studied.\" Read more at http://en.wikipedia.org/wiki/Particle_image_velocimetry.\n", "\n", "Particle Image Velocimetry (PIV) is a non-intrusive state-of-the-art technique for flow measurements (e.g.: Raffel et al., 2007, Adrian, 1991). The PIV technique is based on image recording of the illuminated flow field using seeding particles. The technique is based on illuminating the particles in a plane by forming a coherent light sheet. The light scattered by the particles is recorded on a sequence of image frames. The displacement of the particle images between two consecutive light pulses is determined through evaluation of the PIV recordings and by applying a spatial cross-correlation function as implemented by the OpenPIV resulting with a two dimensional two component velocity field.\n", "\n", "In practice, small tracer particles, common sized are in the order of 10-100 microns, are introduced to the flow. The flow is illuminated twice by means of a laser light sheet forming a plane where the camera is focused on. The time delay between the pulses depends on the mean velocity and the image magnification. It is assumed that the tracer particles follow the local flow velocity between the two consecutive illuminations. The light scattered from the tracer particles is imaged via an optical lens on a digital camera. \n", "The images, acquired as pairs correspond to the two laser pulses, are than correlated using a cross-correlation function and image processing tools in order to provide the velocity field.\n", "\n", "The effectiveness of the measurement results strongly depends on a large number of parameters such as particles concentration, size distribution and shape, illumination source, recording device, and synchronization between the illumination, acquisition and recording systems (Huang et al., 1997). An appropriate choice of the different parameters of the cross correlation analysis (e.g., interrogation area, time between pulses, scaling) will influence the results accuracy. Read more about PIV in the following chapters: Gurka and Kit, in Handbook of Environmental Fluid Mechanics, CRC Press, 2014 http://www.crcnetbase.com/doi/abs/10.1201/b13691-39 or Taylor, Gurka and Liberzon \"Particle Image Velocimetry for Biological Mechanics\" in the Handbook of Imaging in Biological Mechanics, CRC Press, 2015, http://www.crcpress.com/product/isbn/9781466588134.\n", "\n", "\n", "### Open source software to learn the basics\n", "\n", "In principle velocimetry is a method to find out the velocity field of the moving fluid. \"Particle\" image velocimetry is the way to get velocity field from images of small particles, called tracers. The basic principle is to use two images of the same particles with a small time delay between them. For that purpose, typically two laser shots are created and two images are taken.\n", "\n", "This tutorial will follow the most simple analysis path from the two images to the velocity field and some post-analysis. We will use one of many open source packages, the open source particle image velocimetry http://www.openpiv.net" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# import the standard numerical and plotting packages\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from skimage.io import imread" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have downloaded some sample images from PIV challenge, \n", "see http://www.pivchallenge.org/pub/#b or another standard PIV images project: http://www.piv.jp/down/image05e.html" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# load the images\n", "a = imread(\"../images/B005_1.tif\")\n", "b = imread(\"../images/B005_2.tif\")\n", "\n", "fig, axs = plt.subplots(1, 2, figsize=(9, 4))\n", "axs[0].imshow(a, cmap=plt.cm.gray)\n", "axs[1].imshow(b, cmap=plt.cm.gray)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The two images show the positions of the particles at two different times. We can analyze small regions of interest, called interrogation windows. Typically we can start with a size of 32 x 32 pixels or smaller. Until recently, the fast algorithms used powers of 2, so the historical sizes are always powers of 2: 8, 16, 32, 64, 128, ...\n", "\n", "Let's take the first top left windows from each image." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": "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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "win_size = 32\n", "\n", "a_win = a[:win_size, :win_size].copy()\n", "b_win = b[:win_size, :win_size].copy()\n", "\n", "fig, axs = plt.subplots(1, 2, figsize=(9, 4))\n", "axs[0].imshow(a_win, cmap=plt.cm.gray)\n", "axs[1].imshow(b_win, cmap=plt.cm.gray)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that the bright pixels moved between the two frames. We can find out the distance that all the particles moved between frame A and frame B using the principles of least squares or correlations, but let's first try to get it manually.\n", "\n", "If we shift the window IA by some pixels to the right and subtract from IB the shifted IA, we shall see how good the shift predicts the real displacement between the two." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.imshow(b_win - a_win, cmap=plt.cm.gray)\n", "plt.title(\"Without shift\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.imshow(b_win - np.roll(a_win, (1, 0), axis=(0, 1)), cmap=plt.cm.gray)\n", "plt.title(\"Difference when A has been shifted by 1 pixel\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's try to find the best shift algorithmically: shift and calculated the sum of squared differences the minimum is the best shift" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "def match_template(img, template, maxroll=8):\n", " best_dist = np.inf\n", " best_shift = (-1, -1)\n", " for y in range(maxroll):\n", " for x in range(maxroll):\n", " # calculate Euclidean distance\n", " dist = np.sqrt(np.sum((img - np.roll(template, (y, x), axis=(0, 1))) ** 2))\n", " if dist < best_dist:\n", " best_dist = dist\n", " best_shift = (y, x)\n", " return (best_dist, best_shift)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0, (2, 0))" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# let's test that it works by manually rolling (shifting circurlarly) the same\n", "# image\n", "match_template(np.roll(a_win, (2, 0), axis=(0, 1)), a_win)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "best_dist=170.43180454363556\n", "best_shift=(0, 1)\n" ] } ], "source": [ "# indeed, when we find the correct shift, we got zero distance. it's not so in real images:\n", "best_dist, best_shift = match_template(b_win, a_win)\n", "print(f\"{best_dist=}\")\n", "print(f\"{best_shift=}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can draw this as a vector of velocity\n", "\n", "$$\n", " u = \\frac{\\Delta x \\text{ pixels}}{\\Delta t} ,\\qquad v = \\frac{\\Delta y \\text{ pixels}}{\\Delta t}\n", "$$\n", "\n", "where $\\Delta t$ is the time interval (delay) between the two images (or two laser pulses)." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(1, 2, figsize=(9, 4))\n", "axs[0].imshow(np.roll(a_win, best_shift, axis=(0, 1)), cmap='gray')\n", "axs[1].imshow(b_win, cmap='gray')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Well, maybe it's not the best match, but it is already better than nothing.\n", "\n", "The problem now is that manually shifting each image and repeating the loop many times is impractical. However, based on the same principle of finding the right shift, one can get by using a different template matching principle, based on the property called cross-correlation (cross because we use two different images). In short this is an efficient computational algorithm to find out the right shift. You can see more details here: http://paulbourke.net/miscellaneous/correlate/." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Size of the correlation map: 63 x 63\n" ] } ], "source": [ "from scipy.signal import correlate\n", "\n", "cross_corr = correlate(b_win - b_win.mean(), a_win - a_win.mean(), method=\"fft\")\n", "# Note that it's approximately twice as large than the original windows, as we\n", "# can shift a_win by a maximum of it's size - 1 horizontally and vertically\n", "# while still maintaining some overlap between the two windows.\n", "print(\"Size of the correlation map: %d x %d\" % cross_corr.shape)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# let's see what the cross-correlation looks like\n", "from mpl_toolkits.mplot3d import Axes3D\n", "\n", "fig = plt.figure()\n", "ax = fig.add_subplot(projection=\"3d\")\n", "Y, X = np.meshgrid(np.arange(cross_corr.shape[0]), np.arange(cross_corr.shape[1]))\n", "\n", "ax.plot_surface(Y, X, cross_corr, cmap='jet', linewidth=0.2) # type: ignore\n", "plt.title(\"Correlation map — peak is the most probable shift\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "y=30, x=32\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# let's see the same correlation map, from above\n", "plt.imshow(cross_corr, cmap=plt.cm.gray)\n", "\n", "y, x = np.unravel_index(cross_corr.argmax(), cross_corr.shape)\n", "print(f\"{y=}, {x=}\")\n", "\n", "plt.plot(x, y, \"ro\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The image of the correlation map shows the same result that we got manually looping. We need to shift `a_win` to give the best possible correlation between the two windows. If there best correlation would come from no shift, the result would be `(31, 31)`—the center of symmetry." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "dy=-1, dx=1\n" ] } ], "source": [ "dy, dx = y - 31, x - 31\n", "print(f\"{dy=}, {dx=}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can get the first velocity field by repeating this analysis for all small windows. Let's take 32 x 32 pixels windows from each image and do the loop:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "def vel_field(curr_frame, next_frame, win_size):\n", " ys = np.arange(0, curr_frame.shape[0], win_size)\n", " xs = np.arange(0, curr_frame.shape[1], win_size)\n", " dys = np.zeros((len(ys), len(xs)))\n", " dxs = np.zeros((len(ys), len(xs)))\n", " for iy, y in enumerate(ys):\n", " for ix, x in enumerate(xs):\n", " int_win = curr_frame[y : y + win_size, x : x + win_size]\n", " search_win = next_frame[y : y + win_size, x : x + win_size]\n", " cross_corr = correlate(\n", " search_win - search_win.mean(), int_win - int_win.mean(), method=\"fft\"\n", " )\n", " dys[iy, ix], dxs[iy, ix] = (\n", " np.unravel_index(np.argmax(cross_corr), cross_corr.shape)\n", " - np.array([win_size, win_size])\n", " + 1\n", " )\n", " # draw velocity vectors from the center of each window\n", " ys = ys + win_size / 2\n", " xs = xs + win_size / 2\n", " return xs, ys, dxs, dys" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "xs, ys, dxs, dys = vel_field(a, b, 32)\n", "norm_drs = np.sqrt(dxs ** 2 + dys ** 2)\n", "\n", "fig, ax = plt.subplots(figsize=(6, 6))\n", "# we need these flips on y since quiver uses a bottom-left origin, while our\n", "# arrays use a top-right origin\n", "ax.quiver(\n", " xs,\n", " ys[::-1],\n", " dxs,\n", " -dys,\n", " norm_drs,\n", " cmap=\"plasma\",\n", " angles=\"xy\",\n", " scale_units=\"xy\",\n", " scale=0.25,\n", ")\n", "ax.set_aspect(\"equal\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you've followed along this far, great! Now you understand the basics.\n", "\n", "We can also try out a variant of this that uses a search window larger than the interrogation window instead of relying on zero-padding. By avoiding using zero-padding around the search window, movement detection should theoretically be a bit better, assuming that the window sizes are chosen well." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "def vel_field_asymmetric_wins(\n", " curr_frame, next_frame, half_int_win_size, half_search_win_size\n", "):\n", " ys = np.arange(half_int_win_size[0], curr_frame.shape[0], 2 * half_int_win_size[0])\n", " xs = np.arange(half_int_win_size[1], curr_frame.shape[1], 2 * half_int_win_size[1])\n", " dys = np.zeros((len(ys), len(xs)))\n", " dxs = np.zeros((len(ys), len(xs)))\n", " for iy, y in enumerate(ys):\n", " for ix, x in enumerate(xs):\n", " int_win = curr_frame[\n", " y - half_int_win_size[0] : y + half_int_win_size[0],\n", " x - half_int_win_size[1] : x + half_int_win_size[1],\n", " ]\n", " search_win_y_min = y - half_search_win_size[0]\n", " search_win_y_max = y + half_search_win_size[0]\n", " search_win_x_min = x - half_search_win_size[1]\n", " search_win_x_max = x + half_search_win_size[1]\n", " truncated_search_win = next_frame[\n", " max(0, search_win_y_min) : min(b.shape[0], search_win_y_max),\n", " max(0, search_win_x_min) : min(b.shape[1], search_win_x_max),\n", " ]\n", " cross_corr = correlate(\n", " truncated_search_win - np.mean(truncated_search_win),\n", " int_win - np.mean(int_win),\n", " mode=\"valid\",\n", " method=\"fft\",\n", " )\n", " dy, dx = np.unravel_index(np.argmax(cross_corr), cross_corr.shape)\n", " # if the top of the search window got truncated, shift the origin\n", " # up to the top edge of the (non-truncated) search window\n", " if search_win_y_min < 0:\n", " dy += -search_win_y_min\n", " # if the left of the search window got truncated, shift the origin\n", " # over to the left edge of the (non-truncated) search window\n", " if search_win_x_min < 0:\n", " dx += -search_win_x_min\n", " # shift origin to the center of the search window\n", " dy -= half_search_win_size[0] - half_int_win_size[0]\n", " dx -= half_search_win_size[1] - half_int_win_size[1]\n", " dys[iy, ix] = dy\n", " dxs[iy, ix] = dx\n", " return xs, ys, dxs, dys" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "int_win_size=array([32, 32])\n", "search_win_size=array([64, 64])\n", "max velocity that can be detected with these window sizes: [16 16]\n" ] } ], "source": [ "int_win_size = np.array([32, 32])\n", "print(f\"{int_win_size=}\")\n", "assert np.all(np.array(a.shape) % int_win_size == 0)\n", "assert np.all(int_win_size % 2 == 0)\n", "half_int_win_size = int_win_size // 2\n", "\n", "search_win_size = int_win_size * 2\n", "print(f\"{search_win_size=}\")\n", "assert np.all(search_win_size % 2 == 0)\n", "half_search_win_size = search_win_size // 2\n", "assert np.all(search_win_size > int_win_size)\n", "print(\n", " \"max velocity that can be detected with these window sizes: \"\n", " + f\"{half_search_win_size - half_int_win_size}\"\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Making the search window larger compared to the interrogation window would allow for larger velocities to be detected." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "xs_asym, ys_asym, dxs_asym, dys_asym = vel_field_asymmetric_wins(\n", " a, b, half_int_win_size, half_search_win_size\n", ")\n", "norm_drs_asym = np.sqrt(dxs_asym ** 2 + dys_asym ** 2)\n", "\n", "fig, axs = plt.subplots(1, 2, figsize=(12, 6))\n", "axs[0].quiver(\n", " xs,\n", " ys[::-1],\n", " dxs,\n", " -dys,\n", " norm_drs,\n", " cmap=\"plasma\",\n", " angles=\"xy\",\n", " scale_units=\"xy\",\n", " scale=0.25,\n", ")\n", "axs[1].quiver(\n", " xs_asym,\n", " ys_asym[::-1],\n", " dxs_asym,\n", " -dys_asym,\n", " norm_drs_asym,\n", " cmap=\"plasma\",\n", " angles=\"xy\",\n", " scale_units=\"xy\",\n", " scale=0.25,\n", ")\n", "axs[0].set_title(\n", " f\"{win_size} x {win_size} int. win. + \"\n", " f\"{win_size} x {win_size} 0-padded search win.\"\n", ")\n", "axs[1].set_title(\n", " f\"{int_win_size[0]} x {int_win_size[1]} int. win. + \"\n", " f\"{search_win_size[0]} x {search_win_size[0]} unpadded search win.\"\n", ")\n", "ax.set_aspect(\"equal\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Additional examples" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Run this Jupyter notebook without installation:\n", "\n", "Now you can take our online Jupyter notebook and process any pairs of images yourself, on the cloud, http://github.com/openpiv/openpiv-python-example. \n", "\n", "\n", "Download the OpenPIV and try it yourself: https://github.com/OpenPIV\n", "\n", "\n", "\n", "### See multiple examples\n", "\n", "Including how to work with movies, different series of files, all kind of tips and tricks in our repository of Jupyter notebooks in the https://github.com/OpenPIV/openpiv-python-examples\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.8.12 ('echopiv')", "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": "3.8.12" }, "metadata": { "interpreter": { "hash": "41f5f0438dc4e3a82bed3f79924308eb45f1e47bd23729f3ef4bcb36970735b2" } }, "name": "", "vscode": { "interpreter": { "hash": "f83b0c3a4910470a1212112b1707d582432916ed4ba8aec962241a050aa18fae" } } }, "nbformat": 4, "nbformat_minor": 4 }