From 74e4221d4165444b7b55640b72a7eddd5c349567 Mon Sep 17 00:00:00 2001 From: Monica J Emerson <monj@dtu.dk> Date: Mon, 8 Feb 2021 10:10:59 +0100 Subject: [PATCH] Latest updates to ST --- .../StructureTensor2D_exercise.ipynb | 34 +++++++++-------- ...StructureTensor2D_exercise_solutions.ipynb | 36 +++++++++--------- Structure Tensor/structuretensor.png | Bin 454058 -> 453682 bytes 3 files changed, 37 insertions(+), 33 deletions(-) diff --git a/Structure Tensor/StructureTensor2D_exercise.ipynb b/Structure Tensor/StructureTensor2D_exercise.ipynb index ac55066..c885454 100644 --- a/Structure Tensor/StructureTensor2D_exercise.ipynb +++ b/Structure Tensor/StructureTensor2D_exercise.ipynb @@ -12,7 +12,9 @@ "- Visualise the output of the structure tensor. \n", "- Tune the input parameters of the structure tensor.\n", "\n", - "In some parts of code you will be asked to give user input, write in between the comments ###USER INPUT and ###END OF USER INPUT." + "In some parts of code you will be asked to give user input, write in between the comments ###USER INPUT and ###END OF USER INPUT. \n", + "\n", + "Run the script cell by cell by placing the cursor inside the cell and pressing Run or Shift+Return." ] }, { @@ -26,7 +28,7 @@ "- [numpy](www.numpy.org) is the basic package for scientific computing with Python.\n", "- [skimage](https://scikit-image.org/) is one of the top image processing libraries in Python. Today, we will use its intput/output module io to read in the images, and the transform module to...\n", "- [matplotlib](http://matplotlib.org) is the most commonly used package for plotting in Python.\n", - "- [st2d](https://lab.compute.dtu.dk/QIM/structure-tensor) contains the structure tensor implementation for 2D images by V.A. Dahl (vand@dtu.dk).\n", + "- [st2d](https://lab.compute.dtu.dk/QIM/structure-tensor) contains the structure tensor implementation for 2D images by Vedrana A. Dahl (vand@dtu.dk).\n", "- *utilsST* is a Python file containing helper functions for this exercise" ] }, @@ -89,10 +91,10 @@ "source": [ "## Structure tensor functions \n", "The main functionality of the structure tensor is implemented in the two functions below: \n", - "- Compute the Structure Tensor for 2D Data\n", - " S = st2d.structure_tensor(img, sigma, rho)\n", - "- Compute the eigen values for the principal orientations of your structure, and the dominant orientation vector ($vec[0]\\hat{x}+vec[1]\\hat{y}$).\n", - " val,vec = st2d.eig_special(S)\n", + "- Compute the Structure Tensor for 2D Data <br>\n", + "`S = st2d.structure_tensor(img, sigma, rho)`\n", + "- Compute the eigen values for the principal orientations of your structure, and the dominant orientation vector (**vec** $= \\text{vec}[0]\\hat{x}+\\text{vec}[1]\\hat{y}$). <br>\n", + "`val,vec = st2d.eig_special(S)`\n", "\n", "<img src=\"structuretensor.png\" width=\"100%\">\n", "\n", @@ -118,11 +120,11 @@ "\n", "This first part will guide you through the implementation of your first analysis using structure tensor. You are going to write code to:\n", "1. Compute the structure tensor matrix and the orientation vectors.\n", - " Use the st2d functions described above\n", - "2. Calculate the orientation angles and reshape back to an image.\n", - " - Compute the angles[°] from the dominant orientations (vec). \n", - " Use np.pi and one of the trigonometric functions: np.arccos(), np.arcsin() or np.arctan2(). Look at the figure above.\n", - " - Reshape your output with output.reshape(img.shape)" + "> Use the `st2d` functions described above\n", + "2. Calculate the orientation angles and reshape angles back to an image.\n", + "> - Compute the angles[°] from the components of the dominant orientation (__vec__). <br>\n", + ">> Use np.pi and one of the trigonometric functions: `np.arccos()`, `np.arcsin()` or `np.arctan2()`. Look at the figure above.\n", + "> - Reshape your output with `output.reshape(img.shape)`" ] }, { @@ -167,7 +169,7 @@ "# Compute the structure tensor\n", "### USER INPUT HERE ### (≈ 2 lines of code)\n", "S = # compute structure tensor matrix S\n", - "val, vec = # compute dominant orientation vector (vec) and principal orientation weights (val)\n", + "val,vec = # compute dominant orientation vector (vec) and principal orientation weights (val)\n", "### END USER INPUT ### \n", "\n", "print(f'Structure tensor information is carried in a {S.shape} array.')\n", @@ -254,7 +256,7 @@ "\n", "The first output of the structure tensor (`val`) indicates how fast the intensities change around a pixel in the two principal directions. Along the first principal direction of a line, the intensities will not change, and `val[0]` will be very small. Along the second principal direction, the intensities will change fast so `val[1]` will be large. For a circle, both values will be equal.\n", "\n", - "The ratio between the components of `val` will give us the **degree of structural isotropy**. To obtain a more realistic idea of the orientations of our material, we will weigh the dominant orientation by the anisotropy. \n", + "The ratio between the components of `val` will give us the degree of structural **isotropy**. To obtain a more realistic idea of the orientations of our material, we will weigh the dominant orientation by the **anisotropy**. In this way, we will keep the orientation angle for highly anisotropic structures (anisotropy of a line = 1), downweigh the angle as it becomes less reliable, and not show it at all for a circular structure (anisotropy of a circle = 0).\n", "\n", "Can you find the formula for the anisotropy, given `val[0]` and `val[1]`?" ] @@ -330,7 +332,7 @@ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "45259d108df64bb7aff024a2667709d9", + "model_id": "9348b6dffa2740ecb647efda73075c06", "version_major": 2, "version_minor": 0 }, @@ -382,7 +384,7 @@ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "79f20b944a4b4e69af35b30465c329ef", + "model_id": "c63d444ec078465c9b9e0226c3149043", "version_major": 2, "version_minor": 0 }, @@ -430,7 +432,7 @@ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "c857083d2b2644fb87753690d6e57337", + "model_id": "60c02737b9554f67915bde19d5a431df", "version_major": 2, "version_minor": 0 }, diff --git a/Structure Tensor/StructureTensor2D_exercise_solutions.ipynb b/Structure Tensor/StructureTensor2D_exercise_solutions.ipynb index 5846a29..a5eb95f 100644 --- a/Structure Tensor/StructureTensor2D_exercise_solutions.ipynb +++ b/Structure Tensor/StructureTensor2D_exercise_solutions.ipynb @@ -12,7 +12,9 @@ "- Visualise the output of the structure tensor. \n", "- Tune the input parameters of the structure tensor.\n", "\n", - "In some parts of code you will be asked to give user input, write in between the comments ###USER INPUT and ###END OF USER INPUT." + "In some parts of code you will be asked to give user input, write in between the comments ###USER INPUT and ###END OF USER INPUT. \n", + "\n", + "Run the script cell by cell by placing the cursor inside the cell and pressing Run or Shift+Return." ] }, { @@ -26,7 +28,7 @@ "- [numpy](www.numpy.org) is the basic package for scientific computing with Python.\n", "- [skimage](https://scikit-image.org/) is one of the top image processing libraries in Python. Today, we will use its intput/output module io to read in the images, and the transform module to...\n", "- [matplotlib](http://matplotlib.org) is the most commonly used package for plotting in Python.\n", - "- [st2d](https://lab.compute.dtu.dk/QIM/structure-tensor) contains the structure tensor implementation for 2D images by V.A. Dahl (vand@dtu.dk).\n", + "- [st2d](https://lab.compute.dtu.dk/QIM/structure-tensor) contains the structure tensor implementation for 2D images by Vedrana A. Dahl (vand@dtu.dk).\n", "- *utilsST* is a Python file containing helper functions for this exercise" ] }, @@ -89,10 +91,10 @@ "source": [ "## Structure tensor functions \n", "The main functionality of the structure tensor is implemented in the two functions below: \n", - "- Compute the Structure Tensor for 2D Data\n", - " S = st2d.structure_tensor(img, sigma, rho)\n", - "- Compute the eigen values for the principal orientations of your structure, and the dominant orientation vector ($vec[0]\\hat{x}+vec[1]\\hat{y}$).\n", - " val,vec = st2d.eig_special(S)\n", + "- Compute the Structure Tensor for 2D Data <br>\n", + "`S = st2d.structure_tensor(img, sigma, rho)`\n", + "- Compute the eigen values for the principal orientations of your structure, and the dominant orientation vector (**vec** $= \\text{vec}[0]\\hat{x}+\\text{vec}[1]\\hat{y}$). <br>\n", + "`val,vec = st2d.eig_special(S)`\n", "\n", "<img src=\"structuretensor.png\" width=\"100%\">\n", "\n", @@ -118,11 +120,11 @@ "\n", "This first part will guide you through the implementation of your first analysis using structure tensor. You are going to write code to:\n", "1. Compute the structure tensor matrix and the orientation vectors.\n", - " Use the st2d functions described above\n", - "2. Calculate the orientation angles and reshape back to an image.\n", - " - Compute the angles[°] from the dominant orientations (vec). \n", - " Use np.pi and one of the trigonometric functions: np.arccos(), np.arcsin() or np.arctan2(). Look at the figure above.\n", - " - Reshape your output with output.reshape(img.shape)" + "> Use the `st2d` functions described above\n", + "2. Calculate the orientation angles and reshape angles back to an image.\n", + "> - Compute the angles[°] from the components of the dominant orientation (__vec__). <br>\n", + ">> Use np.pi and one of the trigonometric functions: `np.arccos()`, `np.arcsin()` or `np.arctan2()`. Look at the figure above.\n", + "> - Reshape your output with `output.reshape(img.shape)`" ] }, { @@ -166,8 +168,8 @@ "\n", "# Compute the structure tensor\n", "### USER INPUT HERE ### (≈ 2 lines of code)\n", - "S = st2d.structure_tensor(image, sigma, rho) # compute structure tensor matrix S\n", - "val, vec = st2d.eig_special(S) # compute dominant orientation vector (vec) and principal orientation weights (val)\n", + "S = st2d.structure_tensor(image, sigma, rho) # compute structure tensor matrix S\n", + "val, vec = st2d.eig_special(S) # compute dominant orientation vector (vec) and principal orientation weights (val)\n", "### END USER INPUT ### \n", "\n", "print(f'Structure tensor information is carried in a {S.shape} array.')\n", @@ -254,7 +256,7 @@ "\n", "The first output of the structure tensor (`val`) indicates how fast the intensities change around a pixel in the two principal directions. Along the first principal direction of a line, the intensities will not change, and `val[0]` will be very small. Along the second principal direction, the intensities will change fast so `val[1]` will be large. For a circle, both values will be equal.\n", "\n", - "The ratio between the components of `val` will give us the **degree of structural isotropy**. To obtain a more realistic idea of the orientations of our material, we will weigh the dominant orientation by the anisotropy. \n", + "The ratio between the components of `val` will give us the degree of structural **isotropy**. To obtain a more realistic idea of the orientations of our material, we will weigh the dominant orientation by the **anisotropy**. In this way, we will keep the orientation angle for highly anisotropic structures (anisotropy of a line = 1), downweigh the angle as it becomes less reliable, and not show it at all for a circular structure (anisotropy of a circle = 0).\n", "\n", "Can you find the formula for the anisotropy, given `val[0]` and `val[1]`?" ] @@ -330,7 +332,7 @@ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "45259d108df64bb7aff024a2667709d9", + "model_id": "9348b6dffa2740ecb647efda73075c06", "version_major": 2, "version_minor": 0 }, @@ -382,7 +384,7 @@ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "79f20b944a4b4e69af35b30465c329ef", + "model_id": "c63d444ec078465c9b9e0226c3149043", "version_major": 2, "version_minor": 0 }, @@ -430,7 +432,7 @@ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "c857083d2b2644fb87753690d6e57337", + "model_id": "60c02737b9554f67915bde19d5a431df", "version_major": 2, "version_minor": 0 }, diff --git 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