Update capabilities overview notebook

notebooks/capabilities_overview.ipynb

@@ -29,7 +29,9 @@
     "\n",
     "1. $\\gamma = 0$: Pixels with intensities greater than $ \\mu_{\\text{foreground}} $ will pass the threshold\n",
     "2. $\\gamma > 0$: More strict than (1). Smaller $ \\gamma \\Longrightarrow $ fewer pixels pass the threshold\n",
-    "3. $\\gamma < 0$: Less strict than (1). Larger $ \\gamma \\Longrightarrow $ more pixels pass the threshold\n"
+    "3. $\\gamma < 0$: Less strict than (1). Larger $ \\gamma \\Longrightarrow $ more pixels pass the threshold\n",
+    "\n",
+    "**Notes**: The cell area script assumes that the brightest regions of your images are the cells. If this isn't the case, consider including a preprocessing step to make them this way."
    ]
   },
   {
@@ -164,6 +166,53 @@
     "2. A collection of classifications, $ \\hat{y}_{p} $ thresholded at a given value (typically $p_i > 0.5$,\n",
     "$$ \\hat{\\mathbf{y}} = (\\hat{y}_{k}, \\hat{y}_{k-1}, ..., \\hat{y}_0) $$"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "58718ffc",
+   "metadata": {},
+   "source": [
+    "## 4. Microvessel formation\n",
+    "\n",
+    "Microvessel formation is analyzed using a two-step process: semantic binary segmentation and topological data analysis.\n",
+    "\n",
+    "### Semantic Binary Segmentation\n",
+    "A trained U-Net Xception-style model segments microvessels from the image background. The model outputs a probabilistic segmentation, indicating the likelihood of each pixel being part of a vessel.\n",
+    "\n",
+    "Training of the model involves:\n",
+    "\n",
+    "1. Data Preparation: Dataset of fifty high-resolution, manually annotated images, split into training, validation, and test sets.\n",
+    "2. Data Augmentation: Application of transformations such as rotation, cropping, flipping, brightness and contrast alteration, noise addition, gaussian blur, and elastic deformations.\n",
+    "3. Model Training: Conducted with a grid search to determine optimal hyperparameters. The model is trained for fifty epochs.\n",
+    "\n",
+    "Inference on a whole image involves two steps:\n",
+    "1. Segment individual, overlapping tiles on the image, with a similar crop size used during training.\n",
+    "2. Uses code from [Smoothly-Blend-Image-Patches](https://github.com/Vooban/Smoothly-Blend-Image-Patches) to blend the overlapping tiles together, producing a realistic, smooth segmentation of the whole image.\n",
+    "\n",
+    "### Topological Data Analysis\n",
+    "After segmentation, the microvessel network is analyzed using the Disperse algorithm to extract a graph representation, referred to as the Morse skeleton. This step involves:\n",
+    "\n",
+    "1. Preprocessing: Images are preprocessed to remove background noise and isolate the microvessel network.\n",
+    "2. Graph Extraction: The Disperse algorithm extracts a graph representation from the segmented images.\n",
+    "3. Network Simplification: Includes removing branches shorter than a threshold and smoothing branch trajectories. At this point, we can extract a color-coded visualization of the network.\n",
+    "4. Persistence Homology: Utilizes persistent homology to characterize the branching structure of the microvessels, resulting in a persistence barcode. The basic metrics we extract are the average branch length and number of branches."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1d28603f",
+   "metadata": {},
+   "source": [
+    "**Notes**:\n",
+    "- Like the cell area script, the microvessel analysis script assumes that the brightest regions of your images are the cells. If this isn't the case, consider including a preprocessing step to make them this way.\n",
+    "- The script requires a trained model. See notebooks/microvessels_segmentation_training. Recommended: Try using the pretrained model first. If the pretrained model does not work well, use an interactive segmentation tool to annotate 50 or so of your images and train a new model."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2c7aaf7d",
+   "metadata": {},
+   "source": []
   }
  ],
  "metadata": {