![\"\"](\"https://www.googleapis.com/download/storage/v1/b/kaggle-forum-message-attachments/o/inbox%2F30604449%2Fe8f165731e4afa093f0cf5a96d59f067%2Fsheetness.png?generation=1763498803894104&alt=media\")
I'm not a serious contender for this, just a hobbyist who wanted to learn how to train a 3-D model end-to-end and submit something for scoring. But while experimenting with preprocessing and visualizing the data, hit on a small idea which was helpful for me and wanted to share in case helpful for others.
\nImagine a thin flat sheet. Voxels on the surface of the sheet should tend to be very similar to their neighboring voxels in 2 dimensions (X and Y) and very different from their neighbors in (at least) one direction on Z dimension (air above the sheet). Even though the papyrus is rolled into a scroll (not to mention crushed and burnt to a crisp), this would still be more true than not true for surface voxels.
\nI vibecoded a way to calculate the \"sheetness\" of a voxel (how well it matches this platonic ideal of a surface voxel's relationship with its neighbors) over a few different scales of \"neighborhood.\"
\n
example function for implementation below -
\n`import numpy as np\nfrom scipy.ndimage import gaussian_filter, sobel
\ndef compute_sheetness(volume, sigma=1.0, eps=1e-6):\n \"\"\"\n volume: 3D numpy array (float32)\n returns: 3D numpy array of sheetness values in [0, 1]\n \"\"\"\n # Gradients\n gx = sobel(volume, axis=0)\n gy = sobel(volume, axis=1)\n gz = sobel(volume, axis=2)
\n# Structure tensor \nJxx = gaussian_filter(gx*gx, sigma)\nJyy = gaussian_filter(gy*gy, sigma)\nJzz = gaussian_filter(gz*gz, sigma)\nJxy = gaussian_filter(gx*gy, sigma)\nJxz = gaussian_filter(gx*gz, sigma)\nJyz = gaussian_filter(gy*gz, sigma)\n\nsheetness = .zeros_like(volume, dtype=.float32)\n\n# Compute each voxel\n idx .ndindex(volume.shape):\n J = .([\n [Jxx[idx], Jxy[idx], Jxz[idx]],\n [Jxy[idx], Jyy[idx], Jyz[idx]],\n [Jxz[idx], Jyz[idx], Jzz[idx]]\n ])\n w = .linalg.eigvalsh(J)\n w1, w2, w3 = sorted(w, =True)\n\n # Simple sheetness metric\n S = (.(w2) / (.(w1) + eps)) * (.(w3) / (.(w2) + eps))\n sheetness[idx] = .clip(S, , )\n\n sheetness\n`
\nI did some testing and including this as a channel produced a small but meaningful improvement in validation Dice. Someone else might be able to take this and do more with it than I'm able to (happy to chat / brainstorm further). I want to see those scrolls unrolled - good luck, all!
", "messages": [ { "id": "3337125", "postDate": "11/18/2025 20:55:52", "content": "I'm not a serious contender for this, just a hobbyist who wanted to learn how to train a 3-D model end-to-end and submit something for scoring. But while experimenting with preprocessing and visualizing the data, hit on a small idea which was helpful for me and wanted to share in case helpful for others.
\nImagine a thin flat sheet. Voxels on the surface of the sheet should tend to be very similar to their neighboring voxels in 2 dimensions (X and Y) and very different from their neighbors in (at least) one direction on Z dimension (air above the sheet). Even though the papyrus is rolled into a scroll (not to mention crushed and burnt to a crisp), this would still be more true than not true for surface voxels.
\nI vibecoded a way to calculate the \"sheetness\" of a voxel (how well it matches this platonic ideal of a surface voxel's relationship with its neighbors) over a few different scales of \"neighborhood.\"
\n
example function for implementation below -
\n`import numpy as np\nfrom scipy.ndimage import gaussian_filter, sobel
\ndef compute_sheetness(volume, sigma=1.0, eps=1e-6):\n \"\"\"\n volume: 3D numpy array (float32)\n returns: 3D numpy array of sheetness values in [0, 1]\n \"\"\"\n # Gradients\n gx = sobel(volume, axis=0)\n gy = sobel(volume, axis=1)\n gz = sobel(volume, axis=2)
\n# Structure tensor \nJxx = gaussian_filter(gx*gx, sigma)\nJyy = gaussian_filter(gy*gy, sigma)\nJzz = gaussian_filter(gz*gz, sigma)\nJxy = gaussian_filter(gx*gy, sigma)\nJxz = gaussian_filter(gx*gz, sigma)\nJyz = gaussian_filter(gy*gz, sigma)\n\nsheetness = .zeros_like(volume, dtype=.float32)\n\n# Compute each voxel\n idx .ndindex(volume.shape):\n J = .([\n [Jxx[idx], Jxy[idx], Jxz[idx]],\n [Jxy[idx], Jyy[idx], Jyz[idx]],\n [Jxz[idx], Jyz[idx], Jzz[idx]]\n ])\n w = .linalg.eigvalsh(J)\n w1, w2, w3 = sorted(w, =True)\n\n # Simple sheetness metric\n S = (.(w2) / (.(w1) + eps)) * (.(w3) / (.(w2) + eps))\n sheetness[idx] = .clip(S, , )\n\n sheetness\n`
\nI did some testing and including this as a channel produced a small but meaningful improvement in validation Dice. Someone else might be able to take this and do more with it than I'm able to (happy to chat / brainstorm further). I want to see those scrolls unrolled - good luck, all!
", "rawMarkdown": "I'm not a serious contender for this, just a hobbyist who wanted to learn how to train a 3-D model end-to-end and submit something for scoring. But while experimenting with preprocessing and visualizing the data, hit on a small idea which was helpful for me and wanted to share in case helpful for others.\n\nImagine a thin flat sheet. Voxels on the surface of the sheet should tend to be very similar to their neighboring voxels in 2 dimensions (X and Y) and very different from their neighbors in (at least) one direction on Z dimension (air above the sheet). Even though the papyrus is rolled into a scroll (not to mention crushed and burnt to a crisp), this would still be more true than not true for surface voxels.\n\nI vibecoded a way to calculate the \"sheetness\" of a voxel (how well it matches this platonic ideal of a surface voxel's relationship with its neighbors) over a few different scales of \"neighborhood.\" \n\n1. compute local gradients\n2. compute the structure tensor over a small window\n3. take the eigenvalues λ1 ≥ λ2 ≥ λ3\n4. a sheet-like structure has λ1 ≫ λ2 and λ2 ≫ λ3\n5. convert that pattern into a normalized “sheetness” value\n\n\n\nexample function for implementation below -\n\n`import numpy as np\nfrom scipy.ndimage import gaussian_filter, sobel\n\ndef compute_sheetness(volume, sigma=1.0, eps=1e-6):\n \"\"\"\n volume: 3D numpy array (float32)\n returns: 3D numpy array of sheetness values in [0, 1]\n \"\"\"\n # Gradients\n gx = sobel(volume, axis=0)\n gy = sobel(volume, axis=1)\n gz = sobel(volume, axis=2)\n\n # Structure tensor components\n Jxx = gaussian_filter(gx*gx, sigma)\n Jyy = gaussian_filter(gy*gy, sigma)\n Jzz = gaussian_filter(gz*gz, sigma)\n Jxy = gaussian_filter(gx*gy, sigma)\n Jxz = gaussian_filter(gx*gz, sigma)\n Jyz = gaussian_filter(gy*gz, sigma)\n\n sheetness = np.zeros_like(volume, dtype=np.float32)\n\n # Compute eigenvalues at each voxel\n for idx in np.ndindex(volume.shape):\n J = np.array([\n [Jxx[idx], Jxy[idx], Jxz[idx]],\n [Jxy[idx], Jyy[idx], Jyz[idx]],\n [Jxz[idx], Jyz[idx], Jzz[idx]]\n ])\n w = np.linalg.eigvalsh(J)\n w1, w2, w3 = sorted(w, reverse=True)\n\n # Simple sheetness metric\n S = (np.abs(w2) / (np.abs(w1) + eps)) * (np.abs(w3) / (np.abs(w2) + eps))\n sheetness[idx] = np.clip(S, 0, 1)\n\n return sheetness\n`\n\nI did some testing and including this as a channel produced a small but meaningful improvement in validation Dice. Someone else might be able to take this and do more with it than I'm able to (happy to chat / brainstorm further). I want to see those scrolls unrolled - good luck, all!", "votes": null }, { "id": "3341186", "postDate": "11/20/2025 03:14:45", "content": "Interesting post! This remembers me of the Frangi filter which is used to enhance vesselness.
", "rawMarkdown": "Interesting post! This remembers me of the Frangi filter which is used to enhance vesselness.", "votes": null }, { "id": "3351430", "postDate": "11/28/2025 12:03:35", "content": "Interesting idea, would it have a strong bias for the axis along you would apply it? Also would work as post-processing filter?
", "rawMarkdown": "Interesting idea, would it have a strong bias for the axis along you would apply it? Also would work as post-processing filter?", "votes": null } ], "comments": [ { "id": 3341186, "author_name": "giorgioangelotti", "author_url": "", "post_date": "11/20/2025 03:14:45", "content": "Interesting post! This remembers me of the Frangi filter which is used to enhance vesselness.
", "votes": null, "replies": [] }, { "id": 3351430, "author_name": "jirkaborovec", "author_url": "", "post_date": "11/28/2025 12:03:35", "content": "Interesting idea, would it have a strong bias for the axis along you would apply it? Also would work as post-processing filter?
", "votes": null, "replies": [] } ], "raw_markdown_by_id": { "3337125": "I'm not a serious contender for this, just a hobbyist who wanted to learn how to train a 3-D model end-to-end and submit something for scoring. But while experimenting with preprocessing and visualizing the data, hit on a small idea which was helpful for me and wanted to share in case helpful for others.\n\nImagine a thin flat sheet. Voxels on the surface of the sheet should tend to be very similar to their neighboring voxels in 2 dimensions (X and Y) and very different from their neighbors in (at least) one direction on Z dimension (air above the sheet). Even though the papyrus is rolled into a scroll (not to mention crushed and burnt to a crisp), this would still be more true than not true for surface voxels.\n\nI vibecoded a way to calculate the \"sheetness\" of a voxel (how well it matches this platonic ideal of a surface voxel's relationship with its neighbors) over a few different scales of \"neighborhood.\" \n\n1. compute local gradients\n2. compute the structure tensor over a small window\n3. take the eigenvalues λ1 ≥ λ2 ≥ λ3\n4. a sheet-like structure has λ1 ≫ λ2 and λ2 ≫ λ3\n5. convert that pattern into a normalized “sheetness” value\n\n\n\nexample function for implementation below -\n\n`import numpy as np\nfrom scipy.ndimage import gaussian_filter, sobel\n\ndef compute_sheetness(volume, sigma=1.0, eps=1e-6):\n \"\"\"\n volume: 3D numpy array (float32)\n returns: 3D numpy array of sheetness values in [0, 1]\n \"\"\"\n # Gradients\n gx = sobel(volume, axis=0)\n gy = sobel(volume, axis=1)\n gz = sobel(volume, axis=2)\n\n # Structure tensor components\n Jxx = gaussian_filter(gx*gx, sigma)\n Jyy = gaussian_filter(gy*gy, sigma)\n Jzz = gaussian_filter(gz*gz, sigma)\n Jxy = gaussian_filter(gx*gy, sigma)\n Jxz = gaussian_filter(gx*gz, sigma)\n Jyz = gaussian_filter(gy*gz, sigma)\n\n sheetness = np.zeros_like(volume, dtype=np.float32)\n\n # Compute eigenvalues at each voxel\n for idx in np.ndindex(volume.shape):\n J = np.array([\n [Jxx[idx], Jxy[idx], Jxz[idx]],\n [Jxy[idx], Jyy[idx], Jyz[idx]],\n [Jxz[idx], Jyz[idx], Jzz[idx]]\n ])\n w = np.linalg.eigvalsh(J)\n w1, w2, w3 = sorted(w, reverse=True)\n\n # Simple sheetness metric\n S = (np.abs(w2) / (np.abs(w1) + eps)) * (np.abs(w3) / (np.abs(w2) + eps))\n sheetness[idx] = np.clip(S, 0, 1)\n\n return sheetness\n`\n\nI did some testing and including this as a channel produced a small but meaningful improvement in validation Dice. Someone else might be able to take this and do more with it than I'm able to (happy to chat / brainstorm further). I want to see those scrolls unrolled - good luck, all!", "3341186": "Interesting post! This remembers me of the Frangi filter which is used to enhance vesselness.", "3351430": "Interesting idea, would it have a strong bias for the axis along you would apply it? Also would work as post-processing filter?" }, "source": "meta" }