This behavior was also mentioned in the 10th-place solution. \nMany thanks to @tom99763 for the very helpful insight.
\nI also asked ChatGPT about the possible reason for this trend.
\nEach application of a 3×3×3 median filter acts as a local majority vote on the predicted volume. As a result, small artifacts that tend to damage topology are gradually removed, such as:
\nTopological metrics are more sensitive than simple voxel-wise overlap measures to structural errors such as changes in connected components, holes, tunnels, and cavities. Therefore, during the first several iterations, median filtering does more than merely smooth the boundary; it effectively removes small noisy structures that disrupt topology, which makes the topological score more likely to improve.
\nIn other words, in the early stage, repeated median filtering works more like topology repair than simple smoothing.
\nWhen the median filter is applied repeatedly, its effect gradually shifts from noise removal to actual deformation of the structure itself. At that point, several factors can cause the topological score to deteriorate.
\n1. True thin structures are broken.\nIf thin tubular, membranous, or bridge-like structures that should remain connected disappear, the number of connected components increases.
\n2. Nearby structures become merged.\nWhen narrow gaps are filled in, components that should remain separate may merge.
\n3. Small true holes or tunnels are filled.\nIf holes or tunnels that actually exist in the ground truth are removed, the topological agreement, for example in terms of Betti numbers, becomes worse.
\n4. Boundary displacement accumulates.\nAlthough the shape change caused by a single filtering step may be small, repeated filtering accumulates these changes and can eventually alter the local topology substantially.
\nIn short, the early iterations improve the result by removing false topology, whereas later iterations degrade it by destroying true topology.
\nThis suggests that the typical scale of the errors in your prediction is on the order of a few voxels.
\nTherefore, this peak is not likely to be accidental. Rather, it suggests that the turning point lies near the boundary between the typical size of prediction errors and the thickness of true fine structures.
\nThese results suggest that the raw model output is somewhat topologically noisy, but can be substantially improved by post-processing.
\nIn particular, the following are likely:
\nConversely, if the topological score improves only after strong median filtering, this may indicate that the model has not learned topology directly during training, and that the topology is being corrected mainly through post-processing.
", "messages": [ { "id": "3418412", "postDate": "03/08/2026 00:41:54", "content": "This behavior was also mentioned in the 10th-place solution. \nMany thanks to @tom99763 for the very helpful insight.
\nI also asked ChatGPT about the possible reason for this trend.
\nEach application of a 3×3×3 median filter acts as a local majority vote on the predicted volume. As a result, small artifacts that tend to damage topology are gradually removed, such as:
\nTopological metrics are more sensitive than simple voxel-wise overlap measures to structural errors such as changes in connected components, holes, tunnels, and cavities. Therefore, during the first several iterations, median filtering does more than merely smooth the boundary; it effectively removes small noisy structures that disrupt topology, which makes the topological score more likely to improve.
\nIn other words, in the early stage, repeated median filtering works more like topology repair than simple smoothing.
\nWhen the median filter is applied repeatedly, its effect gradually shifts from noise removal to actual deformation of the structure itself. At that point, several factors can cause the topological score to deteriorate.
\n1. True thin structures are broken.\nIf thin tubular, membranous, or bridge-like structures that should remain connected disappear, the number of connected components increases.
\n2. Nearby structures become merged.\nWhen narrow gaps are filled in, components that should remain separate may merge.
\n3. Small true holes or tunnels are filled.\nIf holes or tunnels that actually exist in the ground truth are removed, the topological agreement, for example in terms of Betti numbers, becomes worse.
\n4. Boundary displacement accumulates.\nAlthough the shape change caused by a single filtering step may be small, repeated filtering accumulates these changes and can eventually alter the local topology substantially.
\nIn short, the early iterations improve the result by removing false topology, whereas later iterations degrade it by destroying true topology.
\nThis suggests that the typical scale of the errors in your prediction is on the order of a few voxels.
\nTherefore, this peak is not likely to be accidental. Rather, it suggests that the turning point lies near the boundary between the typical size of prediction errors and the thickness of true fine structures.
\nThese results suggest that the raw model output is somewhat topologically noisy, but can be substantially improved by post-processing.
\nIn particular, the following are likely:
\nConversely, if the topological score improves only after strong median filtering, this may indicate that the model has not learned topology directly during training, and that the topology is being corrected mainly through post-processing.
", "rawMarkdown": "# introduction\nThis behavior was also mentioned in the [10th-place solution](https://www.kaggle.com/competitions/vesuvius-challenge-surface-detection/writeups/10th-place-solution#3416512). \nMany thanks to @tom99763 for the very helpful insight.\n\nI also asked ChatGPT about the possible reason for this trend.\n\n\n## Why does the score improve up to 6–7 iterations?\n\nEach application of a 3×3×3 median filter acts as a local majority vote on the predicted volume. As a result, small artifacts that tend to damage topology are gradually removed, such as:\n\n* isolated noisy voxels,\n* thin spurious branches with a width of 1–2 voxels,\n* small holes,\n* jagged surface irregularities,\n* and accidentally connected thin bridges.\n\nTopological metrics are more sensitive than simple voxel-wise overlap measures to structural errors such as changes in connected components, holes, tunnels, and cavities. Therefore, during the first several iterations, median filtering does more than merely smooth the boundary; it effectively removes small noisy structures that disrupt topology, which makes the topological score more likely to improve.\n\nIn other words, in the early stage, repeated median filtering works more like **topology repair** than simple smoothing.\n\n## Why does the score decrease around the 8th iteration?\n\nWhen the median filter is applied repeatedly, its effect gradually shifts from noise removal to actual deformation of the structure itself. At that point, several factors can cause the topological score to deteriorate.\n\n**1. True thin structures are broken.**\nIf thin tubular, membranous, or bridge-like structures that should remain connected disappear, the number of connected components increases.\n\n**2. Nearby structures become merged.**\nWhen narrow gaps are filled in, components that should remain separate may merge.\n\n**3. Small true holes or tunnels are filled.**\nIf holes or tunnels that actually exist in the ground truth are removed, the topological agreement, for example in terms of Betti numbers, becomes worse.\n\n**4. Boundary displacement accumulates.**\nAlthough the shape change caused by a single filtering step may be small, repeated filtering accumulates these changes and can eventually alter the local topology substantially.\n\nIn short, the early iterations improve the result by removing **false topology**, whereas later iterations degrade it by destroying **true topology**.\n\n## What does the optimum around 6–7 iterations imply?\n\nThis suggests that the typical scale of the errors in your prediction is on the order of a few voxels.\n\n* After 1–3 iterations, noise removal is still insufficient.\n* Around 6–7 iterations, most false topological structures have been removed.\n* After the 8th iteration, destruction of true structures becomes noticeable.\n\nTherefore, this peak is not likely to be accidental. Rather, it suggests that the turning point lies near the boundary between the typical size of prediction errors and the thickness of true fine structures.\n\n## What does this phenomenon tell us?\n\nThese results suggest that the raw model output is somewhat **topologically noisy**, but can be substantially improved by post-processing.\n\nIn particular, the following are likely:\n\n* many thin false-positive fragments or small isolated components are present,\n* small defects or holes exist near the boundary,\n* topological inconsistency is a major source of error,\n* and the coarse location is correct, but the fine-scale structure is still rough.\n\nConversely, if the topological score improves only after strong median filtering, this may indicate that the model has not learned topology directly during training, and that the topology is being corrected mainly through post-processing.", "votes": null }, { "id": "3418440", "postDate": "03/08/2026 03:16:30", "content": "Before the deadline, I experimented with a self-supervised loss function (not in our solution) that performs a closing operation on the predictions and compares them with the original outputs, then penalizing the difference between the two. But I believe a median filter would be more suitable, which would penalize the model more appropriately and encourage better performance on the topology metric. Maybe we don't need strong post processing if training model with this kind of signals.
\ndef iterative_hole_loss_3d(M_prob, gt_mask, kernel_sizes=(3,5,7), n_iter=5):\n loss = 0.0\n valid_mask = gt_mask != 2\n M_prob = M_prob * valid_mask\n gt_mask = gt_mask * valid_mask\n\n for _ in range(n_iter):\n for k in kernel_sizes:\n pad = k // 2\n dilated = F.max_pool3d(M_prob, kernel_size=k, stride=1, padding=pad)\n closed = -F.max_pool3d(-dilated, kernel_size=k, stride=1, padding=pad)\n hole_map = (closed - M_prob).clamp(min=0)\n loss += (hole_map * gt_mask).mean()\n M_prob = torch.max(M_prob, closed)\n return loss\nBefore the deadline, I experimented with a self-supervised loss function (not in our solution) that performs a closing operation on the predictions and compares them with the original outputs, then penalizing the difference between the two. But I believe a median filter would be more suitable, which would penalize the model more appropriately and encourage better performance on the topology metric. Maybe we don't need strong post processing if training model with this kind of signals.
\ndef iterative_hole_loss_3d(M_prob, gt_mask, kernel_sizes=(3,5,7), n_iter=5):\n loss = 0.0\n valid_mask = gt_mask != 2\n M_prob = M_prob * valid_mask\n gt_mask = gt_mask * valid_mask\n\n for _ in range(n_iter):\n for k in kernel_sizes:\n pad = k // 2\n dilated = F.max_pool3d(M_prob, kernel_size=k, stride=1, padding=pad)\n closed = -F.max_pool3d(-dilated, kernel_size=k, stride=1, padding=pad)\n hole_map = (closed - M_prob).clamp(min=0)\n loss += (hole_map * gt_mask).mean()\n M_prob = torch.max(M_prob, closed)\n return loss\n