Elongated structures #152
Elongated structures #152
Conversation
Morgane-des-Ligneris
requested review from
pierreelliott,
nathanpainchaud,
ThierryJudge,
PierreRouge,
JulietteMoreau,
maylis-j,
robintrmbtt and
CaroleFri
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Interesting article ! Could be a little bit more synthetic but I'm sure your presentation will be.
I'm now wondering what is the fundamental difference between distance-heatmaps as presented here and level sets, I feel like level sets already include a distance to the point of interest ? As here the heatmaps are built based on level-sets.
Great review
| &= \int_C w(x - y) dy | ||
| \end{align*}$$ | ||
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| To be faster than while using a numerical integration and to generalize the description, $$H(x)$$ is simlified. They make the assumption that $$w(x)$$ is symetric $$w(x) = w(y)$$ for all $$\vert \vert x \vert \vert \underset{2}{} = \vert \vert y \vert \vert \underset{2}{}$$. |
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than when using a numerical integration
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I think the phrasing can lead to some confusion (I had the same initial reaction as Nicolas), so I would suggest maybe something like (+ a fix to a typo in simplified and symmetric 😉):
| To be faster than while using a numerical integration and to generalize the description, $$H(x)$$ is simlified. They make the assumption that $$w(x)$$ is symetric $$w(x) = w(y)$$ for all $$\vert \vert x \vert \vert \underset{2}{} = \vert \vert y \vert \vert \underset{2}{}$$. | |
| $$H(x)$$ is simplified to i) be faster than when using a numerical integration, and ii) to generalize the description. They make the assumption that $$w(x)$$ is symmetric $$w(x) = w(y)$$ for all $$\vert \vert x \vert \vert \underset{2}{} = \vert \vert y \vert \vert \underset{2}{}$$. |
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| If $$C$$ is an infinite straight line, the evaluation of the integral simplifies to $$h : \mathbb{R} \rightarrow \mathbb{R}$$ which only depends on the distance to the line C : | ||
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| $$(4) \quad H(x)= h(f(x))$$ |
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I'm not so sure what is h(.) as it has not been defined before
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just above "the evaluation of the integral simplifies to h"
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| ## Numerical approximation and implementation | ||
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I think this image could be bigger
| - **calculate distance value for each spatial position inside** : distance from the spatial position to the original curve | ||
| - **heatmap calculation** : resolve multiple distance estimates from overlapping bounding boxes then evaluate the distance values with the distance dependent function. | ||
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| **Curve parameterization** |
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Is this the following of the previous list ? If not maybe it would be clearer to add a small sentence to indicate what is going on
| - Minimum distance : only the estimator with the smallest point-to-line distance is used for evaluating the distance-dependent function. Easily parallelized, it allows the heatmap generation algorithm to be executed at linear time complexity | ||
| - Inverse distance weighting (IDW) : allows the contribution of all distance estimates. | ||
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| **Selection of the distance-dependant function** |
| ## CNN-based estimation error for different signal and heatmap configurations | ||
| Signal simulation model and ASSD metric to assess the accuracy of these approximations (*Simulated signals of chest X-ray, 2D experiment) | ||
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| - the custom catheter signal is estimated with minimal error across heatmap configuration | ||
| - strength of the signal has minimal impact | ||
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| *The influence of signal and heatmap width* |
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I think you might be using bullet lists too much, not doing lists forces you to be more synthetic I think
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| ## Application to 2D and 3D representation problems | ||
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| ## Anatomiacal structure detection on knee radiographs (2D experiment) |
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| D relies on the global orientation of the bone ⇒ contextual anatomical structure | ||
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bigger figures please
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| *Perspectives* | ||
| - it would be helpful to separate structures into separate output channels (even if they can’t be matched between different images of volumes) | ||
| - using a neural network to approximate knots and B-spline curve approximation parameters for signal reconstruction is a promising idea |
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I'm surprised I didn't see the word "knot" before
| cite: | ||
| authors: "Kordon, F., Stiglmayr, M., Maier, A. et al. " | ||
| title: "A principled representation of elongated structures using heatmaps" | ||
| venue: "Nature, sientific reports" |
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Capitalization + small typo 😉
| venue: "Nature, sientific reports" | |
| venue: "Nature, Scientific Reports" |
| - Create a target function that CNN can well aproximate | ||
| - Convert the curve into a heatmap through a convolution with a filter function | ||
| - Linear time complexity | ||
| - Applicalble to various surgical 2D and 3D data task |
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Typo:
| - Applicalble to various surgical 2D and 3D data task | |
| - Applicable to various surgical 2D and 3D data task |
| &= \int_C w(x - y) dy | ||
| \end{align*}$$ | ||
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| To be faster than while using a numerical integration and to generalize the description, $$H(x)$$ is simlified. They make the assumption that $$w(x)$$ is symetric $$w(x) = w(y)$$ for all $$\vert \vert x \vert \vert \underset{2}{} = \vert \vert y \vert \vert \underset{2}{}$$. |
There was a problem hiding this comment.
I think the phrasing can lead to some confusion (I had the same initial reaction as Nicolas), so I would suggest maybe something like (+ a fix to a typo in simplified and symmetric 😉):
| To be faster than while using a numerical integration and to generalize the description, $$H(x)$$ is simlified. They make the assumption that $$w(x)$$ is symetric $$w(x) = w(y)$$ for all $$\vert \vert x \vert \vert \underset{2}{} = \vert \vert y \vert \vert \underset{2}{}$$. | |
| $$H(x)$$ is simplified to i) be faster than when using a numerical integration, and ii) to generalize the description. They make the assumption that $$w(x)$$ is symmetric $$w(x) = w(y)$$ for all $$\vert \vert x \vert \vert \underset{2}{} = \vert \vert y \vert \vert \underset{2}{}$$. |
It is a long article, I will try to go through it quickly tomorrow, so please let me know if some parts should be simplified. Thank you.