Anatomically-Informed Multiple Linear Assignment Problems for White Matter Bundle Segmentation

Bradley Caron; Daniel Bullock; Emanuele Olivetti; Franco Pestilli; Giulia Bert\`o; Paolo Avesani

arxiv: 1907.07077 · v1 · pith:S3G5CUFWnew · submitted 2019-07-16 · 📡 eess.IV · cs.CV

Anatomically-Informed Multiple Linear Assignment Problems for White Matter Bundle Segmentation

Giulia Bert\`o , Paolo Avesani , Franco Pestilli , Daniel Bullock , Bradley Caron , Emanuele Olivetti This is my paper

Pith reviewed 2026-05-24 20:30 UTC · model grok-4.3

classification 📡 eess.IV cs.CV

keywords white matter bundle segmentationtractographylinear assignment problemanatomical priorsstreamline matchingbrain connectivityexample-based segmentation

0 comments

The pith

Adding anatomical position priors to the Linear Assignment Problem cost function improves white matter bundle segmentation accuracy, especially for small bundles.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper extends an example-based segmentation method that solves the Linear Assignment Problem for matching streamlines to bundle templates. It augments the geometric cost with quantified prior information on bundle anatomical position so that both sources of knowledge influence the assignment simultaneously. A sympathetic reader would care because tractogram segmentation supports studies of brain connectivity and clinical applications where small or variable bundles matter. The work reports that the combined approach yields higher accuracy than the purely geometric baseline, with the largest gains on small bundles.

Core claim

By including prior anatomical information within the optimization process of the Linear Assignment Problem, the proposed method achieves a significant improvement over the original geometric-only approach, particularly on small bundles.

What carries the argument

Anatomically-informed multiple Linear Assignment Problems, which modify the cost matrix of the standard LAP to incorporate both geometric similarity and anatomical position priors during streamline-to-bundle assignment.

If this is right

Segmentation accuracy rises most for small or low-density bundles that are otherwise prone to omission.
The joint optimization balances geometric fidelity with expected anatomical location, reducing false positives from nearby bundles.
The same cost-augmentation technique can be applied to any LAP-based assignment task that admits spatial priors.
Multiple bundles can be segmented in one pass by solving several informed LAP instances.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The method could support automated pipelines for large-scale connectome studies where manual curation of small bundles is impractical.
If the anatomical priors are derived from population atlases, the approach may generalize across subjects with different tract geometries.
Testing the same prior-augmented cost on non-brain assignment problems, such as vessel or fiber tracking in other organs, would reveal broader utility.

Load-bearing premise

Prior anatomical information about bundle position can be reliably quantified and added to the LAP cost function without introducing bias or reducing the quality of geometric matching.

What would settle it

On a held-out set of tractograms with expert-labeled bundles, compare Dice or overlap scores between the anatomically-informed LAP and the original LAP; if scores are statistically indistinguishable or lower, the central claim fails.

read the original abstract

Segmenting white matter bundles from human tractograms is a task of interest for several applications. Current methods for bundle segmentation consider either only prior knowledge about the relative anatomical position of a bundle, or only its geometrical properties. Our aim is to improve the results of segmentation by proposing a method that takes into account information about both the underlying anatomy and the geometry of bundles at the same time. To achieve this goal, we extend a state-of-the-art example-based method based on the Linear Assignment Problem (LAP) by including prior anatomical information within the optimization process. The proposed method shows a significant improvement with respect to the original method, in particular on small bundles.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This extends the LAP bundle segmentation method with anatomical priors in the cost function and claims gains on small bundles, but the abstract gives no metrics or details to judge whether the gains are real.

read the letter

The paper takes the existing Linear Assignment Problem approach to white matter bundle segmentation and modifies the cost function to include both geometric matching and prior anatomical position information. The new element is that single optimization step that balances the two instead of handling them separately. That is a direct and logical extension of the prior work, and it targets a real practical issue in tractography where small bundles are hard to recover reliably. The abstract frames the problem cleanly and states the goal without overclaiming the broader impact. The central claim is that the combined method improves results, especially on small bundles. The soft spot is that the abstract supplies none of the usual evidence: no datasets, no quantitative metrics, no error bars, no statistical tests, and no description of how the anatomical priors are turned into costs or how the single weighting parameter is chosen or normalized. Without those, it is impossible to tell whether the reported improvement follows from the construction or from some other factor. The stress-test point about missing normalization details lands because the abstract does not address it. If the full paper contains the experiments and code, that would change the picture, but based on what is here the evidence link is missing. This is for people already working on assignment-based or example-based bundle segmentation in neuroimaging. A reader tracking incremental method tweaks in that niche could get value from the full version if the validation holds up. I would send it to peer review so the authors can supply the missing evaluation details and let referees check the weighting and normalization steps.

Referee Report

2 major / 0 minor

Summary. The paper proposes extending a state-of-the-art example-based white matter bundle segmentation method that relies on the Linear Assignment Problem (LAP) by incorporating prior anatomical information directly into the optimization. The central claim is that this anatomically-informed approach yields significant improvements over the original LAP method, especially for small bundles.

Significance. If the quantitative results hold under proper validation, the work would offer a practical way to combine anatomical priors with geometric matching in tractogram segmentation, addressing a known weakness of purely geometric methods on sparse small bundles. The approach is a direct, incremental extension of an established optimization technique rather than an entirely new framework.

major comments (2)

[Abstract] Abstract: the claim of 'significant improvement ... in particular on small bundles' is asserted without any accompanying evaluation metrics, datasets, statistical tests, error bars, or baseline comparisons, so the data-to-claim link cannot be assessed from the provided description.
[Method] Method description (extension of LAP): the single free parameter that weights the anatomical-position term against the geometric cost is introduced without explicit normalization, per-subject scaling, or selection procedure; this directly affects whether the added prior improves or biases matching quality on small bundles, which is load-bearing for the central claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below and indicate revisions made to the manuscript.

read point-by-point responses

Referee: [Abstract] Abstract: the claim of 'significant improvement ... in particular on small bundles' is asserted without any accompanying evaluation metrics, datasets, statistical tests, error bars, or baseline comparisons, so the data-to-claim link cannot be assessed from the provided description.

Authors: The abstract is intentionally concise as a high-level summary. The full manuscript contains the requested details (datasets, metrics, statistical tests, error bars, and baseline comparisons) in the Experiments and Results sections. To strengthen the abstract-to-claim link without exceeding length limits, we have added a short clause referencing the quantitative evaluation protocol. revision: partial
Referee: [Method] Method description (extension of LAP): the single free parameter that weights the anatomical-position term against the geometric cost is introduced without explicit normalization, per-subject scaling, or selection procedure; this directly affects whether the added prior improves or biases matching quality on small bundles, which is load-bearing for the central claim.

Authors: We agree the parameter description requires more precision. The revised manuscript now specifies the normalization of the anatomical term, per-subject scaling to account for tractogram size variation, and the cross-validation procedure used for its selection. These additions clarify that the prior does not introduce bias on small bundles. revision: yes

Circularity Check

0 steps flagged

No circularity; extension of external LAP method with independent anatomical priors

full rationale

The paper presents an extension of a known state-of-the-art LAP-based segmentation method by incorporating prior anatomical information as an additional term in the cost function. This addition draws from external sources (atlas or population data) rather than deriving from the optimization itself or from self-citations that bear the central claim. No self-definitional reductions, fitted inputs renamed as predictions, or load-bearing self-citation chains appear in the described derivation. The reported improvements on small bundles follow from the explicit inclusion of independent geometric and anatomical terms, making the approach self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The method rests on standard assumptions of the Linear Assignment Problem and likely requires at least one weighting parameter to balance anatomical and geometric terms; no invented entities are described.

free parameters (1)

weighting factor for anatomical vs geometric cost
Required to combine the two information sources inside the optimization; value not stated in abstract.

axioms (1)

standard math The Linear Assignment Problem formulation admits an efficient solution for tractogram sizes encountered in practice.
Background assumption inherited from prior LAP work in computer vision.

pith-pipeline@v0.9.0 · 5648 in / 1089 out tokens · 24622 ms · 2026-05-24T20:30:41.790526+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

17 extracted references · 17 canonical work pages · 1 internal anchor

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Anatomically-Informed Multiple Linear Assignment Problems for White Matter Bundle Segmentation

INTRODUCTION Segmenting anatomical structures in the white matter of the human brain is useful in many different applications, such as surgical planning, population studies, and diagnosis or monitoring of brain diseases [1, 2]. The information about the orientation of the ﬁbers composing such anatomical structures can be estimated in-vivo by diffusion Mag...

work page internal anchor Pith review Pith/arXiv arXiv 1907
[2]

Basic notation We denote a streamline with a sequence of n points as s = ( x1,..., xn), where xi∈ R3,∀i

METHODS 2.1. Basic notation We denote a streamline with a sequence of n points as s = ( x1,..., xn), where xi∈ R3,∀i. Usually, n is in the order of 101− 102 and differs across streamlines. The entire set of streamlines of the white matter of a brain is known as thetractogram, T ={s1,...,s M}, where in general M is in the order of 105− 106. A white matter ...

work page
[3]

EXPERIMENTS 3.1. Materials We randomly selected 130 healthy subjects from the publicly available Human Connectome Project (HCP) dMRI dataset [11] (90 gradients; b=2000; voxel size=1.25 mm isotropic). For each subject, tractograms of 750k streamlines were obtained using constrained spherical deconvolution (CSD) [12] and ensemble probabilistic tracking [13]...

work page doi:10.25663/brainlife.app.122 2000
[4]

In all the cases we obtained a mean DSC between 0.80 and 0.87, which means that the overlap with the ground truth is at least 80%

DISCUSSION Table 1 illustrates that, on average, the proposed multi-LAP-anat method outperforms the multi-LAP method of [9], for all the bundles considered. In all the cases we obtained a mean DSC between 0.80 and 0.87, which means that the overlap with the ground truth is at least 80%. Streamlines composing the same anatomical bundle not only have a simi...

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Automatic tractography segmentation using a highdimensional white matter atlas,

Lauren J. O’Donnell and Carl-Fredrik F. Westin, “Automatic tractography segmentation using a highdimensional white matter atlas,” in IEEE Trans. Med. Imag, 2007, pp. 1562–1575

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Tract Proﬁles of White Matter Properties: Automating Fiber-Tract Quantiﬁcation,

Jason D. Yeatman, Robert F. Dougherty, Nathaniel J. Myall, Brian A. Wandell, and Heidi M. Feldman, “Tract Proﬁles of White Matter Properties: Automating Fiber-Tract Quantiﬁcation,”PLoS ONE, vol. 7, no. 11, pp. e49790+, Nov. 2012

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Demian Wassermann, Nikos Makris, Yogesh Rathi, Martha Shenton, Ron Kikinis, Marek Kubicki, and Carl-Fredrik F. Westin, “The white matter query language: a novel approach for describing human white matter anatomy.,” Brain structure & function, vol. 221, pp. 4705–4721, Jan. 2016

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Identifying White-Matter Fiber Bundles in DTI Data Using an Automated Proximity-Based Fiber-Clustering Method,

Song Zhang, S. Correia, and D. H. Laidlaw, “Identifying White-Matter Fiber Bundles in DTI Data Using an Automated Proximity-Based Fiber-Clustering Method,” IEEE Transactions on Visualization and Computer Graphics, vol. 14, no. 5, pp. 1044–1053, Sept. 2008

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An Example-Based Multi-Atlas Approach to Automatic Labeling of White Matter Tracts,

Sang W. Yoo, Pamela Guevara, Yong Jeong, Kwangsun Yoo, Joseph S. Shin, Jean-Francois Mangin, and Joon-Kyung Seong, “An Example-Based Multi-Atlas Approach to Automatic Labeling of White Matter Tracts,” PloS one, vol. 10, no. 7, 2015

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Nusrat Sharmin, Emanuele Olivetti, and Paolo Avesani, “White Matter Tract Segmentation as Multiple Linear Assignment Problems,” Frontiers in Neuroscience, vol. 11, Feb. 2018

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J-Donald Tournier, Fernando Calamante, and Alan Connelly, “Robust determination of the ﬁbre orientation distribution in diffusion MRI: Non-negativity constrained super-resolved spherical deconvolution,” NeuroImage, vol. 35, no. 4, pp. 1459–1472, May 2007

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[1] [1]

Anatomically-Informed Multiple Linear Assignment Problems for White Matter Bundle Segmentation

INTRODUCTION Segmenting anatomical structures in the white matter of the human brain is useful in many different applications, such as surgical planning, population studies, and diagnosis or monitoring of brain diseases [1, 2]. The information about the orientation of the ﬁbers composing such anatomical structures can be estimated in-vivo by diffusion Mag...

work page internal anchor Pith review Pith/arXiv arXiv 1907

[2] [2]

Basic notation We denote a streamline with a sequence of n points as s = ( x1,..., xn), where xi∈ R3,∀i

METHODS 2.1. Basic notation We denote a streamline with a sequence of n points as s = ( x1,..., xn), where xi∈ R3,∀i. Usually, n is in the order of 101− 102 and differs across streamlines. The entire set of streamlines of the white matter of a brain is known as thetractogram, T ={s1,...,s M}, where in general M is in the order of 105− 106. A white matter ...

work page

[3] [3]

EXPERIMENTS 3.1. Materials We randomly selected 130 healthy subjects from the publicly available Human Connectome Project (HCP) dMRI dataset [11] (90 gradients; b=2000; voxel size=1.25 mm isotropic). For each subject, tractograms of 750k streamlines were obtained using constrained spherical deconvolution (CSD) [12] and ensemble probabilistic tracking [13]...

work page doi:10.25663/brainlife.app.122 2000

[4] [4]

In all the cases we obtained a mean DSC between 0.80 and 0.87, which means that the overlap with the ground truth is at least 80%

DISCUSSION Table 1 illustrates that, on average, the proposed multi-LAP-anat method outperforms the multi-LAP method of [9], for all the bundles considered. In all the cases we obtained a mean DSC between 0.80 and 0.87, which means that the overlap with the ground truth is at least 80%. Streamlines composing the same anatomical bundle not only have a simi...

work page

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Automatic tractography segmentation using a highdimensional white matter atlas,

Lauren J. O’Donnell and Carl-Fredrik F. Westin, “Automatic tractography segmentation using a highdimensional white matter atlas,” in IEEE Trans. Med. Imag, 2007, pp. 1562–1575

work page 2007

[6] [6]

Tract Proﬁles of White Matter Properties: Automating Fiber-Tract Quantiﬁcation,

Jason D. Yeatman, Robert F. Dougherty, Nathaniel J. Myall, Brian A. Wandell, and Heidi M. Feldman, “Tract Proﬁles of White Matter Properties: Automating Fiber-Tract Quantiﬁcation,”PLoS ONE, vol. 7, no. 11, pp. e49790+, Nov. 2012

work page 2012

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Virtual in vivo interactive dissection of white matter fasciculi in the human brain.,

Marco Catani, Robert J. Howard, Sinisa Pajevic, and Derek K. Jones, “Virtual in vivo interactive dissection of white matter fasciculi in the human brain.,” NeuroImage, vol. 17, no. 1, pp. 77–94, Sept. 2002

work page 2002

[8] [8]

Reproducibility of quantitative tractography methods applied to cerebral white matter.,

Setsu Wakana, Arvind Caprihan, Martina M. Panzenboeck, James H. Fallon, Michele Perry, Randy L. Gollub, Kegang Hua, Jiangyang Zhang, Hangyi Jiang, Prachi Dubey, Ari Blitz, Peter van Zijl, and Susumu Mori, “Reproducibility of quantitative tractography methods applied to cerebral white matter.,”NeuroImage, vol. 36, no. 3, pp. 630–644, July 2007

work page 2007

[9] [9]

Recognition of white matter bundles using local and global streamline-based registration and clustering.,

Eleftherios Garyfallidis, Marc-Alexandre A. C ˆot´e, Francois Rheault, Jasmeen Sidhu, Janice Hau, Laurent Petit, David Fortin, Stephen Cunanne, and Maxime Descoteaux, “Recognition of white matter bundles using local and global streamline-based registration and clustering.,” NeuroImage, vol. 170, pp. 283–295, Apr. 2018

work page 2018

[10] [10]

The white matter query language: a novel approach for describing human white matter anatomy.,

Demian Wassermann, Nikos Makris, Yogesh Rathi, Martha Shenton, Ron Kikinis, Marek Kubicki, and Carl-Fredrik F. Westin, “The white matter query language: a novel approach for describing human white matter anatomy.,” Brain structure & function, vol. 221, pp. 4705–4721, Jan. 2016

work page 2016

[11] [11]

Identifying White-Matter Fiber Bundles in DTI Data Using an Automated Proximity-Based Fiber-Clustering Method,

Song Zhang, S. Correia, and D. H. Laidlaw, “Identifying White-Matter Fiber Bundles in DTI Data Using an Automated Proximity-Based Fiber-Clustering Method,” IEEE Transactions on Visualization and Computer Graphics, vol. 14, no. 5, pp. 1044–1053, Sept. 2008

work page 2008

[12] [12]

An Example-Based Multi-Atlas Approach to Automatic Labeling of White Matter Tracts,

Sang W. Yoo, Pamela Guevara, Yong Jeong, Kwangsun Yoo, Joseph S. Shin, Jean-Francois Mangin, and Joon-Kyung Seong, “An Example-Based Multi-Atlas Approach to Automatic Labeling of White Matter Tracts,” PloS one, vol. 10, no. 7, 2015

work page 2015

[13] [13]

White Matter Tract Segmentation as Multiple Linear Assignment Problems,

Nusrat Sharmin, Emanuele Olivetti, and Paolo Avesani, “White Matter Tract Segmentation as Multiple Linear Assignment Problems,” Frontiers in Neuroscience, vol. 11, Feb. 2018

work page 2018

[14] [14]

Solving the Rectangular assignment problem and applications,

J. Bijsterbosch and A. V olgenant, “Solving the Rectangular assignment problem and applications,” Annals of Operations Research, vol. 181, pp. 443–462, June 2010

work page 2010

[15] [15]

Advances in diffusion MRI acquisition and processing in the Human Connectome Project.,

Stamatios N. Sotiropoulos, Saad Jbabdi, Junqian Xu, Jesper L. Andersson, Steen Moeller, Edward J. Auerbach, Matthew F. Glasser, Moises Hernandez, Guillermo Sapiro, Mark Jenkinson, David A. Feinberg, Essa Yacoub, Christophe Lenglet, David C. Van Essen, Kamil Ugurbil, Timothy E. Behrens, and WU-Minn HCP Consortium, “Advances in diffusion MRI acquisition and...

work page 2013

[16] [16]

Robust determination of the ﬁbre orientation distribution in diffusion MRI: Non-negativity constrained super-resolved spherical deconvolution,

J-Donald Tournier, Fernando Calamante, and Alan Connelly, “Robust determination of the ﬁbre orientation distribution in diffusion MRI: Non-negativity constrained super-resolved spherical deconvolution,” NeuroImage, vol. 35, no. 4, pp. 1459–1472, May 2007

work page 2007

[17] [17]

Ensemble Tractography.,

Hiromasa Takemura, Cesar F. Caiafa, Brian A. Wandell, and Franco Pestilli, “Ensemble Tractography.,” PLoS computa- tional biology, vol. 12, no. 2, Feb. 2016

work page 2016