Functional Map-Based Shape Collection Matching and Analysis for Modeling Breast Shape Evolution During Radiotherapy

PhD Thesis Defense by Pierre Galmiche
11/28/2024

Co-directed by:

Reviewers:

Examiners:

Hyewon Seo, Directrice de Recherche CNRS
Université de Strasbourg

Michel de Mathelin, Professeur des Universités
Université de Strasbourg

Dmitry Sokolov, Professeur des Universités
Université de Lorraine

Stefanie Wuhrer, Chargée de Recherche INRIA
Université de Grenoble

Mohamed Daoudi, Professeur des Universités
Université de Lille

Georges Noël, PU-PH
Université de Strasbourg

Table of Contents

Medical Context

The Breast Cancer Treatment

According to the World Health Organization’s 2022 statistics:

• 670,000 deaths worldwide in 2022
• 50 % of breast cancer cases occur in women without specific risk factors other than gender and age
• Most common cancer among women in 157 out of 185 countries

→ Research to improve the treatment.

The Breast Cancer Treatment

Can be summarized into three main components:

• Surgery to remove tumor
• Radiation therapy to prevent recurrence
• Chemotherapy to prevent cancer spread

Radiotherapy by Seo et al. (2019)

→ We focus on radiation therapy.

Breast Radiotherapy

Radiotherapy by Seo et al. (2019)

Radiation therapy by VisionRT (2024)

Breast Radiotherapy

Involves several steps:

• Treatment planning

Treatment planning

Breast Radiotherapy

Involves several steps:

• Treatment planning
• Centering CT scan acquisition

CT scan of patient ET55

Breast Radiotherapy

Involves several steps:

• Treatment planning
• Centering CT scan acquisition
• Organs at Risk contouring

Radiotherapy Structures

Breast Radiotherapy

Involves several steps:

• Treatment planning
• Centering CT scan acquisition
• Organs at Risk contouring
• Dose optimization

Dose Map

Breast Radiotherapy

Involves several steps:

• Treatment planning
• Centering CT scan acquisition
• Organs at Risk contouring
• Dose optimization
• Validation and treatment

Radiotherapy treatment

Breast Radiotherapy

Is a complex treatment:

• Wide variability in side effects
• Dose is planned once before treatment
• followed by 5-7 weeks of treatment

Radiotherapy treatment

What about breast changes during treatment?

Breast Radiotherapy

Clinical experience showed changes in breast shape during treatment.

→ We want to learn more about such changes:

• How much does the treated breast change during the treatment?

• Does it impact the radiation dose?

• Is the initially planned dose still optimal for a given session?

ICANS data

The ICANS clinical trial

Objective: Study morphological changes in breast during radiotherapy and their effect on administrated dose.

• Conducted from 02/22/2018 to 05/07/2020 at the Centre Paul Strauss
• 60 patients, 33 irradiation sessions
• Using a hand-held, optical, non-ionizing surface scanner
• 11 additional surfaces, acquired before, during and after treatment

Artec EVA hand-held scanner

Data for one patient

ICANS clinical trial patient information

Patient Data used

Various representations of the patient bust:

• Point Cloud (left)
• Voxels (center)
• Dense mesh (right)

ICANS patient data

→ This data comes with challenges.

Thanks Robin for you work on K3D lib!

Challenges

Surfaces are not initially aligned:

AH32 raw data

Challenges

Bust coverage changes across acquisitions:

Raw data: Acquisitions B and S1

Challenges

No correspondence between the various surfaces:

Raw data: Acquisitions B and S1

→ No ground truth correspondences.

Challenges

Identify the treated breast (ROI\(^1\)) on all surfaces:

CT annotations ✓

Scans acquisitions ✗

→ Our approach to deal with these challenges.

Our Approach

Objective & Constraints

Objective: Assist clinicians in measuring breast changes during treatment by using ICANS data.

Constraints:

• Partial correspondences
• Shape collections analysis
• Robust to noise
• Efficient

ICANS data

Approach

Three main steps:

1. Find correspondences between patient surfaces
2. Model breast and bust changes from correspondences
3. Measure dosimetric impact of breast changes

Approach

We developed and implemented a contribution for each step:

1. Groupwise correspondence refinement with a ROI focus (Galmiche and Seo (2023))
2. Intra- and inter- patient shape analysis approaches
   (to be submitted)
3. Estimation of the dosimetric impact of the computed breast deformations (Arbor et al. (2024))

Approach: Some background work

Shape matching: Definition

Definition

Shape Matching Problem:

Given \(N\) input shapes \(S_1 , S_2 , \ldots , S_N\) , find a meaningful relation between their elements.

Sparse correspondences by Kaick et al. (2011)

→ How to optimize correspondences?

Shape matching approaches:

Our focus for ICANS data:

• Partiality

Partial shapes by Kaick et al. (2011)

Shape matching approaches:

Our focus for ICANS data:

• Partiality
• Pairwise VS groupwise approaches

Shape collection by Kaick et al. (2011)

Shape matching approaches:

Our focus for ICANS data:

• Partiality
• Pairwise VS groupwise approaches
• Application: registration/shape analysis

Shape matching applications by Kaick et al. (2011)

→ Which method should we use?

Shape matching approaches: Many frameworks

Extensive research has been conducted on various approaches:

• Large Deformation Diffeomorphic Metric Mapping (LDDMM)
• Deep Learning (DL) frameworks
• Functional Maps
• Hybrid approaches: LDDMM + DL …

→ We chose the Functional Maps approach.

Functional Maps: Our choice for ICANS data

Many advantages:

• Compact shape and correspondences representations
• Efficient optimization, even on partial/dense data
• Offers powerful intrinsic analysis tools
• Easily integrates with other approaches

→ What are Functional Maps?

Functional Maps: Definition

Functional Maps by Ovsjanikov et al. (2016)

→ How to optimize such maps?

Functional Maps: Default pipeline

Spectral Coefficients by Ovsjanikov et al. (2016)

Functional Maps: Default pipeline

Main ideas:

• \(f \approx \sum_{i=1}^{k} \underbrace{\langle f , \phi_i^{\mathcal{M}} \rangle}_{a_i} \phi_i^{\mathcal{M}}\)
• \(k\) eigenfunctions of Laplace Beltrami Operator for \(\phi\) \(\implies a=\phi^{-1} f\)
• \(\{f, g\} \implies A, B\)

Spectral Coefficients by Ovsjanikov et al. (2016)

→ \(C^* = arg\,min_{C} \left\lVert CA - B \right\rVert^2 + E_{reg}(C)\)

Functional Maps: Default pipeline

The Laplace Beltrami Operator (LBO) eigenfunctions:

• Smooth functions
• Invariant to shape isometries
• Coarse to fine representation

→ Good for shape matching and analysis

Eigenfunctions on bust data

Functional Maps for ICANS data

Existing methods to deal with our challenges:

• Partiality: Fully Spectral Partial Shape Matching (FSPM)
  → Litany et al. (2017)

Functional Maps: FSPM for Partial Correspondences

Fully Spectral Partial Shape Matching → Litany et al. (2017)

• FM slope when partiality

Partial FM slope by Rodolà et al. (2016)

Functional Maps: FSPM

Partial FM slope by Rodolà et al. (2016)

Functional Maps: FSPM

Fully Spectral Partial Shape Matching → Litany et al. (2017)

• FM slope when partiality
• Fully spectral optimization

Partial FM slope by Rodolà et al. (2016)

Functional Maps: FSPM

Fully Spectral Partial Shape Matching → Litany et al. (2017)

• FM slope when partiality
• Fully spectral optimization
• New basis on full shape

New basis by Litany et al. (2017)

Functional Maps: FSPM

New basis by Litany et al. (2017)

Functional Maps: FSPM

Fully Spectral Partial Shape Matching → Litany et al. (2017)

• FM slope when partiality
• Fully spectral optimization
• New basis on full shape

New basis by Litany et al. (2017)

→ \(\min_{Q \in S(K,r)} \underbrace{off(Q^T \Lambda^{S_i} Q)}_{\text{smoothing term}} + \mu \underbrace{\left\lVert A_r - Q^TB \right\rVert_{2,1}}_{\text{data term}}\)

Functional Maps for ICANS data

Existing methods to deal with our challenges:

• Partiality: Fully Spectral Partial Shape Matching (FSPM)
  → Litany et al. (2017)

• Accuracy: ZoomOut → Simone Melzi et al. (2019)

Functional Maps: ZoomOut Refinement

Main concept:

• Low-frequency FM
• Up-sampling refinement
• FM - pointwise map conversions

ZoomOut upsampling strategy by Simone Melzi et al. (2019)

Functional Maps: ZoomOut Refinement

ZoomOut upsampling strategy by Simone Melzi et al. (2019)

Functional Maps for ICANS data

Existing methods to deal with our challenges:

• Partiality: Fully Spectral Partial Shape Matching (FSPM)
  → Litany et al. (2017)
• Accuracy: ZoomOut → Simone Melzi et al. (2019)

• Groupwise correspondences and analysis: Limit Shapes → Huang et al. (2019)

Groupwise Refinement: Cycle Consistency

Core idea:

• Transfer from \(S_0\) to \(S_1\)
• from \(S_1\) to \(S_2\)
• from \(S_2\) back to \(S_0\)

→ Should not change information.

Cycle consistency illustration

Functional Maps: “Limit Shapes”

Core idea:

• \(C_{i_1,i_k} C_{i_k ,i_{k-1}} \ldots C_{i_2,i_1} = I\)
• \(\approx\) to find CCLB\(^1\) \(\{Y_i\}_{i=1}^n\)
• s.t. \(C_{i,j}Y_i \simeq Y_j \quad \forall i,j\)

Our Functional Map Network (FMN)

→ \(Y = arg\,min_{Y} \sum_{(i,j) \in \mathcal{E}} \omega_{ij} \left\lVert C_{i,j}Y_i - Y_j \right\rVert_F^2\)

Functional Maps: “Limit Shapes”

Our Functional Map Network (FMN)

Functional Maps: “Limit Shapes”

Core idea:

• \(L_{id} \approx\) average shape of the patient \(id\)

→ \(L_{id}\): Domain in which compare \(\neq\) shapes

Our Functional Map Network (FMN)

Functional Maps: “Limit Shapes”

Shape analysis with shape differences operators:

• “Intrinsic” variability

• \(D_i^A = Y_i^T Y_i\) and \(D_i^C = \Lambda_0^{-1} Y_i^T \Lambda^{S_i} Y_i\)

• \(F=\sum_{i,j} (D_i -D_j)^2\)

• \(H= \sum_{(i,j) \notin \mathcal{S}} (D_i^g-D_j^g)^2\) \(- \sum_{(i,j) \in \mathcal{S}} (D_i^g-D_j^g)^2\)

Shape variability by Huang et al. (2019)

→ Eigenfunctions of F/H show sorted variability

Functional Maps: “Limit Shapes”

Shape differences variability by Huang et al. (2019)

Functional Maps for ICANS data

Existing methods to deal with our challenges:

• Partiality: Fully Spectral Partial Shape Matching (FSPM)
  → Litany et al. (2017)
• Accuracy: ZoomOut → Simone Melzi et al. (2019)
• Groupwise correspondences and analysis: Limit Shapes → Huang et al. (2019)

• Focus on the treated breast: Localized Manifold Harmonics (LMH) → S. Melzi et al. (2017)

Functional Maps: LMH

Localized Manifold Harmonics by S. Melzi et al. (2017)

Functional Maps: LMH

Main concept:

• Need a Region of Interest
• Create ROI-localized basis
• Less sensitive to partiality

Localized Manifold Harmonics by S. Melzi et al. (2017)

Functional Maps: LMH

Main concept:

• Need a Region of Interest
• Create ROI-localized basis
• Less sensitive to partiality
• Compatible with MH

LMH Functional Maps by S. Melzi et al. (2017)

Functional Maps: LMH

LMH Functional Maps by S. Melzi et al. (2017)

Functional Maps: LMH

LMH Functional Maps by S. Melzi et al. (2017)

→ ✓ Background work

Our Contributions

Contributions

1) Groupwise correspondence refinement with a ROI focus
(Galmiche and Seo (2023))

Groupwise refinement with a ROI focus

Approach:

1. Initialize partial correspondences with FSPM

S1 to CT FSPM colormap transfer

Groupwise refinement with a ROI focus

S1 to CT FSPM colormap transfer

Groupwise refinement with a ROI focus

FSPM CT-to-scans colormap transfer

Groupwise refinement with a ROI focus

Approach:

1. Initialize partial correspondences with FSPM

S1 to CT FSPM colormap transfer

→ ROI focus?

Groupwise refinement with a ROI focus

ROI focus:

ROI definition on CT

Groupwise refinement with a ROI focus

ROI focus:

• Use CT annotations (left)
• Remesh CT point cloud (right)
• Create ROI mask on CT mesh (right)

ROI definition on CT

→ Transfer ROI mask to scan acquisitions

Groupwise refinement with a ROI focus

ROI transfer to scan acquisitions:

CT-to-scan FSPM ROI transfer

Groupwise refinement with a ROI focus

FSPM for partial correspondences:

• Partial correspondences
• Colormap transfers
• Not accurate enough for ROI transfer

CT-to-scan FSPM ROI transfer

→ We need to refine these pairwise correspondences.

Groupwise refinement with a ROI focus

Approach:

2. Refine them with “Bidirectional Partial ZoomOut”:

• In both direction
• Adapted for partiality
• Maps forming cycles

FSPM+bidirZM colormap transfer

Groupwise refinement with a ROI focus

FSPM+bidirZM colormap transfer

Groupwise refinement with a ROI focus

FSPM CT-to-scans colormap transfer

FSPM+bidirZM colormap transfer

→ ROI transfer

Groupwise refinement with a ROI focus

Improved ROI transfer:

CT-to-scan FSPM+bidirZM ROI transfer

Groupwise refinement with a ROI focus

ROI transfer results:

• Smoother transfer
• Better localization
• Still shifts around the ROI

CT-to-scan FSPM ROI transfer

CT-to-scan FSPM+bidirZM ROI transfer

→ Groupwise correspondences refinement + ROI focus

Groupwise refinement with a ROI focus

Approach:

3. Compute LMH on treated breast region

LMH on patient ROI

→ Improve the treated breast representation

Groupwise refinement with a ROI focus

Approach:

4. Optimize cycle consistent FM

Our Functional Map Network (FMN)

Groupwise refinement with a ROI focus

Approach:

4. Optimize cycle consistent FM

→ with MH only

→ with LMH only (ours)

LMH Functional Maps by S. Melzi et al. (2017)

Groupwise refinement with a ROI focus

Results: consistent LMH

LMH (top) VS Consistent LMH (ours, bottom)

Groupwise refinement with a ROI focus

Results: Better ROI transfer on bust data

ROI transfers with Consistent

→ Synthetic data

Groupwise refinement with a ROI focus

Results: Better ROI transfer on synthetic data

ROI transfer with pairwise (top), groupwise (middle), and our approach (bottom)

→ Quantitative improvement?

Groupwise refinement with a ROI focus

Results: Pointwise cyclic errors

Pointwise cyclic error illustration

Groupwise refinement with a ROI focus

Average pointwise cyclic errors on the shark

Shape	S1	S2	S3	S4	S5
Pairwise	34.62	22.79	18.27	15.69	30.96
Groupwise	1.15	1.04	0.88	1.57	2.10
Ours	1.11	0.98	0.81	1.46	1.19
Pairwise ROI	18.44	18.18	15.09	7.36	19.41
Groupwise ROI	1.57	1.62	1.48	1.99	5.02
Ours ROI	1.44	1.29	1.04	1.11	1.04

→ Shape analysis

Contributions

1) Groupwise correspondence refinement with a ROI focus
(Galmiche and Seo (2023))

2) Multi-collection Shape Analysis on ICANS data (to be submitted)

a) Initialize Intra-patient correspondences

Intra-patient correspondences

b) Construct inter-patient correspondences

Core idea:

• \(L_{id} \approx\) average shape of the patient \(id\)
• \(G \approx\) average patient

Cross-Collections FMN

→ \(G\): Domain in which compare \(\neq\) patients

b) Construct inter-patient correspondences

Core idea:

• \(C_{L_1,L_k} C_{L_k ,L_{k-1}} \ldots C_{L_2,L_1} = I\)
• \(\approx\) to find GLB\(^1\) \(\{G_i\}_{i=1}^n\)
• s.t. \(C_{L_i,L_j}G_i \simeq G_j \quad \forall L_i,L_j\)

Cross-Collections FMN

→ \(G = arg\,min_{G} \sum_{(i,j) \in \mathcal{E}} \omega_{ij} \left\lVert C_{L_i,L_j}G_i - G_j \right\rVert_F^2\)

b) Construct inter-patient correspondences

Cross-Collections FMN

b) Construct inter-patient correspondences

Cross-Collections FMN

→ \(G \approx\) average patient domain

b) Construct inter-patient correspondences

Inter-patient colormap transfer

c) Variability: Intrinsic analysis

Global shape variability in \(G\):

• Difference operators \(D_i\)
• \(D_i^g = G_i^{-1} D_i\) (ours)
• \(F=\sum_{i,j} (D_i^g -D_j^g)^2\)

→ Eigenfunctions of F for global variability

\(D_i\) projection in \(G\)

c) Variability: Intrinsic analysis

Results: Pairwise distinctive functions

Intrinsic conformal variability

c) Variability: Intrinsic analysis

Results: Intra-patient global distinctive functions

Intrinsic conformal variability

c) Variability: Intrinsic analysis

Results: Intra-patient global distinctive functions

Intrinsic conformal variability

c) Variability: Intrinsic analysis

Results: Inter-patient global distinctive functions

Right breast patients: intrinsic area global variability

c) Variability: Intrinsic analysis

Inter-session shape variability in \(G\):

• Difference operators \(D_i\)
• \(D_i^g = G_i^{-1} D_i\) (ours)
• \(H= \sum_{(i,j) \notin s} (D_i^g-D_j^g)^2\) \(- \sum_{(i,j) \in s} (D_i^g-D_j^g)^2\)

→ Eigenfunctions of H for inter-session variability

\(D_i\) projection in \(G\)

c) Variability: Intrinsic analysis

Results: Inter-session distinctive functions

Left breast patients: intrinsic conformal inter-session variability

→ How to measure euclidean displacements?

d) Variability: Extrinsic analysis

Extrinsic analysis approach

ROI alignment

Is difficult as the whole bust changes non-rigidly:

• We use correspondences to transfer ROI band region from CT to scans

ROI band transfer

ROI alignment

Is difficult as the whole bust changes non-rigidly:

• We use correspondences to transfer ROI band region from CT to scans
• Filter both ROI with curvature threshold

Curvature filtering

ROI alignment

Is difficult as the whole bust changes non-rigidly:

• We use correspondences to transfer ROI band region from CT to scans
• Filter both ROI with curvature threshold
• We align the selected points with a trimmed ICP

Scan ROI alignment on CT skin

Extrinsic changes

ROI cut definition

Extrinsic changes

Breast S25 deformation

Extrinsic changes

Breast extrinsic changes: displacements amplitude on ROI cut

→ Displacements amplitudes

Extrinsic changes

Per-session average displacement amplitude (mm)

SA	SB	S1	S5
1.21±0.58	1.20±0.69	1.51±0.64	1.36±0.45
S10	S15	S20	S25
1.47±0.60	1.25±0.40	1.68±0.85	1.84±1.05
S33	M1	M3	Sessions avg
1.62±0.78	1.98±0.62	2.82±1.56	1.62±0.72

Extrinsic changes

Per-session average breast volume changes relative to the CT ROI (%)

SA	SB	S1	S5
2.17±1.62	2.02±1.97	3.31±2.51	2.89±2.37
S10	S15	S20	S25
2.77±2.45	2.11±2.05	3.24±3.13	5.34±6.30
S33	M1	M3	Sessions avg
2.77±3.46	4.45±3.04	9.93±6.98	3.54±3.16

Extrinsic changes

• CT-session average ROI displacement \(\simeq 1.62 ± 0.72\) mm
• Breast Volume changes from scan displacements \(\simeq 3.54 ± 3.16\)% / CT
• Inter-session / patient variability

→ Dosimetric impact?

ROI cut definition

Breast extrinsic changes

Contributions

1) Groupwise correspondence refinement with a ROI focus
(Galmiche and Seo (2023))

2) Multi-collection Shape Analysis on ICANS data (to be submitted)

3) Estimation of the dosimetric impact of the computed breast deformations (Arbor et al. (2024))

From Surface Changes to Irradiation Dose Impact

Skin dose in radiotherapy is a key issue to reduce patient side effects.

• Dose calculations remains a challenge in the skin region.
• Objective: recalculate the skin dose for each treatment session.

→ Our approach using the ICANS data

From Surface Changes to Irradiation Dose Impact

Approach

From Surface Changes to Irradiation Dose Impact

Results:

• Breast changes on CT

IA58 CT/S25 Slice 2 CT deformation

From Surface Changes to Irradiation Dose Impact

Results:

• Breast changes on CT
• Dose changes on CT

LD49 Results

From Surface Changes to Irradiation Dose Impact

Results:

• Breast changes on CT
• Dose changes on CT
• More voxels with high dose in skin region

→ More skin dose than planned

LD49 skin voxels dose histogram
Arbor et al. (2024)

From Surface Changes to Irradiation Dose Impact

Results:

IA58 Results

ET55 Results

LD49 Results

→ Record such potential dose changes.

From Surface Changes to Irradiation Dose Impact

Results:

IA58 Results

ET55 Results

LD49 Results

→ Correlations with patient skin reactions?

Conclusions and Perspectives

Conclusions

During this thesis:

• We studied SOTA approaches for partial and groupwise shape matching on the ICANS medical data
• We developed and implemented 3 contributions:
  • Groupwise correspondences refinement with a ROI focus (Galmiche and Seo (2023))
  • Intra- and inter- patient shape collection analysis on ICANS data (to be submitted)
  • Estimation of the dosimetric impact of the measured breast changes (Arbor et al. (2024))

Conclusions

During this thesis, we also implemented:

• Dashboard for automation

Radiotherapy structures visualization

Conclusions

During this thesis, we also implemented:

• Dashboard for automation

Patient correspondences computation

Conclusions

During this thesis, we also implemented:

• Dashboard for automation
• User-interfaces to navigate between results

Pairwise shape analysis

Conclusions

During this thesis, we also implemented:

• Dashboard for automation
• User-interfaces to navigate between results

Groupwise shape analysis

Conclusions

From our experiments, we observed:

• A high variability in breast shape change during radiotherapy:
  • \(\simeq 2\)mm displacement amplitude in ROI
  • high patient/session variability: \(S_{25}\)
  • Other bust variations: intrinsic tool
• Recomputing the dose taking into account breast changes leads to modified skin dose

Perspectives

There are many possible continuations of this work:

• Continue skin dosimetric impact evaluation + correlations
• Test our approach on Surface Guided Radiotherapy (SGRT) surface data
• Explore ROI focused intrinsic analysis on shape collections
• Test deep learning functional map approaches

Thank you !

• Clinical trial patients
• Jury
• Hyewon and Michel
• Clara, Philippe, Yvan, Nicolas, Delphine
• MLMS team

MLMS team

Backup slides

Shape Variability: Intrinsic analysis

Results: PCA in the global domain

Sessions Principal Component Analysis (PCA)

References

Arbor, Nicolas, Laurent Bartolucci, Botao Dai, Halima El Azhar, Pierre Galmiche, Delphine Jarnet, Michel de Mathelin de Papigny, Philippe Meyer, and Hyewon Seo. 2024. “Skin dose in breast radiation therapy: Monte Carlo calculations from deformed vector fields (DVF)-driven CT images.” In The 20th international conference on the use of computers in radiation therapy (ICCR), 834–36. Lyon, France. https://hal.science/hal-04753072.

Galmiche, Pierre, and Hyewon Seo. 2023. “Groupwise Shape Correspondence Refinement with a Region of Interest Focus.” Computer Graphics Forum 42 (7): e14934. https://doi.org/10.1111/cgf.14934.

Huang, Ruqi, Panos Achlioptas, Leonidas Guibas, and Maks Ovsjanikov. 2019. “Limit Shapes – A Tool for Understanding Shape Differences and Variability in 3D Model Collections.” Computer Graphics Forum 38 (5): 187–202. https://doi.org/10.1111/cgf.13799.

Kaick, Oliver van, Hao Zhang, Ghassan Hamarneh, and Daniel Cohen-Or. 2011. “A Survey on Shape Correspondence: O. Van Kaick Et Al. / A Survey on Shape Correspondence.” Computer Graphics Forum 30 (6): 1681–1707. https://doi.org/10.1111/j.1467-8659.2011.01884.x.

Litany, O., E. Rodolà, A. M. Bronstein, and M. M. Bronstein. 2017. “Fully Spectral Partial Shape Matching.” Computer Graphics Forum 36 (2): 247–58. https://doi.org/10.1111/cgf.13123.

Melzi, Simone, Jing Ren, Emanuele Rodolà, Abhishek Sharma, Peter Wonka, and Maks Ovsjanikov. 2019. “ZoomOut: Spectral Upsampling for Efficient Shape Correspondence.” ACM Transactions on Graphics 38 (6): 1–14. https://doi.org/10.1145/3355089.3356524.

Melzi, S., E. Rodolà, U. Castellani, and M. M. Bronstein. 2017. “Localized Manifold Harmonics for Spectral Shape Analysis.” Computer Graphics Forum 37 (6): 20–34. https://doi.org/10.1111/cgf.13309.

Ovsjanikov, Maks, Etienne Corman, Michael Bronstein, Emanuele Rodolà, Mirela Ben-Chen, Leonidas Guibas, Frederic Chazal, and Alex Bronstein. 2016. “SIGGRAPH ASIA 2016 COURSE NOTES,” 60.

Rodolà, E., L. Cosmo, M. M. Bronstein, A. Torsello, and D. Cremers. 2016. “Partial Functional Correspondence.” Computer Graphics Forum 36 (1): 222–36. https://doi.org/10.1111/cgf.12797.

Seo, Anna, Jong-Moon Hwang, Jong-Min Lee, and Tae-Du Jung. 2019. “Changes in Pectoral Muscle Volume During Subacute Period After Radiation Therapy for Breast Cancer: A Retrospective up to 4-Year Follow-up Study.” Scientific Reports 9 (1): 7038. https://doi.org/10.1038/s41598-019-43163-0.

VisionRT. 2024. “Safer Radiation Therapy.” https://www.saferradiationtherapy.com/radiation-therapy-deep-inspiration-breath-hold/.