Partial Matching in the Space of Varifolds

Antonsanti, Pierre-Louis; Glaunès, Joan Alexis; Benseghir, Thomas; Jugnon, Vincent; Kaltenmark, Irène

doi:10.1007/978-3-030-78191-0_10

Cited by 7 publications

(11 citation statements)

References 23 publications

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“…Therefore, Jfalse(ufalse) vanishes whenever Γ⊂Su, up to a zero Lebesgue measure set. There is a whole zoo of cost functions for partial shape-matching (see the reviews [39,40] and reference therein), sometimes involving frameworks such as varifolds [5,41] or functional maps [42]. Most of them fit into our optimal control formulation, and some of them are even differentiable.…”

Section: Towards An Optimal Control Formulationmentioning

confidence: 99%

“…Several methods for anatomical registration focus on the surface-matching problem [2][3][4][5][6]. They aim to compute a diffeomorphism between the initial liver boundary and the observed surface, and their performance is measured in terms of surface similarity between the source and target surfaces.…”

Section: Introductionmentioning

confidence: 99%

“…They aim to compute a diffeomorphism between the initial liver boundary and the observed surface, and their performance is measured in terms of surface similarity between the source and target surfaces. Pure surface-matching may be relevant for our problem when the observation represents the whole deformed boundary, or at least a large part [5], so that a volume displacement field can be reasonably computed from the reconstructed surface correspondence. In the augmented surgery setting, though, only one side of the liver appears in the camera field of view, and the observed point cloud typically covers less than 50% of the deformed boundary.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Organ registration from partial surface data in augmented surgery from an optimal control perspective

Cotin,

Mestdagh,

Privat

2024

Proc. R. Soc. A.

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We address the problem of organ registration in augmented surgery, where the deformation of the patient’s organ is reconstructed in real-time from a partial observation of its surface. Physics-based registration methods rely on adding artificial forces to drive the registration, which may result in implausible displacement fields. In this paper, we look at this inverse problem through the lens of optimal control, in an attempt to reconstruct a physically consistent surface load. The resulting optimization problem features an elastic model, a least-squares data attachment term based on orthogonal projections, and an admissible set of surface loads defined prior to reconstruction in the mechanical model. After a discussion about the existence of solutions, we analyse the necessary optimality conditions and use them to derive a suitable optimization algorithm. We implement an adjoint method and we test our approach on multiple examples, including the so-called Sparse Data Challenge . We obtain very promising results, that illustrate the feasibility of our approach with linear and nonlinear models.

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Section: Towards An Optimal Control Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Organ registration from partial surface data in augmented surgery from an optimal control perspective

Cotin,

Mestdagh,

Privat

2024

Proc. R. Soc. A.

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“…One of the successful embedding‐based approaches has been established by the functional map framework. Originally presented in Ovsjanikov et al [OBCS*12] and considerably extended in several follow‐up works [RMOW20,RCB*15,AGB*21,HAGO19], it represents correspondences between shapes as a linear transformation or mapping between their respective function spaces. This allows most constraints (descriptor preservation, operator commutativity, or landmark correspondences) to be linear, making the map inference very efficient.…”

Section: Introductionmentioning

confidence: 99%

Groupwise Shape Correspondence Refinement with a Region of Interest Focus

Galmiche,

Seo

2023

Computer Graphics Forum

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While collections of scan shapes are becoming more prevalent in many real‐world applications, finding accurate and dense correspondences across multiple shapes remains a challenging task. In this work, we introduce a new approach for refining non‐rigid correspondences among a collection of 3D shapes undergoing non‐rigid deformation. Our approach incorporates a Region Of Interest (ROI) into the refinement process, which is specified by the user on one shape within the collection. Based on the functional map framework and more specifically on the notion of cycle‐consistency, our formulation improves the overall matching consistency while prioritizing that of the region of interest. Specifically, the initial pairwise correspondences are refined by first defining the localized harmonics that are confined within the transferred ROI on each shape, and subsequently applying the CCLB (Canonical Consistent Latent Basis) framework both on the global and the localized harmonics. This leads to an enhanced matching accuracy for both the ROIs and the overall shapes across the collection. We evaluate our method on various synthetic and real scan datasets, in comparison with the state‐of‐the‐art techniques.

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“…In particular we apply the registration to the whole volumes, and must control the deformations in order to generate anatomically relevant ones. We study the clinical application of the proposed partial matching term for The present paper is an extension of Antonsanti et al (2021) from the 2021 Information Processing in Medical Imaging conference in which we introduced the partial matching in the space of varifolds.…”

Section: Introductionmentioning

confidence: 99%

How to Register a Live onto a Liver ? Partial Matching in the Space of Varifolds

Antonsanti

Benseghir

Jugnon

et al. 2022

Melba

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Partial shapes correspondences is a problem that often occurs in computer vision (occlusion, evolution in time...). In medical imaging, data may come from different modalities and be acquired under different conditions which leads to variations in shapes and topologies. In this paper we use an asymmetric data dissimilarity term applicable to various geometric shapes like sets of curves or surfaces, assessing the embedding of a shape into another one without relying on correspondences. It is designed as a data attachment for the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework, allowing to compute a meaningful deformation of one shape onto a subset of the other. We refine it in order to control the resulting non-rigid deformations and provide consistent deformations of the shapes along with their ambient space. We show that partial matching can be used for robust multi-modal liver registration between a Computed Tomography (CT) volume and a Cone Beam Computed Tomography (CBCT) volume. The 3D imaging of the patient CBCT at point of care that we call __live__ is truncated while the CT pre-intervention provides a full visualization of the __liver__. The proposed method allows the truncated surfaces from CBCT to be aligned non-rigidly, yet realistically, with surfaces from CT with an average distance of $2.6mm(+/- 2.2)$. The generated deformations extend consistently to the liver volume, and are evaluated on points of interest for the physicians, with an average distance of $5.8mm (+/- 2.7)$ for vessels bifurcations and $5.13mm (+/- 2.5)$ for tumors landmarks. Such multi-modality volumes registrations would help the physicians in the perspective of navigating their tools in the patient's anatomy to locate structures that are hardly visible in the CBCT used during their procedures.<br>Our code is available at <a href='https://github.com/plantonsanti/PartialMatchingVarifolds'>https://github.com/plantonsanti/PartialMatchingVarifolds</a>.

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Partial Matching in the Space of Varifolds

Cited by 7 publications

References 23 publications

Organ registration from partial surface data in augmented surgery from an optimal control perspective

Organ registration from partial surface data in augmented surgery from an optimal control perspective

Groupwise Shape Correspondence Refinement with a Region of Interest Focus

How to Register a Live onto a Liver ? Partial Matching in the Space of Varifolds

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