Elastic Shape Analysis of Surfaces with Second-Order Sobolev Metrics: A Comprehensive Numerical Framework

Hartman, Emmanuel; Sukurdeep, Yashil; Klassen, Eric; Charon, Nicolas; Bauer, Martin

doi:10.1007/s11263-022-01743-0

Cited by 21 publications

(4 citation statements)

References 68 publications

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“…There has also been recent research on elastic methods focused on surfaces (Hartman et al, 2023;Jermyn et al, 2017;Pierson et al, 2021). As described in Hartman et al (2023), the techniques here can be categorised into two sections, those that apply to parameterised surfaces and those on unparameterised surfaces (i.e., containing no known point landmarks). Methods of elastic shape analysis can play an important role in ML, whether this is with classical methods or combined with the latest DL tools.…”

Section: Landmark-free Morphometricsmentioning

confidence: 99%

Challenges and opportunities in applying AI to evolutionary morphology

He,

Mulqueeney,

Watt

et al. 2024

Preprint

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Artificial intelligence (AI) is poised to transform many aspects of society, and the study of evolutionary morphology is no exception. Machine learning-grade methods of AI such as Principal Component Analysis (PCA) and Cluster Analysis have been commonplace in evolutionary morphology for decades, but the last decade has seen increasing application of Deep Learning to ecology and evolutionary biology, opening up the potential to circumvent longstanding barriers to rapid, big data analysis of phenotype. Here we review the current state of AI methods available for the study of evolutionary morphology and discuss the prospectus for near-term advances in specific subfields of this research area, including the potential of new AI methods that have not yet been applied to the study of morphological evolution. We introduce the main available AI techniques, categorising them into three stages based on their order of appearance: (i) Machine Learning, (ii) Deep Learning with neural networks and (iii) the most recent advancements in large-scale models and multimodal learning. Next, we present existing AI approaches and case studies using AI for evolutionary morphology, including image capture and segmentation, feature recognition, morphometrics, phylogenetics, and biomechanics. Finally, we discuss areas where there is potential, but no current application of AI to key areas in evolutionary morphology. Combined, these advancements and potential developments have the capacity to transform the evolutionary analysis of organismal phenotype into evolutionary phenomics, launch it fully in the “Big Data'' sphere, and align it with genomics and other areas of bioinformatics.

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Section: Landmark-free Morphometricsmentioning

confidence: 99%

Challenges and opportunities in applying AI to evolutionary morphology

He,

Mulqueeney,

Watt

et al. 2024

Preprint

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“…A whole category of existing methods for intra-operative registration is inherited from socalled elastic image registration methods [12,Section II.A.1], where a cost function is minimized to enforce landmark or surface correspondence, while an elastic model is used to regularize the displacement field [13][14][15][16][17]. These methods simulate fictitious forces that attract the liver towards the observed surface, in the same fashion as the Iterative Closest Point algorithm [18].…”

Section: Introductionmentioning

confidence: 99%

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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“…Recognizing the similarity and correspondences between two nonrigid shapes is a fundamental problem in computer vision and graphics (Van Kaick et al 2011;Sahillioglu 2020), such as shape analysis (Hartman et al 2023), style transfer (Sumner and Popović 2004), pose estimation (Jiang et al 2022), and texture mapping (Ezuz and Ben-Chen 2017). Unlike rigid alignment with easy parametric modeling, the complexity of nonrigid transformation and the existence of unknown outliers make such a problem intractable to be modeled.…”

Section: Introductionmentioning

confidence: 99%

Locality Preserving Refinement for Shape Matching with Functional Maps

Xia,

Lu,

Gao

et al. 2024

AAAI

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In this paper, we address the nonrigid shape matching with outliers by a novel and effective pointwise map refinement method, termed Locality Preserving Refinement. For accurate pointwise conversion from a given functional map, our method formulates a two-step procedure. Firstly, starting with noisy point-to-point correspondences, we identify inliers by leveraging the neighborhood support, which yields a closed-form solution with linear time complexity. After obtained the reliable correspondences of inliers, we refine the pointwise correspondences for outliers using local linear embedding, which operates in an adaptive spectral similarity space to further eliminate the ambiguities that are difficult to handle in the functional space. By refining pointwise correspondences with local consistency thus embedding geometric constraints into functional spaces, our method achieves considerable improvement in accuracy with linearithmic time and space cost. Extensive experiments on public benchmarks demonstrate the superiority of our method over the state-of-the-art methods. Our code is publicly available at https://github.com/XiaYifan1999/LOPR.

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Elastic Shape Analysis of Surfaces with Second-Order Sobolev Metrics: A Comprehensive Numerical Framework

Cited by 21 publications

References 68 publications

Challenges and opportunities in applying AI to evolutionary morphology

Challenges and opportunities in applying AI to evolutionary morphology

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

Locality Preserving Refinement for Shape Matching with Functional Maps

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