Supervised deep learning of elastic SRV distances on the shape space of curves

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

doi:10.1109/cvprw53098.2021.00499

Cited by 6 publications

(3 citation statements)

References 16 publications

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“…The choice of metric here can sometimes greatly affect the results, and naturally there are times where a landmark-free elastic (e.g., geodesic) metric can be better suited to the algorithm than standard (often linear) metrics. Furthermore, there have recently been studies that have incorporated DL techniques with elastic metrics, such as in Hartman et al (2021). Here, a Siamese neural network was trained to predict square root velocity distances between curves, such as the boundary curves of leaves from the notable Swedish Leaf Dataset (Söderkvist, 2016(Söderkvist, , 2001.…”

Section: Machine Learning Algorithms With Elastic Metrics ML Algorith...mentioning

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: Machine Learning Algorithms With Elastic Metrics ML Algorith...mentioning

confidence: 99%

Challenges and opportunities in applying AI to evolutionary morphology

He,

Mulqueeney,

Watt

et al. 2024

Preprint

View full text Add to dashboard Cite

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“…Note that this is comparable to the correlation of elastic distances between functions on the line that are either computed using dynamic programming or computed using an exact algorithm, cf. [19,54,32].…”

Section: 2mentioning

confidence: 99%

The Square Root Normal Field Distance and Unbalanced Optimal Transport

Bauer¹,

Hartman²,

Klassen³

2021

Preprint

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This paper explores a novel connection between two areas: shape analysis of surfaces and unbalanced optimal transport. Specifically, we characterize the square root normal field (SRNF) shape distance as the pullback of the Wasserstein-Fisher-Rao (WFR) unbalanced optimal transport distance. In addition we propose a new algorithm for computing the WFR distance and present numerical results that highlight the effectiveness of this algorithm. As a consequence of our results we obtain a precise method for computing the SRNF shape distance directly on piecewise linear surfaces and gain new insights about the degeneracy of this distance.Contents 2020 Mathematics Subject Classification. 49Q10.

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“…More specifically, we train a deep convolutional neural network to learn SRV distances, using training data consisting of pairs of discretized functions or curves, together with the SRV distance between them as labels. Our source code is publicly available on github [7].…”

Section: Introductionmentioning

confidence: 99%

Supervised deep learning of elastic SRV distances on the shape space of curves

Hartman¹,

Sukurdeep²,

Charon³

et al. 2021

Preprint

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Motivated by applications from computer vision to bioinformatics, the field of shape analysis deals with problems where one wants to analyze geometric objects, such as curves, while ignoring actions that preserve their shape, such as translations, rotations, or reparametrizations. Mathematical tools have been developed to define notions of distances, averages, and optimal deformations for geometric objects. One such framework, which has proven to be successful in many applications, is based on the square root velocity (SRV) transform, which allows one to define a computable distance between spatial curves regardless of how they are parametrized. This paper introduces a supervised deep learning framework for the direct computation of SRV distances between curves, which usually requires an optimization over the group of reparametrizations that act on the curves. The benefits of our approach in terms of computational speed and accuracy are illustrated via several numerical experiments.

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Supervised deep learning of elastic SRV distances on the shape space of curves

Cited by 6 publications

References 16 publications

Challenges and opportunities in applying AI to evolutionary morphology

Challenges and opportunities in applying AI to evolutionary morphology

The Square Root Normal Field Distance and Unbalanced Optimal Transport

Supervised deep learning of elastic SRV distances on the shape space of curves

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