Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence

Donati, Nicolas; Sharma, Abhishek; Ovsjanikov, Maks

doi:10.1109/cvpr42600.2020.00862

Cited by 129 publications

(169 citation statements)

References 35 publications

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“…This yields better pointwise maps (color transfer) with improvement in bijectivity (errors in red). plied in both axiomatic [28,16,14,32] and learning-based [18,35,13,8] settings. However, one of the recurring issues of virtually all works in this domain, is defining and using the exact relation between functional and pointwise maps.…”

Section: Sourcementioning

confidence: 99%

Fast Sinkhorn Filters: Using Matrix Scaling for Non-Rigid Shape Correspondence with Functional Maps

Pai

Ren

Melzi

et al. 2021

2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

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Section: Sourcementioning

confidence: 99%

Fast Sinkhorn Filters: Using Matrix Scaling for Non-Rigid Shape Correspondence with Functional Maps

Pai

Ren

Melzi

et al. 2021

2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

Self Cite

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“…Lim et al [2018] apply recurrent neural networks (RNNs) to compute vertex features after unrolling local neighborhoods into prescribed spiral patterns. Deep functional maps [Litany et al 2017] largely rely on precomputed features for geometric information, although some recent efforts bring this correspondence method closer to end-to-end [Donati et al 2020;.…”

Section: Neural Network On Meshesmentioning

confidence: 99%

HodgeNet

Smirnov

Solomon

2021

ACM Trans. Graph.

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Fig. 1. Mesh segmentation results on the full-resolution MIT animation dataset. Each mesh in the dataset contains 20,000 faces (10,000 vertices). We show an example ground truth segmentation in the bottom-left. In contrast to previous works, which downsample each mesh by more than 10×, we efficiently process dense meshes both at train and test time.Constrained by the limitations of learning toolkits engineered for other applications, such as those in image processing, many mesh-based learning algorithms employ data flows that would be atypical from the perspective of conventional geometry processing. As an alternative, we present a technique for learning from meshes built from standard geometry processing modules and operations. We show that low-order eigenvalue/eigenvector computation from operators parameterized using discrete exterior calculus is amenable to efficient approximate backpropagation, yielding spectral per-element or per-mesh features with similar formulas to classical descriptors like the heat/wave kernel signatures. Our model uses few parameters, generalizes to high-resolution meshes, and exhibits performance and time complexity on par with past work.

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“…Instead of using precomputed SHOT or WKS descriptors as the functions in a functional maps framework, several recent methods focus on learning spectral descriptors via the functional characterization of the vertices/point clouds of polygon models [36,60]. These approaches use specialized neural network architectures (e.g., PointNet++) or novel convolutional kernels (GCCN, MDGCN.…”

Section: Learning Intrinsic Features From Surfacesmentioning

confidence: 99%

“…[61][62][63][64]) capable of exploiting the geometric features of point-clouds or triangular meshes. These descriptor learning models replace the Siamese ResNet architecture of FMNet with spatial feature extractors that have been implemented in a Siamese way [60]. Given the unstructured point clouds, they create new features that are invariant to translation, rotation, and point order.…”

Section: Learning Intrinsic Features From Surfacesmentioning

confidence: 99%

Automated morphological phenotyping using learned shape descriptors and functional maps: A novel approach to geometric morphometrics

Thomas

Shen

et al. 2021

Preprint

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The methods of geometric morphometrics are commonly used to quantify morphology in a broad range of biological sciences. The application of these methods to large datasets is constrained by manual landmark placement limiting the number of landmarks and introducing observer bias. To move the field forward, we need to automate morphological phenotyping in ways that capture comprehensive representations of morphological variation with minimal observer bias. Here, we present Morphological Variation Quantifier (morphVQ), a shape analysis pipeline for quantifying, analyzing, and exploring shape variation in the functional domain. morphVQ uses descriptor learning to estimate the functional correspondence between whole triangular meshes in lieu of landmark configurations. With functional maps between pairs of specimens in a dataset we can analyze and explore shape variation. morphVQ uses Consistent ZoomOut refinement to improve these functional maps and produce a new representation of shape variation, area-based and conformal (angular) latent shape space differences (LSSDs). We compare this new representation of shape variation to shape variables obtained via manual digitization and auto3DGM, an existing approach to automated morphological phenotyping. We find that LSSDs compare favorably to modern 3DGM and auto3DGM while being more computationally efficient. By characterizing whole surfaces, our method incorporates more morphological detail in shape analysis. We can classify known biological groupings, such as Genus affiliation with comparable accuracy. The shape spaces produced by our method are similar to those produced by modern 3DGM and to auto3DGM, and distinctiveness functions derived from LSSDs show us how shape variation differs between groups. morphVQ can capture shape in an automated fashion while avoiding the limitations of manually digitized landmarks, and thus represents a novel and computationally efficient addition to the geometric morphometrics toolkit.

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Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence

Cited by 129 publications

References 35 publications

Fast Sinkhorn Filters: Using Matrix Scaling for Non-Rigid Shape Correspondence with Functional Maps

Fast Sinkhorn Filters: Using Matrix Scaling for Non-Rigid Shape Correspondence with Functional Maps

HodgeNet

Automated morphological phenotyping using learned shape descriptors and functional maps: A novel approach to geometric morphometrics

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