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This paper focuses on the registration problem of shape graphs, where a shape graph is a set of nodes connected by articulated curves with arbitrary shapes. This registration requires optimization over the permutation group, made challenging by differences in nodes (in terms of numbers, locations) and edges (in terms of shapes, placements, and sizes) across graphs. We tackle this registration problem using a neuralnetwork architecture with an unsupervised loss function based on the elastic shape metric for curves. This architecture results in (1) state-of-the-art matching performance and (2) an order of magnitude reduction in the computational cost relative to baseline approaches. We demonstrate the effectiveness of the proposed approach using both simulated data and real-world 2D retinal blood vessels and 3D microglia graphs.
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SrvfRegNet: Elastic Function Registration Using Deep Neural Networks
Registering functions (curves) using time warpings (re-parameterizations) is central to many computer vision and shape analysis solutions. While traditional registration methods minimize penalized-L2 norm, the elastic Riemannian metric and square-root velocity functions (SRVFs) have resulted in significant improvements in terms of theory and practical performance. This solution uses the dynamic programming algorithm to minimize the L2 norm between SRVFs of given functions. However, the computational cost of this elastic dynamic programming framework – O(nT 2 k) – where T is the number of time samples along curves, n is the number of curves, and k < T is a parameter – limits its use in applications involving big data. This paper introduces a deep-learning approach, named SRVF Registration Net or SrvfRegNet to overcome these limitations. SrvfRegNet architecture trains by optimizing the elastic metric-based objective function on the training data and then applies this trained network to the test data to perform fast registration. In case the training and the test data are from different classes, it generalizes to the test data using transfer learning, i.e., retraining of only the last few layers of the network. It achieves the state-of-the-art alignment performance albeit at much reduced computational cost. We demonstrate the efficiency and efficacy of this framework using several standard curve datasets.
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- PAR ID:
- 10339553
- Date Published:
- Journal Name:
- 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW)
- Page Range / eLocation ID:
- 4457 to 4466
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/CVPRW53098.2021.00503
