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Abstract We introduce parametric level-set enhanced to improve reconstruction (PaLEnTIR), a significantly enhanced parametric level-set (PaLS) method addressing the restoration and reconstruction of piecewise constant objects. Our key contribution involves a unique PaLS formulation utilizing a single level-set function to restore scenes containing multi-contrast piecewise constant objects without requiring knowledge of the number of objects or their contrasts. Unlike standard PaLS methods employing radial basis functions (RBFs), our model integrates anisotropic basis functions (ABFs), thereby expanding its capacity to represent a wider class of shapes. Furthermore, PaLEnTIR streamlines the model by reducing redundancy and indeterminacy in the parameterization, resulting in improved numerical performance. We compare PaLEnTIR’s performance to state-of-the art alternatives via a diverse collection of experiments encompassing denoising, deconvolution, sparse and limited angle of view x-ray computed tomography (2D and 3D), and nonlinear diffuse optical tomography tasks using both real and simulated data sets.
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Neural Fields as Learnable Kernels for 3D Reconstruction
We present Neural Kernel Fields: a novel method for reconstructing implicit 3D shapes based on a learned kernel ridge regression. Our technique achieves state-of-the-art results when reconstructing 3D objects and large scenes from sparse oriented points, and can reconstruct shape categories outside the training set with almost no drop in accuracy. The core insight of our approach is that kernel methods are extremely effective for reconstructing shapes when the chosen kernel has an appropriate inductive bias. We thus factor the problem of shape reconstruction into two parts: (1) a backbone neural network which learns kernel parameters from data, and (2) a kernel ridge regression that fits the input points on-the-fly by solving a simple positive definite linear system using the learned kernel. As a result of this factorization, our reconstruction gains the benefits of datadriven methods under sparse point density while maintaining interpolatory behavior, which converges to the ground truth shape as input sampling density increases. Our experiments demonstrate a strong generalization capability to objects outside the train-set category and scanned scenes. Source code and pretrained models are available at https:// nv-tlabs.github.io/nkf.
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- PAR ID:
- 10329470
- Date Published:
- Journal Name:
- IEEE Computer Society Conference on Computer Vision and Pattern Recognition
- ISSN:
- 2332-564X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
