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Register a new userImplicit reconstructions of thin leaf surfaces from large, noisy point clouds
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Added by
Timothy Moroney
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Thin surfaces, such as the leaves of a plant, pose a significant challenge for implicit surface reconstruction techniques, which typically assume a closed, orientable surface. We show that by approximately interpolating a point cloud of the surface (augmented with off-surface points) and restricting the evaluation of the interpolant to a tight domain around the point cloud, we need only require an orientable surface for the reconstruction. We use polyharmonic smoothing splines to fit approximate interpolants to noisy data, and a partition of unity method with an octree-like strategy for choosing subdomains. This method enables us to interpolate an N-point dataset in O(N) operations. We present results for point clouds of capsicum and tomato plants, scanned with a handheld device. An important outcome of the work is that sufficiently smooth leaf surfaces are generated that are amenable for droplet spreading simulations.
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Measurement data in linear systems arising from real-world applications often suffers from both large, sparse corruptions, and widespread small-scale noise. This can render many popular solvers ineffective, as the least squares solution is far from the desired solution, and the underlying consistent system becomes harder to identify and solve. QuantileRK is a member of the Kaczmarz family of iterative projective methods that has been shown to converge exponentially for systems with arbitrarily large sparse corruptions. In this paper, we extend the analysis to the case where there are not only corruptions present, but also noise that may affect every data point, and prove that QuantileRK converges with the same rate up to an error threshold. We give both theoretical and experimental results demonstrating QuantileRKs strength.
We consider the problem of reconstructing the position and the time-dependent optical properties of a linear dispersive medium from OCT measurements. The medium is multi-layered described by a piece-wise inhomogeneous refractive index. The measurement data are from a frequency-domain OCT system and we address also the phase retrieval problem. The parameter identification problem can be formulated as an one-dimensional inverse problem. Initially, we deal with a non-dispersive medium and we derive an iterative scheme that is the core of the algorithm for the frequency-dependent parameter. The case of absorbing medium is also addressed.
The first numerical implementation of a D-bar method in 3D using electrode data is presented. Results are compared to Calderons method as well as more common TV and smoothness regularization-based methods. D-bar methods are based on tailor-made non-linear Fourier transforms involving the measured current and voltage data. Low-pass filtering in the non-linear Fourier domain is used to stabilize the reconstruction process. D-bar methods have shown great promise in 2D for providing robust real-time absolute and time-difference conductivity reconstructions but have yet to be used on practical electrode data in 3D, until now. Results are presented for simulated data for conductivity and permittivity with disjoint non-radially symmetric targets on spherical domains and noisy voltage data. The 3D D-bar and Calderon methods are demonstrated to provide comparable quality to their 2D CGO counterparts, and hold promise for real-time reconstructions.
We prove the support recovery for a general class of linear and nonlinear evolutionary partial differential equation (PDE) identification from a single noisy trajectory using $ell_1$ regularized Pseudo-Least Squares model~($ell_1$-PsLS). In any associative $mathbb{R}$-algebra generated by finitely many differentiation operators that contain the unknown PDE operator, applying $ell_1$-PsLS to a given data set yields a family of candidate models with coefficients $mathbf{c}(lambda)$ parameterized by the regularization weight $lambdageq 0$. The trace of ${mathbf{c}(lambda)}_{lambdageq 0}$ suffers from high variance due to data noises and finite difference approximation errors. We provide a set of sufficient conditions which guarantee that, from a single trajectory data denoised by a Local-Polynomial filter, the support of $mathbf{c}(lambda)$ asymptotically converges to the true signed-support associated with the underlying PDE for sufficiently many data and a certain range of $lambda$. We also show various numerical experiments to validate our theory.
This paper presents a novel unsupervised approach to reconstruct human shape and pose from noisy point cloud. Traditional approaches search for correspondences and conduct model fitting iteratively where a good initialization is critical. Relying on large amount of dataset with ground-truth annotations, recent learning-based approaches predict correspondences for every vertice on the point cloud; Chamfer distance is usually used to minimize the distance between a deformed template model and the input point cloud. However, Chamfer distance is quite sensitive to noise and outliers, thus could be unreliable to assign correspondences. To address these issues, we model the probability distribution of the input point cloud as generated from a parametric human model under a Gaussian Mixture Model. Instead of explicitly aligning correspondences, we treat the process of correspondence search as an implicit probabilistic association by updating the posterior probability of the template model given the input. A novel unsupervised loss is further derived that penalizes the discrepancy between the deformed template and the input point cloud conditioned on the posterior probability. Our approach is very flexible, which works with both complete point cloud and incomplete ones including even a single depth image as input. Our network is trained from scratch with no need to warm-up the network with supervised data. Compared to previous unsupervised methods, our method shows the capability to deal with substantial noise and outliers. Extensive experiments conducted on various public synthetic datasets as well as a very noisy real dataset (i.e. CMU Panoptic) demonstrate the superior performance of our approach over the state-of-the-art methods. Code can be found url{https://github.com/wangsen1312/unsupervised3dhuman.git}
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