676 research outputs found
Detail-preserving and Content-aware Variational Multi-view Stereo Reconstruction
Accurate recovery of 3D geometrical surfaces from calibrated 2D multi-view
images is a fundamental yet active research area in computer vision. Despite
the steady progress in multi-view stereo reconstruction, most existing methods
are still limited in recovering fine-scale details and sharp features while
suppressing noises, and may fail in reconstructing regions with few textures.
To address these limitations, this paper presents a Detail-preserving and
Content-aware Variational (DCV) multi-view stereo method, which reconstructs
the 3D surface by alternating between reprojection error minimization and mesh
denoising. In reprojection error minimization, we propose a novel inter-image
similarity measure, which is effective to preserve fine-scale details of the
reconstructed surface and builds a connection between guided image filtering
and image registration. In mesh denoising, we propose a content-aware
-minimization algorithm by adaptively estimating the value and
regularization parameters based on the current input. It is much more promising
in suppressing noise while preserving sharp features than conventional
isotropic mesh smoothing. Experimental results on benchmark datasets
demonstrate that our DCV method is capable of recovering more surface details,
and obtains cleaner and more accurate reconstructions than state-of-the-art
methods. In particular, our method achieves the best results among all
published methods on the Middlebury dino ring and dino sparse ring datasets in
terms of both completeness and accuracy.Comment: 14 pages,16 figures. Submitted to IEEE Transaction on image
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A mixed regularization approach for sparse simultaneous approximation of parameterized PDEs
We present and analyze a novel sparse polynomial technique for the
simultaneous approximation of parameterized partial differential equations
(PDEs) with deterministic and stochastic inputs. Our approach treats the
numerical solution as a jointly sparse reconstruction problem through the
reformulation of the standard basis pursuit denoising, where the set of jointly
sparse vectors is infinite. To achieve global reconstruction of sparse
solutions to parameterized elliptic PDEs over both physical and parametric
domains, we combine the standard measurement scheme developed for compressed
sensing in the context of bounded orthonormal systems with a novel mixed-norm
based regularization method that exploits both energy and sparsity. In
addition, we are able to prove that, with minimal sample complexity, error
estimates comparable to the best -term and quasi-optimal approximations are
achievable, while requiring only a priori bounds on polynomial truncation error
with respect to the energy norm. Finally, we perform extensive numerical
experiments on several high-dimensional parameterized elliptic PDE models to
demonstrate the superior recovery properties of the proposed approach.Comment: 23 pages, 4 figure
Graph Spectral Image Processing
Recent advent of graph signal processing (GSP) has spurred intensive studies
of signals that live naturally on irregular data kernels described by graphs
(e.g., social networks, wireless sensor networks). Though a digital image
contains pixels that reside on a regularly sampled 2D grid, if one can design
an appropriate underlying graph connecting pixels with weights that reflect the
image structure, then one can interpret the image (or image patch) as a signal
on a graph, and apply GSP tools for processing and analysis of the signal in
graph spectral domain. In this article, we overview recent graph spectral
techniques in GSP specifically for image / video processing. The topics covered
include image compression, image restoration, image filtering and image
segmentation
Semi-Sparsity for Smoothing Filters
In this paper, we propose an interesting semi-sparsity smoothing algorithm
based on a novel sparsity-inducing optimization framework. This method is
derived from the multiple observations, that is, semi-sparsity prior knowledge
is more universally applicable, especially in areas where sparsity is not fully
admitted, such as polynomial-smoothing surfaces. We illustrate that this
semi-sparsity can be identified into a generalized -norm minimization in
higher-order gradient domains, thereby giving rise to a new "feature-aware"
filtering method with a powerful simultaneous-fitting ability in both sparse
features (singularities and sharpening edges) and non-sparse regions
(polynomial-smoothing surfaces). Notice that a direct solver is always
unavailable due to the non-convexity and combinatorial nature of -norm
minimization. Instead, we solve the model based on an efficient half-quadratic
splitting minimization with fast Fourier transforms (FFTs) for acceleration. We
finally demonstrate its versatility and many benefits to a series of
signal/image processing and computer vision applications
A new nonlocal nonlinear diffusion equation for image denoising and data analysis
In this paper we introduce and study a new feature-preserving nonlinear
anisotropic diffusion for denoising signals. The proposed partial differential
equation is based on a novel diffusivity coefficient that uses a nonlocal
automatically detected parameter related to the local bounded variation and the
local oscillating pattern of the noisy input signal. We provide a mathematical
analysis of the existence of the solution of our nonlinear and nonlocal
diffusion equation in the two dimensional case (images processing). Finally, we
propose a numerical scheme with some numerical experiments which demonstrate
the effectiveness of the new method
Bilateral Filter: Graph Spectral Interpretation and Extensions
In this paper we study the bilateral filter proposed by Tomasi and Manduchi,
as a spectral domain transform defined on a weighted graph. The nodes of this
graph represent the pixels in the image and a graph signal defined on the nodes
represents the intensity values. Edge weights in the graph correspond to the
bilateral filter coefficients and hence are data adaptive. Spectrum of a graph
is defined in terms of the eigenvalues and eigenvectors of the graph Laplacian
matrix. We use this spectral interpretation to generalize the bilateral filter
and propose more flexible and application specific spectral designs of
bilateral-like filters. We show that these spectral filters can be implemented
with k-iterative bilateral filtering operations and do not require expensive
diagonalization of the Laplacian matrix
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