Non-local Filter Research Articles

Fusion of range and color images for denoising and resolution enhancement with a non-local filter

We present an integrated method for post-processing of range data which removes outliers, smoothes the depth values and enhances the lateral resolution in order to achieve visually pleasing 3D models from low-cost depth sensors with additional (registered) color images. The algorithm is based on the non-local principle and adapts the original NL-Means formulation to the characteristics of typical depth data. Explicitly handling outliers in the sensor data, our denoising approach achieves unbiased reconstructions from error-prone input data. Taking intra-patch similarity into account, we reconstruct strong discontinuities without disturbing artifacts and preserve fine detail structures, obtaining piece-wise smooth depth maps. Furthermore, we exploit the dependencies of the depth data with additionally available color information and increase the lateral resolution of the depth maps. We finally discuss how to parallelize the algorithm in order to achieve fast processing times that are adequate for post-processing of data from fast depth sensors such as time-of-flight cameras.

Nonlocal variational model and filter algorithm to remove multiplicative noise

The nonlocal (NL) means filter proposed by Buades, Coll, and Morel (SIAM Multiscale Model. Simul. 4(2), 490-530, 2005), which makes full use of the redundancy information in images, has shown to be very efficient for image denoising with Gauss noise added. On the basis of the NL method and a striver to minimize the conditional mean-square error, we design a NL means filter to remove multiplicative noise, and combining the NL filter to regularity method, we propose a NL total variational (TV) model and present a fast iterated algorithm for it. Experiments demonstrate that our algorithm is better than TV method; it is superior in preserving small structures and textures and can obtain an improvement in peak signal-to-noise ratio.

A filtered-wall formulation for large-eddy simulation of wall-bounded turbulence

Simulating high Reynolds number wall-bounded turbulence using large-eddy simulation (LES) requires modeling the subgrid force in the bulk of the flow and instantaneous viscous and pressure stresses at the wall. Here, LES of turbulent channel flow is conducted at Reτ=590 using a filtered-wall formulation, in which a buffer region with u=0 is attached adjacent to the wall, and the underlying velocity field defined over the extended domain is filtered using a nonlocal filter (in this case, a Fourier cutoff filter) in all directions. The instantaneous wall stress is computed by first prescribing a target velocity field for the filtered velocity inside the buffer and then minimizing the error between the actual and target velocity at every time step. The optimal LES (OLES) approach is used to model the subgrid force in terms of the resolved velocity field via linear stochastic estimation. The correlations required to carry out this stochastic estimation are computed from direct numerical simulation (DNS). Results of the LES simulation show reasonable agreement with filtered DNS statistics. Also, simulations performed after introducing modifications to the linear OLES kernel show that the positive eigenvalues in the kernel and the skew-symmetric part of the kernel play important roles in LES of wall-bounded turbulence.

Efficient Nonlocal Means for Denoising of Textural Patterns

This paper contributes two novel techniques in the context of image restoration by nonlocal filtering. First, we introduce an efficient implementation of the nonlocal means filter based on arranging the data in a cluster tree. The structuring of data allows for a fast and accurate preselection of similar patches. In contrast to previous approaches, the preselection is based on the same distance measure as used by the filter itself. It allows for large speedups, especially when the search for similar patches covers the whole image domain, i.e., when the filter is truly nonlocal. However, also in the windowed version of the filter, the cluster tree approach compares favorably to previous techniques in respect of quality versus computational cost. Second, we suggest an iterative version of the filter that is derived from a variational principle and is designed to yield nontrivial steady states. It reveals to be particularly useful in order to restore regular, textured patterns.

Impurity states and interlayer tunneling in high temperature superconductors.

We argue that the scanning tunneling microscope (STM) images of resonant states generated by doping Zn or Ni impurities into Cu-O planes of BSCCO are the result of quantum interference of the impurity signal coming from several distinct paths. The impurity image seen on the surface is greatly affected by interlayer tunneling matrix elements. We find that the optimal tunneling path between the STM tip and the metal (Cu, Zn, or Ni) d(x(2)-y(2)) orbitals in the Cu-O plane involves intermediate excited states. This tunneling path leads to the fourfold nonlocal filter of the impurity state in Cu-O plane that explains the experimental impurity spectra. Applications of the tunneling filter to the Cu vacancy defects and "direct" tunneling into Cu-O planes are also discussed.

Region of Interest Reconstruction of Tomographic Images using Filter Banks

A new technique for ROI image reconstruction from projections using filter banks is reported in this paper. It is known that the convolution back projection operator, used for reconstruction of images from 1D-projections, has a non-local filter which requires global projection data. In X-ray tomography, the exposure time of the object to harmful radiation is thereby increased. Recently, it has been proved that this filtering operation can be done on a chosen wavelet function instead of the projections. This localizes the filter and leads to ROI image reconstruction with reduced projections. This concept was extended using 2D and 1D MRA filter banks, in which the filters are combined with the non-local CBP filter to get short length filters. In this paper it is proved that the presence of unwanted information in all previous algorithms is due to aliasing and a new technique is proposed for reconstruction without any aliasing. The proposed scheme is implemented using Shepp-Logan phantom head image and the performance is compared.