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Efficient Beltrami Flow Using a Short Time Kernel [chapter]

Alon Spira, Ron Kimmel, Nir Sochen
2003 Lecture Notes in Computer Science  
À Ø ÜÔ ¾ Ø À ½ Ø À ¼ Ø ¾ À ½ Ø · À ¼ ¾ Ø ¿ · À ½ ¾ Ø ¾ · Ç´½ Ø µ ÜÔ ¾ Ø À ¼ ¾ Ø ¿ · À ½ ¾ À ¼ Ø ¾ · Ç´½ Ø µ ÜÔ ¾ Ø ´½ µ ÓÖ Ø Ö Ø Ò × Ó ÕÙ Ø ÓÒ´½ µ Û ÐÙÐ Ø Ã Ã Ù À ¼ Ø ¾À ¼ Ø ¾ ¾À ½ Ø · Ç´½µ ÜÔ ¾ Ø ´¾¼µ  ...  ¾ ´¿µ Û Ö Á ¸ Á Ù º ÓÖ ÓÐÓÖ Ñ × ´Ù ½ Ù ¾ µ Ù ½ Ù ¾ Á ½´Ù½ Ù ¾ µ Á ¾´Ù½ Ù ¾ µ Á ¿´Ù½ Ù ¾ µ ´ µ Û Ö Á ½ Á ¾ Á ¿ Ö Ø Ø Ö ÓÐÓÖ ÓÑÔÓÒ ÒØ×´ ÓÖ Ò×Ø Ò Ö ¸ Ö Ò Ò ÐÙ ÓÖ Ø Ê ÓÐÓÖ ×Ô µº Ì Ñ ØÖ Ó Ø ×Ô ¹ ØÙÖ Ñ Ò ÓÐ  ... 
doi:10.1007/3-540-44935-3_35 fatcat:6jhxupzlkbdytjgvbsr2tjccaq

A Short- Time Beltrami Kernel for Smoothing Images and Manifolds

Alon Spira, Ron Kimmel, Nir Sochen
2007 IEEE Transactions on Image Processing  
We introduce a short-time kernel for the Beltrami image enhancing flow.  ...  On a practical level, the use of the kernel allows arbitrarily large time steps as opposed to the existing explicit numerical schemes for the Beltrami flow.  ...  We, therefore, develop a short-time kernel that if used iteratively, has an equivalent effect to that of the Beltrami flow. The main idea behind the kernel is presented in Fig. 2 for a 1-D signal.  ... 
doi:10.1109/tip.2007.894253 pmid:17547140 fatcat:bjfxfzuokra55fpizzfsensr4i

On Semi-implicit Splitting Schemes for the Beltrami Color Flow [chapter]

Lorina Dascal, Guy Rosman, Xue-Cheng Tai, Ron Kimmel
2009 Lecture Notes in Computer Science  
The Beltrami flow is an efficient non-linear filter, that was shown to be effective for color image processing.  ...  Usually, this flow is implemented by explicit schemes, that are stable only for small time steps and therefore require many iterations.  ...  As an alternative to the explicit scheme, an approximation using the short time kernel of the Beltrami operator was suggested in [4] .  ... 
doi:10.1007/978-3-642-02256-2_22 fatcat:eml44g24grbq7ad7bkgx7utssy

Polyakov Action Minimization for Efficient Color Image Processing [chapter]

Guy Rosman, Xue-Cheng Tai, Lorina Dascal, Ron Kimmel
2012 Lecture Notes in Computer Science  
It was proven to be useful for color image processing as it models a meaningful coupling between the color channels.  ...  Here, we propose to use an augmented Lagrangian approach to design an efficient and accurate regularization framework for color image processing by minimizing the Polyakov action.  ...  In future work we intend to add a robust fidelity term [36] , and explore other possible applications for our framework.  ... 
doi:10.1007/978-3-642-35740-4_5 fatcat:k7pe6jc4rnczzovi6gui3pxsru

On Semi-implicit Splitting Schemes for the Beltrami Color Image Filtering

Guy Rosman, Lorina Dascal, Xue-Cheng Tai, Ron Kimmel
2011 Journal of Mathematical Imaging and Vision  
The Beltrami flow is an efficient nonlinear filter, that was shown to be effective for color image processing.  ...  Usually, this flow is implemented by explicit schemes, that are stable only for very small time steps and therefore require many iterations.  ...  Open Access This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided  ... 
doi:10.1007/s10851-010-0254-y fatcat:qbug3puwf5d7pgndvtprdo5g7a

Efficient Beltrami Flow in Patch-Space [chapter]

Aaron Wetzler, Ron Kimmel
2012 Lecture Notes in Computer Science  
As a motivation we demonstrate the performance of the Beltrami filter in patch-space, and provide useful implementation considerations that allow for parameter tuning and efficient implementation on hand-held  ...  Image selective smoothing, often referred to as a denoising filter, amounts to the process of area minimization of the image surface by mean curvature flow.  ...  The same can be said for the short time Beltrami kernel as described by Spira et al. in [10] where it is approximated by finding local geodesic distances on the manifold via the fast marching method  ... 
doi:10.1007/978-3-642-24785-9_12 fatcat:hichdzmkcbgxnguz7z3sdfyajq

Edge Preserving Filters using Geodesic Distances on Weighted Orthogonal Domains

Luca Bertelli, B.S. Manjunath
2007 Proceedings of IEEE international conference on image processing  
The weight function is computed to capture the underlying structure of the image manifold, but allowing at the same time to efficiently solve, using the Fast Marching algorithm on orthogonal domains, the  ...  We introduce a framework for image enhancement, which smooths images while preserving edge information.  ...  det(M)M −1 ∇I i (11) In [7] an iterative implementation of the PDE is replaced with a one step filter using a short time kernel.  ... 
doi:10.1109/icip.2007.4378956 dblp:conf/icip/BertelliM07 fatcat:vrs54og2fjgq3c356alfb2ahpy

Efficient Beltrami Image Filtering via Vector Extrapolation Methods

Guy Rosman, Lorina Dascal, Avram Sidi, Ron Kimmel
2009 SIAM Journal of Imaging Sciences  
The Beltrami framework, introduced in As an alternative to the explicit scheme, an approximation using the short time kernel for the Beltrami operator was suggested in [40] .  ...  Unlike related nonlinear filters such as the total variation (TV) filter [23, 1, 8] , which can be computed efficiently using semiimplicit schemes [43] , the Beltrami flow is usually implemented by an  ...  Functionals using the Beltrami flow for regularization can be written in the general form Ψ = α 2 3 a=1 ||KI a − I a 0 || 2 + S(X), where K is a bounded linear operator.  ... 
doi:10.1137/080728391 fatcat:tjvq3pizdzcrdpxi5wu7lkn2nq

Multi-scale anisotropic heat diffusion based on normal-driven shape representation

Shengfa Wang, Tingbo Hou, Zhixun Su, Hong Qin
2011 The Visual Computer  
The anisotropic heat diffusion is conducted using the weighted heat kernel convolution governed by local geometry.  ...  This diffusion is an efficient multi-scale procedure that rigorously conserves the total heat.  ...  Therefore, heat kernels often start from a moderate scale and ignore short-time scales.  ... 
doi:10.1007/s00371-011-0582-y fatcat:pbmkc63k3nfbhnaehhjjccv3t4

Color Image Enhancement by a Forward-and-Backward Adaptive Beltrami Flow [chapter]

Nir A. Sochen, Guy Gilboa, Yehoshua Y. Zeevi
2000 Lecture Notes in Computer Science  
To control and stabilize the process, a nonlinear structure tensor is incorporated. The structure tensor is locally adjusted according to a gradient-type measure.  ...  The Beltrami diffusion-type process, reformulated for the purpose of image processing, is generalized to an adaptive forward-andbackward process and applied in localized image features' enhancement and  ...  The evolution is a consequence of a non-linear PDE. No global (timewise) kernels can be associated with these non-linear PDE's. Short time kernels for these processes were derived recently in [15] .  ... 
doi:10.1007/10722492_25 fatcat:gr5y4xvdlncaxhw6dxzyowzfh4

Diffusion-based clustering analysis of coherent X-ray scattering patterns of self-assembled nanoparticles

Hao Huang, Shinjae Yoo, Konstantine Kaznatcheev, Kevin G. Yager, Fang Lu, Dantong Yu, Oleg Gang, Andrei Fluerasu, Hong Qin
2014 Proceedings of the 29th Annual ACM Symposium on Applied Computing - SAC '14  
Data management and analysis is becoming a bottleneck in this technique.  ...  We test our methods using scattering images of two-dimensional nanoparticle assemblies. The experimental results show the effectiveness of our algorithm on real world scientific data.  ...  To extend the camera dynamic range exposures with short (10 ms) and long (200 ms) dwell times were stitched to provide a single scattering image with appreciable scattering intensity extending to a reciprocal  ... 
doi:10.1145/2554850.2554914 dblp:conf/sac/HuangYKYLYGFQ14 fatcat:jgid2fkl2vffnb2bwlxazxenui

Temperature distribution descriptor for robust 3D shape retrieval

Yi Fang, Mengtian Sun, Karthik Ramani
2011 CVPR 2011 WORKSHOPS  
TD descriptor is driven by by heat kernel. The TD descriptor understands the shape by evaluating the surface temperature distribution evolution with time after applying unit heat at each vertex.  ...  It is therefore of great interest to develop the efficient shape retrieval engines that, given a query object, return similar 3D objects.  ...  Feddersen Chair Professorship support, Purdue University support for Faculty Study in a second discpline, and the School of Mechanical Engineering.  ... 
doi:10.1109/cvprw.2011.5981684 dblp:conf/cvpr/FangSR11 fatcat:lqertvvvuzavlotrorgls3ph3q

A Geometric Approach for Regularization of the Data Term in Stereo-Vision

Rami Ben-Ari, Nir Sochen
2008 Journal of Mathematical Imaging and Vision  
Since the data is often noisy a-priori, preference is required to result a smooth disparity (or piecewise smooth).  ...  On the other hand, the global methods consider a non-regularized data term with a smoothing constraint imposed directly on the disparity.  ...  Approximation by Short Time Kernel A more intuitive way to understand the Beltrami flow is via the short-time kernel technique [34, 38, 35] .  ... 
doi:10.1007/s10851-008-0066-5 fatcat:7bkdknh7hnfqlieiakbyiiusk4

A Learning Framework for Diffeomorphic Image Registration based on Quasi-conformal Geometry [article]

Qiguang Chen, Zhiwen Li, Lok Ming Lui
2021 arXiv   pre-print
The basic idea is to design a CNN mapping image pairs to deformation fields. QCRegNet consists of the estimator network and the Beltrami solver network (BSNet).  ...  The estimator network takes image pair as input and outputs the Beltrami coefficient (BC).  ...  The convolutional layers used in (d) and (e) have 64 kernels.  ... 
arXiv:2110.10580v1 fatcat:qbwaxls6abgdpnba4uejdao3je

Kernel Learning for Data-Driven Spectral Analysis of Koopman Operators

Naoya Takeishi
2019 Asian Conference on Machine Learning  
The performance of this method with a finite amount of data depends on the choice of the kernel function used in diffusion maps, which creates a need for kernel selection.  ...  In this paper, we propose a method to learn the kernel function adaptively to obtain better performance in approximating spectra of the Koopman operator using the Galerkin approximation with diffusion  ...  This is somewhat similar to a common configuration of machine learning, i.e., splitting data into training and test sets.  ... 
dblp:conf/acml/Takeishi19 fatcat:afeyqtwftfagperf3mke6dqegq
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