We propose a novel texture clustering method. A classical type of(approximate) shift invariant discrete wavelet transform(DWT),dual tree DWT,is used to decompose texture images. Multiple signatures are generated from ...We propose a novel texture clustering method. A classical type of(approximate) shift invariant discrete wavelet transform(DWT),dual tree DWT,is used to decompose texture images. Multiple signatures are generated from the obtained high-frequency bands. A locality preserving approach is applied subsequently to project data from high-dimensional space to low-dimensional space. Shift invariant DWT can represent image texture information efficiently in combination with a histogram signature,and the local geometrical structure of the dataset is preserved well during clustering. Experimental results show that the proposed method remarkably outperforms traditional ones.展开更多
We show asymmetric multi-channel sampling on a series of a shift invariant spaces ∑a^m=1v（φ（ta）） with a series of Riesz generators ∑a^m=1φ（ta） in L2（R）, where each channeled signal is assigned a uniform bu...We show asymmetric multi-channel sampling on a series of a shift invariant spaces ∑a^m=1v（φ（ta）） with a series of Riesz generators ∑a^m=1φ（ta） in L2（R）, where each channeled signal is assigned a uniform but distinct sampling rate. We use Fourier duality between ∑a^m=1v（φ（ta））and L2[0, 2π] to find conditions under which there is a stable asymmetric multi-channel sampling formula on ∑a^m=1v（φ（ta））.展开更多
Generalized sampling in a shift invariant subspace V of L2（R） is considered. A function f in V is processed with different filters Lm and then one tries to reconstruct f from the samples L^mf（j＇k）. We develop a t...Generalized sampling in a shift invariant subspace V of L2（R） is considered. A function f in V is processed with different filters Lm and then one tries to reconstruct f from the samples L^mf（j＇k）. We develop a theory of how to do this in the case when V possesses a shift invariant frame. Special attention is paid to the question： How to obtain dual frames with compact support？展开更多
For a backward shift invariant subspace N in H^2（Г^2）, the operators Sz and Sw on N are defined by Sz = PNTz｜N and Sw, = PNTw｜N, where PN is the orthogonal projection from L^2（Г^2） onto N. We give a characteri...For a backward shift invariant subspace N in H^2（Г^2）, the operators Sz and Sw on N are defined by Sz = PNTz｜N and Sw, = PNTw｜N, where PN is the orthogonal projection from L^2（Г^2） onto N. We give a characterization of N satisfying rank [Sz, Sw^＊] = 1.展开更多
We study shift invariant spaces generated by refinable distributions. We classify the summation and the intersection of shift invariant spaces generated by refinable distributions,and prove that they are also shift in...We study shift invariant spaces generated by refinable distributions. We classify the summation and the intersection of shift invariant spaces generated by refinable distributions,and prove that they are also shift invariant spaces generated by refinable distributions.展开更多
A complete answer to the shiftability of a principal shift invariant spaces and a scaled version is given. The congruence of spectrum plays a kernel role. It characterizes essentially the shiftability and the scale ...A complete answer to the shiftability of a principal shift invariant spaces and a scaled version is given. The congruence of spectrum plays a kernel role. It characterizes essentially the shiftability and the scale of any principal shift variant spaces. Some examples relative to signal analysis are discussed associated with an explanation to the failure of generalizing Shannon s sampling theorem from band limitted to band pass case.展开更多
In this paper, we proposed a metric to measure the shift invariance of the three different contourlet transforms. And then, using the same structure texture image retrieval system which use subband coefficients energy...In this paper, we proposed a metric to measure the shift invariance of the three different contourlet transforms. And then, using the same structure texture image retrieval system which use subband coefficients energy, standard deviation and kurtosis features with Canberra distance, we gave a comparison of their texture description abilities. Experimental results show that contourlet-2.3 texture image retrieval system has almost retrieval rates with non-sub sampled contourlet system;the two systems have better retrieval results than the original contourlet retrieval system. On the other hand, for the relatively lower redundancy, we recommend using contourlet- 2.3 as texture description transform.展开更多
In the light of some assumptions that are very close to the practical working conditions,a very complicated polishing process of optical element can be simplified as a linear and shift invariant system that is relatd ...In the light of some assumptions that are very close to the practical working conditions,a very complicated polishing process of optical element can be simplified as a linear and shift invariant system that is relatd only to the speed,pres- sure and time of processing.In polishing,the removed material can be represented and entreated by the convolution of the removal function of polishing head and the dwell function.The properties of removal function are presented.The assumptions and methods given by the author have been shown to be correct and applicable by experiments using a ring lap to polish the optical surfac.展开更多
In this paper,a new method for dealing with substructure chain is presented.Here,a substructure chain means a structure consisting of a number of identical substructures connected in series.This method is parallel to ...In this paper,a new method for dealing with substructure chain is presented.Here,a substructure chain means a structure consisting of a number of identical substructures connected in series.This method is parallel to the expansion method in the structural analysis according to the transverse section.The method of shift invariance and that of initial parameter and transfer matrix,their mutual-relation and com- bined use,as well as the analysis of the eigenproblem on the transverse section,and the expansion method based on the eigenvectors are described in this paper.展开更多
With the explosive growth of commercial Iogos, high quality logo images are needed for training logo detection or recognition systems, especially for famous Iogos or new commercial brands. This paper focuses on automa...With the explosive growth of commercial Iogos, high quality logo images are needed for training logo detection or recognition systems, especially for famous Iogos or new commercial brands. This paper focuses on automatic collecting representative logo images from the internet without any human labeling or seed images. We propose multiple dictionary invariant sparse coding to solve this problem. This work can automatically provide prototypes, representative images, or weak labeled training images for logo detection, logo recognition, trademark infringement detection, brand protection, and ad-targeting. The experiment results show that our method increases the mean average precision for 25 types of Iogos to 80.07% whereas the original search engine results only have 32% representative logo images. The top images collected by our method are accurate and reliable enough for practical applications in the future.展开更多
The goal of this paper is to achieve a computational model and corresponding efficient algorithm for obtaining a sparse representation of the fitting surface to the given scattered data. The basic idea of the model is...The goal of this paper is to achieve a computational model and corresponding efficient algorithm for obtaining a sparse representation of the fitting surface to the given scattered data. The basic idea of the model is to utilize the principal shift invariant(PSI) space and the l_1 norm minimization. In order to obtain different sparsity of the approximation solution, the problem is represented as a multilevel LASSO(MLASSO)model with different regularization parameters. The MLASSO model can be solved efficiently by the alternating direction method of multipliers. Numerical experiments indicate that compared to the AGLASSO model and the basic MBA algorithm, the MLASSO model can provide an acceptable compromise between the minimization of the data mismatch term and the sparsity of the solution. Moreover, the solution by the MLASSO model can reflect the regions of the underlying surface where high gradients occur.展开更多
基金supported by the Hi-Tech Research and Development Program (863) of China (Nos. 2007AA01Z311 and 2007AA04Z1A5)the National Basic Research Program (973) of China (No. 2009CB32 0804)+1 种基金the National Research Foundation for the Doctoral Program of Higher Education of China (No. 20060335114)the Science and Technology Program of Zhejiang Province, China (No. 2007C21006)
文摘We propose a novel texture clustering method. A classical type of(approximate) shift invariant discrete wavelet transform(DWT),dual tree DWT,is used to decompose texture images. Multiple signatures are generated from the obtained high-frequency bands. A locality preserving approach is applied subsequently to project data from high-dimensional space to low-dimensional space. Shift invariant DWT can represent image texture information efficiently in combination with a histogram signature,and the local geometrical structure of the dataset is preserved well during clustering. Experimental results show that the proposed method remarkably outperforms traditional ones.
文摘We show asymmetric multi-channel sampling on a series of a shift invariant spaces ∑a^m=1v（φ（ta）） with a series of Riesz generators ∑a^m=1φ（ta） in L2（R）, where each channeled signal is assigned a uniform but distinct sampling rate. We use Fourier duality between ∑a^m=1v（φ（ta））and L2[0, 2π] to find conditions under which there is a stable asymmetric multi-channel sampling formula on ∑a^m=1v（φ（ta））.
文摘Generalized sampling in a shift invariant subspace V of L2（R） is considered. A function f in V is processed with different filters Lm and then one tries to reconstruct f from the samples L^mf（j＇k）. We develop a theory of how to do this in the case when V possesses a shift invariant frame. Special attention is paid to the question： How to obtain dual frames with compact support？
基金supported by Grant-in-Aid for Scientific Research (No. 16340037)Japan Society for the Promotion of Science
文摘For a backward shift invariant subspace N in H^2（Г^2）, the operators Sz and Sw on N are defined by Sz = PNTz｜N and Sw, = PNTw｜N, where PN is the orthogonal projection from L^2（Г^2） onto N. We give a characterization of N satisfying rank [Sz, Sw^＊] = 1.
基金supported by National Natural Science Foundation of China (Grant No. 10871180)Projects of International Cooperation and Exchanges NSFC-NSF (Grant No. 10911120394)
文摘We study shift invariant spaces generated by refinable distributions. We classify the summation and the intersection of shift invariant spaces generated by refinable distributions,and prove that they are also shift invariant spaces generated by refinable distributions.
文摘A complete answer to the shiftability of a principal shift invariant spaces and a scaled version is given. The congruence of spectrum plays a kernel role. It characterizes essentially the shiftability and the scale of any principal shift variant spaces. Some examples relative to signal analysis are discussed associated with an explanation to the failure of generalizing Shannon s sampling theorem from band limitted to band pass case.
文摘In this paper, we proposed a metric to measure the shift invariance of the three different contourlet transforms. And then, using the same structure texture image retrieval system which use subband coefficients energy, standard deviation and kurtosis features with Canberra distance, we gave a comparison of their texture description abilities. Experimental results show that contourlet-2.3 texture image retrieval system has almost retrieval rates with non-sub sampled contourlet system;the two systems have better retrieval results than the original contourlet retrieval system. On the other hand, for the relatively lower redundancy, we recommend using contourlet- 2.3 as texture description transform.
文摘In the light of some assumptions that are very close to the practical working conditions,a very complicated polishing process of optical element can be simplified as a linear and shift invariant system that is relatd only to the speed,pres- sure and time of processing.In polishing,the removed material can be represented and entreated by the convolution of the removal function of polishing head and the dwell function.The properties of removal function are presented.The assumptions and methods given by the author have been shown to be correct and applicable by experiments using a ring lap to polish the optical surfac.
基金Project supported by National Natural Science Foundation of China.
文摘In this paper,a new method for dealing with substructure chain is presented.Here,a substructure chain means a structure consisting of a number of identical substructures connected in series.This method is parallel to the expansion method in the structural analysis according to the transverse section.The method of shift invariance and that of initial parameter and transfer matrix,their mutual-relation and com- bined use,as well as the analysis of the eigenproblem on the transverse section,and the expansion method based on the eigenvectors are described in this paper.
基金National Key Basic Research and Development(973)Program of China(Nos.2012CB316301 and 2013CB329403)National Natural Science Foundation of China(No.91120011)+1 种基金Tsinghua University Initiative Scientific Research Program(No.20121088071)Basic Research Foundation of Tsinghua National Laboratory for Information Science and Technology(TNList)
文摘With the explosive growth of commercial Iogos, high quality logo images are needed for training logo detection or recognition systems, especially for famous Iogos or new commercial brands. This paper focuses on automatic collecting representative logo images from the internet without any human labeling or seed images. We propose multiple dictionary invariant sparse coding to solve this problem. This work can automatically provide prototypes, representative images, or weak labeled training images for logo detection, logo recognition, trademark infringement detection, brand protection, and ad-targeting. The experiment results show that our method increases the mean average precision for 25 types of Iogos to 80.07% whereas the original search engine results only have 32% representative logo images. The top images collected by our method are accurate and reliable enough for practical applications in the future.
基金supported by National Natural Science Foundation of China(Grant Nos.11526098,11001037,11290143 and 11471066)the Research Foundation for Advanced Talents of Jiangsu University(Grant No.14JDG034)+1 种基金the Natural Science Foundation of Jiangsu Province(Grant No.BK20160487)the Fundamental Research Funds for the Central Universities(Grant No.DUT15LK44)
文摘The goal of this paper is to achieve a computational model and corresponding efficient algorithm for obtaining a sparse representation of the fitting surface to the given scattered data. The basic idea of the model is to utilize the principal shift invariant(PSI) space and the l_1 norm minimization. In order to obtain different sparsity of the approximation solution, the problem is represented as a multilevel LASSO(MLASSO)model with different regularization parameters. The MLASSO model can be solved efficiently by the alternating direction method of multipliers. Numerical experiments indicate that compared to the AGLASSO model and the basic MBA algorithm, the MLASSO model can provide an acceptable compromise between the minimization of the data mismatch term and the sparsity of the solution. Moreover, the solution by the MLASSO model can reflect the regions of the underlying surface where high gradients occur.
