Fusion Coefficients Research Articles

From quantum Bäcklund transforms to topological quantum field theory

We derive the quantum analogue of a Bäcklund transformation for the quantized Ablowitz–Ladik chain, a space discretization of the nonlinear Schrödinger equation. The quantization of the Ablowitz–Ladik chain leads to the q-boson model. Using a previous construction of Baxter’s Q-operator for this model by the author, a set of functional relations is obtained which matches the relations of a one-variable classical Bäcklund transform to all orders in . We construct also a second Q-operator and show that it is closely related to the inverse of the first. The multi-Bäcklund transforms generated from the Q-operator define the fusion matrices of a 2D TQFT and we derive a linear system for the solution to the quantum Bäcklund relations in terms of the TQFT fusion coefficients.

Simple-current algebra constructions of 2+1-dimensional topological orders

Self-consistent (non-)abelian statistics in 2+1D are classified by modular tensor categories (MTC). In recent works, a simplified axiomatic approach to MTCs, based on fusion coefficients $N^{ij}_k$ and spins $s_i$, was proposed. A numerical search based on these axioms led to a list of possible (non-)abelian statistics, with rank up to $N=7$. However, there is no guarantee that all solutions to the simplified axioms are consistent and can be realised by bosonic physical systems. In this paper, we use simple-current algebra to address this issue. We explicitly construct many-body wave functions, aiming to realize the entries in the list (\ie realize their fusion coefficients $N^{ij}_k$ and spins $s_i$). We find that all entries can be constructed by simple-current algebra plus conjugation under time reversal symmetry. This supports the conjecture that simple-current algebra is a general approach that allows us to construct all (non-)abelian statistics in 2+1D. It also suggests that the simplified theory based on $(N^{ij}_k,s_i)$ is a classifying theory at least for simple bosonic 2+1D topological orders (up to invertible topological orders).

A Novel Image Fusion Algorithm for Visible and PMMW Images based on Clustering and NSCT

Aiming at the fusion of visible and Passive Millimeter Wave (PMMW) images, a novel algorithm based on clustering and NSCT (Nonsubsampled Contourlet Transform) is proposed. It takes advantages of the particular ability of PMMW image in presenting metal target and uses the clustering algorithm for PMMW image to extract the potential target regions. In the process of fusion, NSCT is applied to both input images, and then the decomposition coefficients on different scale are combined using different rules. At last, the fusion image is obtained by taking the inverse NSCT of the fusion coefficients. Some methodologies are used to evaluate the fusion results. Experiments demonstrate the superiority of the proposed algorithm for metal target detection compared to wavelet transform and Laplace transform.

A fusion algorithm for infrared and visible images based on saliency analysis and non-subsampled Shearlet transform

This paper proposed a novel fusion method for the infrared and visible image based on the accurate extraction of the target region. Firstly, the super-pixels-based saliency analysis method is used to extract the salient regions of the infrared image and obtain the coarse contour of the infrared target. Then the multi-directional detection operators and the adaptive threshold algorithm are used to refine the boundary of the target region and obtain the fusion decision map. In order to capture the details of the visible image, non-subsampled Shearlet transform (NSST) is used to select the fusion coefficients of the background. Experimental results indicate that the proposed method is superior to other state of the-art methods in subjective visual and objective performance.

Fusion of remote sensing images based on pyramid decomposition with Baldwinian Clonal Selection Optimization

In this paper, we put forward a novel fusion method for remote sensing images based on the contrast pyramid (CP) using the Baldwinian Clonal Selection Algorithm (BCSA), referred to as CPBCSA. Compared with classical methods based on the transform domain, the method proposed in this paper adopts an improved heuristic evolutionary algorithm, wherein the clonal selection algorithm includes Baldwinian learning. In the process of image fusion, BCSA automatically adjusts the fusion coefficients of different sub-bands decomposed by CP according to the value of the fitness function. BCSA also adaptively controls the optimal search direction of the coefficients and accelerates the convergence rate of the algorithm. Finally, the fusion images are obtained via weighted integration of the optimal fusion coefficients and CP reconstruction. Our experiments show that the proposed method outperforms existing methods in terms of both visual effect and objective evaluation criteria, and the fused images are more suitable for human visual or machine perception.

Crystal Approach to Affine Schubert Calculus

We apply crystal theory to affine Schubert calculus, Gromov-Witten invariants for the complete flag manifold, and the positroid stratification of the positive Grassmannian. We introduce operators on decompositions of elements in the type-$A$ affine Weyl group and produce a crystal reflecting the internal structure of the generalized Young modules whose Frobenius image is represented by stable Schubert polynomials. We apply the crystal framework to products of a Schur function with a $k$-Schur function, consequently proving that a subclass of 3-point Gromov-Witten invariants of complete flag varieties for $\mathbb C^n$ enumerate the highest weight elements under these operators. Included in this class are the Schubert structure constants in the (quantum) product of a Schubert polynomial with a Schur function $s_\lambda$ for all $|\lambda^\vee|< n$. Another by-product gives a highest weight formulation for various fusion coefficients of the Verlinde algebra and for the Schubert decomposition of certain positroid classes.

A New Effective Image Fusion Algorithm Based on NSCT and PCNN

NonSubsampled Contourlet Transform (NSCT) has the characteristics of multi-scale, multi-directional, multi-resolution and shift invariance. Because of down sampling, traditional contourlet transform will cause Gibbs phenomenon, NSCT can overcome the disadvantage, obtaining better fusion image. Due to Pulse Coupled Neural Networks (PCNN) excellent biological characteristics, it has already been widely applied to image processing. In this paper, we will combining NSCT and PCNN, making full use of their advantages and applying to image fusion. The original image is by NSCT transform, getting the decomposition coefficients and then calculating its spatial frequency, input them to PCNN. According to the firing times select fusion coefficients. Experiment result has shown that, compared with the typical wavelet transform and contourlet transform method, the method proposed in this paper whether in subjective or objective is better than other methods. 1548-7741/Copyright © 2015 Binary Information Press

Rock fracture image acquisition using two kinds of lighting and fusion on a wavelet transform

In order to obtain more precise information regarding rock fractures, images of a rock sample using two different light sources were acquired and fused. For image acquisition, an epoxy resin liquid was first injected into a fracture zone in situ, and when the epoxy resin was dry, the rock core sample, including the epoxy resin, was removed from the rock base. The rock core sample was then cut into multiple slices and images of the slices using ultraviolet (UV) and visible lighting were acquired. In order to fuse two slice images, an algorithm based on the redundant lifting, non-separable wavelet transform was studied and utilised. Fusion includes three primary steps for each pair of slice images: (1) applying the redundant lifting, non-separable wavelet transform to each image, and then approximating the two images separately; (2) fusing the approximated images corresponding to the decomposition level using certain rules and fusion operators for obtaining fusion coefficients; and (3) applying the fused wavelet coefficients to the redundant lifting non-separable wavelet transform. The results show that combining the proposed method of image acquisition and the image fusion algorithm is not only effective at obtaining a large volume of detailed rock fracture information, it is also an economical and easy to use method. By applying the new method, rock fractures can be easily detected, and many different parameters in different rock engineering applications can be measured and analyzed.

The Verlinde formula in logarithmic CFT

In rational conformal field theory, the Verlinde formula computes the fusion coefficients from the modular S-transformations of the characters of the chiral algebra's representations. Generalising this formula to logarithmic models has proven rather difficult for a variety of reasons. Here, a recently proposed formalism [1] for the modular properties of certain classes of logarithmic theories is reviewed, and refined, using simple examples. A formalism addressing fusion rules in simple current extensions is also reviewed as a means to tackle logarithmic theories to which the proposed modular formalism does not directly apply.

Fusion of visible and infrared images using multiobjective evolutionary algorithm based on decomposition

Integration of images from different sensing modalities can produce information that cannot be obtained by viewing the sensor outputs separately and consecutively. In order to enhance the contrast of the fused image and reduce the loss of fine details in the process of image fusion, an innovative fusion method of visible and infrared images is presented in this paper, which uses a multiobjective evolutionary algorithm based decomposition (MOEA/D). First of all, we employ contrast pyramid (CP) decomposition into every level of each original image. Second, MOEA/D is introduced to optimize fusion coefficients, thus the weighted coefficients can be adjusted automatically according to fitness function. Finally, obtain the fused images by the weight integration of the optimal fusion coefficients and CP reconstruction. Experimental results show that the fusion algorithm proposed in this paper achieves better effect than the other fusion algorithms both in visual effect and quantitative metrics, and the fused images are more suitable for human visual or machine perception.

Fusion of Infrared and Visible Images Based on Pulse Coupled Neural Network and Nonsubsampled Contourlet Transform

This paper presents a new fusion algorithm which can effectively solve the problem that has unobvious infrared target and low contrast in infrared and visible image fusion. This paper's innovation point is its fusion rule. Other algo- rithms' fusion rules usually use pulse coupled neural network (PCNN) and region characteristics to select low frequency or bandpass subband coefficients. The proposed algorithm innovatively applies improved PCNN and region characteris- tics to the selection of both low frequency and bandpasssubband coefficients in nonsubsampled contourled transform (NSCT) domain. First, the subband coefficients of original image are obtained by NSCT. Then, the decomposed subband coefficients are processed by using PCNN, whose fire mapping images are obtained. The method of region standard de- viation isused to choose the fusion coefficients of fire mapping image, which satisfies to get more image information in low frequency part. For bandpass subband coefficients' fire mapping image, the method based on region energy is adopted for the fusion coefficients, which makes the bandpass part captures more energy. Finally, the fused image can be obtained by inverse transform of NSCT. Compared with typical wavelet-based, NSCT-based, NSCT-PCNN based fusion algorithms, experiment shows that the new proposed algorithm improves the fused image'sobjective evaluation index sig- nificantly, obtainsa prominent infrared target and better fusion image quality.

A new contrast based multimodal medical image fusion framework

Medical image fusion plays an important role in clinical applications such as image-guided surgery, image-guided radiotherapy, noninvasive diagnosis, and treatment planning. The main motivation is to fuse different multimodal information into a single output. In this instance, we propose a novel framework for spatially registered multimodal medical image fusion, which is primarily based on the non-subsampled contourlet transform (NSCT). The proposed method enables the decomposition of source medical images into low- and high-frequency bands in NSCT domain. Different fusion rules are then applied to the varied frequency bands of the transformed images. Fusion coefficients are achieved by the following fusion rule: low-frequency components are fused using an activity measure based on the normalized Shannon entropy, which essentially selects low-frequency components from the focused regions with high degree of clearness. In contrast, high-frequency components are fused using the directive contrast, which essentially collects all the informative textures from the source. Integrating these fusion rules, more spatial feature and functional information can be preserved and transferred into the fused images. The performance of the proposed framework is illustrated using four groups of human brain and two clinical bone images from different sources as our experimental subjects. The experimental results and comparison with other methods show the superior performance of the framework in both subjective and objective assessment criteria.

PCNN-Based Image Fusion in Compressed Domain

This paper addresses a novel method of image fusion problem for different application scenarios, employing compressive sensing (CS) as the image sparse representation method and pulse-coupled neural network (PCNN) as the fusion rule. Firstly, source images are compressed through scrambled block Hadamard ensemble (SBHE) for its compression capability and computational simplicity on the sensor side. Local standard variance is input to motivate PCNN and coefficients with large firing times are selected as the fusion coefficients in compressed domain. Fusion coefficients are smoothed by sliding window in order to avoid blocking effect. Experimental results demonstrate that the proposed fusion method outperforms other fusion methods in compressed domain and is effective and adaptive in different image fusion applications.

A Study on Performance Improvement Due to Linear Fusion in Biometric Authentication Tasks

In this paper, we initiate a theoretical study on ${N}$ -expert fusion ( ${N}~\boldsymbol {\geq }~2$ ) in the context of biometric authentication (BA). Optimal fusion weights, which depend on performances and variances of, and correlations among individual base-experts have been found, and we also give and prove some new theorems that serve as the basis for analyzing the performance of the overall system. Our conclusion is that provided that optimal weights are used as fusion coefficients, linear fusion will definitely lead to a better performance than the best individual expert. This contradicts many existing conclusions, which assert that fusion is not always beneficial and that performance improvement due to fusion is guaranteed only when some conditions as to base-experts’ performances, variances, and correlations are satisfied. Besides, for the first time the definition of correlation in the context of BA is clearly and explicitly given to avoid the long-standing ambiguity and vagueness concerning this term, and we make an initial attempt to propose and investigate three types of correlation coefficients. Furthermore, the connection between our proposed optimal fusion method and Fisher’s discriminant is discussed. Extensive experiments have been conducted to confirm our theoretical results and construct counter-examples for the existing conclusions.

Bosonic Ghosts at c = 2 as a Logarithmic CFT

Motivated by Wakimoto free field realisations, the bosonic ghost system of central charge $c=2$ is studied using a recently proposed formalism for logarithmic conformal field theories. This formalism addresses the modular properties of the theory with the aim being to determine the (Grothendieck) fusion coefficients from a variant of the Verlinde formula. The key insight, in the case of bosonic ghosts, is to introduce a family of parabolic Verma modules which dominate the spectrum of the theory. The results include S-transformation formulae for characters, non-negative integer Verlinde coefficients, and a family of modular invariant partition functions. The logarithmic nature of the corresponding ghost theories is explicitly verified using the Nahm-Gaberdiel-Kausch fusion algorithm.

The infrared and visible image fusion algorithm based on target separation and sparse representation

Although the fused image of the infrared and visible image takes advantage of their complementary, the artifact of infrared targets and vague edges seriously interfere the fusion effect. To solve these problems, a fusion method based on infrared target extraction and sparse representation is proposed. Firstly, the infrared target is detected and separated from the background rely on the regional statistical properties. Secondly, DENCLUE (the kernel density estimation clustering method) is used to classify the source images into the target region and the background region, and the infrared target region is accurately located in the infrared image. Then the background regions of the source images are trained by Kernel Singular Value Decomposition (KSVD) dictionary to get their sparse representation, the details information is retained and the background noise is suppressed. Finally, fusion rules are built to select the fusion coefficients of two regions and coefficients are reconstructed to get the fused image. The fused image based on the proposed method not only contains a clear outline of the infrared target, but also has rich detail information.

Face recognition based on pixel-level and feature-level fusion of the top-level’s wavelet sub-bands

The traditional wavelet-based approaches directly use the low frequency sub-band of wavelet transform to extract facial features. However, the high frequency sub-bands also contain some important information corresponding to the edge and contour of face, reflecting the details of face, especially the top-level’s high frequency sub-bands. In this paper, we propose a novel technique which is a joint of pixel-level and feature-level fusion at the top-level’s wavelet sub-bands for face recognition. We convert the problem of finding the best pixel-level fusion coefficients of high frequency wavelet sub-bands to two optimization problems with the help of principal component analysis and linear discriminant analysis, respectively; and propose two alternating direction methods to solve the corresponding optimization problems for finding transformation matrices of dimension reduction and optimal fusion coefficients of the high frequency wavelet sub-bands. The proposed methods make full use of four top-level’s wavelet sub-bands rather than the low frequency sub-band only. Experiments are carried out on the FERET, ORL and AR face databases, which indicate that our methods are effective and robust.

A fusion method for visible and infrared images based on contrast pyramid with teaching learning based optimization

This paper proposes a novel image fusion scheme based on contrast pyramid (CP) with teaching learning based optimization (TLBO) for visible and infrared images under different spectrum of complicated scene. Firstly, CP decomposition is employed into every level of each original image. Then, we introduce TLBO to optimizing fusion coefficients, which will be changed under teaching phase and learner phase of TLBO, so that the weighted coefficients can be automatically adjusted according to fitness function, namely the evaluation standards of image quality. At last, obtain fusion results by the inverse transformation of CP. Compared with existing methods, experimental results show that our method is effective and the fused images are more suitable for further human visual or machine perception.

Infrared and visible image fusion based on random projection and sparse representation

A new image fusion approach for infrared and visible images is explored, combining fusion with data compression based on sparse representation and compressed sensing. The proposed approach first compresses the sensing data by random projection and then obtains sparse coefficients on compressed samples by sparse representation. Finally, the fusion coefficients are combined with the fusion impact factor and the fused image is reconstructed from the combined sparse coefficients. Experimental results validate its rationality and effectiveness, which can achieve comparable fusion quality on the less-compressed sensing data.

A Remote Sensing Image Fusion Algorithm Based on the Second Generation Curvelet Transform and DS Evidence Theory

A new method of remote sensing image fusion is proposed based on the second generation Curvelet transform and Dempster-Shafer (DS) evidence theory. In this paper, the remote sensing images are decomposed by the Curvelet transform to get the coefficients and optimize the high coefficients with DS evidence theory. Firstly, the high resolution and multispectral remote sensing images are decomposed by the Curvelet transform to get the Curvelet transform coefficients of all layers (Coarse, Detail and Fine scale layer). Secondly, the Coarse scale layer is used the maximum fusion rule. The Detail scale layer is used by the weighted average fusion rule. The Fine scale layer is optimized by the DS evidence theory. Get the three features of the Fine scale layer coefficients. The three features are the variance, information entropy and energy. Use the features to be some parameters belief function and the plausibility function. Then compose the mass function and get new fusion coefficients. Finally, the fused image is obtained by the inverse Curvelet transform. The experimental results show that the new algorithm can more effectively than wavelet and other traditional fusion algorithms such as HIS, brovey in the remote sensing image fusion.