Symmetry Filter Research Articles

Implementation of distributed arithmetic-based symmetrical 2-D block finite impulse response filter architectures.

Background: This paper presents an efficient two-dimensional (2-D) finite impulse response (FIR) filter using block processing for two different symmetries. Architectures for a general filter (without symmetry) and two symmetrical filters (diagonal and quadrantal symmetry) are implemented. The proposed architectures need fewer multipliers because of the symmetry of the filter coefficients. Methods: A distributed arithmetic (DA)- based multiplication method is used in the proposed architecture. A dual-port memory-based lookup table (DP-MLUT) is used in the multiplication instead of lookup-table (LUT) to reduce the area and power of the FIR filter. The filter's throughput is increased by using block processing. Memory reuse and memory sharing methods are introduced, which reduces the need for many registers and hence the circuit complexity. The architectures are written in Verilog Hardware Description Language and synthesized using Genus Synthesis tool-19.1 in 45nm technology with a generic library of Cadence vendor constraints. The synthesis tool generates the area, delay, and power reports. Power consumption of architectures is calculated with an image size of 64 X 64 and at 20 MHz frequency. Results: Compared to existing architectures, the synthesis results show improvements in power, area, area delay product (ADP), and power delay product (PDP). The proposed MLUT-based 2-D block Quadrantal Symmetry Filter (QSF) for length 8 with block size 4 consumes 58.94% less power, occupies 59.5% less area, 48.44% less ADP and 47.78% less PDP compared to best existing methods. Conclusions: A novel DA-based 2-D block FIR filter architecture with various symmetries is realized. Symmetry is incorporated into the filter coefficients to minimize the number of multipliers. The LUT size is optimized by odd multiples or even multiples storage techniques. Also, the overall area of the architecture is decreased by DP-LUT-based multipliers. The proposed filter architecture is area-power-efficient. It is best suited for applications that have fixed coefficients.

Integration of Design for Additive Manufacturing Constraints With Multimaterial Topology Optimization of Lattice Structures for Optimized Thermal and Mechanical Properties

Abstract The design of multimaterial lattice structures with optimized elasticity tensor, coefficient of thermal expansion (CTE), and thermal conductivity is the main objective of the research presented in this article. In addition, the additive manufacturability of the lattice structure is addressed using a prismatic density filter to eliminate support structures, and an octant symmetry filter is used to design symmetric lattices. A density-based topology optimization model is formulated with a homogenization method and solved using a sequential linear programming method to obtain the desired unit cell geometry of the lattice structure. The optimized unit cell obtained has high mechanical stiffness, a low CTE, and low thermal conductivity. A finite element analysis is carried out on the optimized lattice structure and an equivalent cube of computed effective properties (with the same loading and boundary conditions) to validate the computed homogenized material properties. The results from the finite element analysis show that the methodology followed to generate the lattice structure is accurate. Such lattice structures with tailored material properties can be used in aerospace parts that are subjected to mechanical and thermal loads. The complex multimaterial geometry produced from the topology optimization routine presented here is intended explicitly for the manufacture of parts using the directed energy deposition process with multiple material deposition nozzles.

Complete factorization for poly-phase matrix with linear phase based on semi-rank orthogonal projection matrix

This paper puts forward a new factorization, named the semi-rank factorization, for para-unitary poly-phase matrix with linear phase, and reveals the equivalent relationship between the orthogonal projection matrix and the linear phase, and characterizes the orthogonal projection matrix. The semi-rank factorization has the completeness property no matter for even or odd number of channels. In addition, a decomposition technique for the starting block matrix is developed using the reflection matrix. The semi-rank factorization provides an efficient and compact representation for multi-band filter banks with linear phase. In particular, the complete representation for multi-band symmetry filter banks with odd number of channels is brand new. As a result, the programmable algorithms are obtained for designs of optimal filter banks based on the complete representation. The optimal examples are presented to illustrate the excellent performance on image compression.

Symmetry Incorporated Cost-Effective Architectures for Two-Dimensional Digital Filters

Professor Fettweis as far back as 1977 published a paper generalizing McClellan transformation to obtain circular symmetry in 2-D and spherical, hyper-spherical symmetries in multidimensional digital filters [1]. This survey paper presents stateof-the-art two-dimensional (2-D) VLSI digital filter architectures possessing various symmetries in the filter magnitude response. Preceding the symmetry structures, a generalized formulation is given that allows the derivation of various new 2-D VLSI filter structures of any order without global broadcast. Following this, two types (namely, Type 1 [20] and Type 3 [21], [25], [26]) of cost-effective 2-D magnitude symmetry filter architectures possessing diagonal, four-fold rotational, quadrantal, and octagonal symmetries with reduced number of multipliers are given. By combining the identities of the Types-1 and 3 symmetry filter structures, multimode 2-D symmetry filters which enable the above four symmetry modes are discussed. The Type-1 and Type-3 multimode filters can result in a 65.3% cost reduction in terms of number of multipliers compared with the sum of the multipliers of the four individual Type-1 symmetry filter structures studied in this paper. Furthermore, Type-3 has shorter critical path than Type-1 multimode filter. The paper is concluded with the presentation of a 2-D filter design example and a corresponding structure.

Car manufacturer and model recognition based on scale invariant feature transform

Vehicle analysis involves licence plate recognition, vehicle type recognition, and car manufacturer and model recognition. Car manufacturer and model recognition plays an important role in providing supplementary information to licence plate recognition for the unique identification of a car. In this paper, we propose a framework to recognition car manufacturer and its model based on scale invariant feature transform (SIFT). We first detect a moving car using frame differences; the resultant binary image is used to detect the frontal view of a car by a symmetry filter. The detected frontal view is then used to identify a car based on SIFT algorithm. Experimental results show that our proposed framework achieves favourable recognition accuracy.

Automatic 2-D/3-D Vessel Enhancement in Multiple Modality Images Using a Weighted Symmetry Filter.

Automated detection of vascular structures is of great importance in understanding the mechanism, diagnosis, and treatment of many vascular pathologies. However, automatic vascular detection continues to be an open issue because of difficulties posed by multiple factors, such as poor contrast, inhomogeneous backgrounds, anatomical variations, and the presence of noise during image acquisition. In this paper, we propose a novel 2-D/3-D symmetry filter to tackle these challenging issues for enhancing vessels from different imaging modalities. The proposed filter not only considers local phase features by using a quadrature filter to distinguish between lines and edges, but also uses the weighted geometric mean of the blurred and shifted responses of the quadrature filter, which allows more tolerance of vessels with irregular appearance. As a result, this filter shows a strong response to the vascular features under typical imaging conditions. Results based on eight publicly available datasets (six 2-D data sets, one 3-D data set, and one 3-D synthetic data set) demonstrate its superior performance to other state-of-the-art methods.

Efficient palmprint identification using novel symmetry filter and alignment refinement

This paper presents a robust algorithm for line orientation code-based palmprint identification in which we propose a novel symmetry filter and an efficient alignment refinement technique. The main idea of the symmetry filter is to compute the approximate magnitude of the Gabor filter based on the modified finite Radon transform MFRAT, the so-called GMFRAT filter. The advantages of GMFRAT filters are that: 1 they are capable of quickly computing orientation codes; 2 they remarkably reduce remarkably the sizes of these features. The alignment refinement technique, which uses local orientation patterns, is also proposed to solve the problem of rotations and translations caused by an imperfect preprocessing phase. Based on our alignment refinement, the matching algorithm is designed. The experimental results obtained using the public databases of the Hong Kong Polytechnic University and the Indian Institute of Technology Delhi demonstrate the effectiveness of the proposed method.

Electronic structure of magnetic semiconductor CdCr2Te4: A possible spin-dependent symmetry filter

We present a theoretical investigation of the electronic and magnetic structure of spinel CdCr2Te4 using density functional theory, its extensions via onsite Hubbard U interactions, and a screened-hybrid-functional exchange potential. We find that the ground state is semiconducting within the latter approach, and within this magnetic-semiconducting system, we compute the complex band structure, finding a slowly decaying evanescent Δ̃1 state possibly suitable for realizing a spin-dependent symmetry filter effect.

Segmentation of Blood Vessel Structures in Retinal Fundus Images with Logarithmic Gabor Filters

The analysis of blood vessel structures in the retinal fundus images is important for the diagnosis of many diseases. Vessel segmentation can assist in the detection of pathological changes which are possible indicators for arteriosclerosis, retinopathy, micro aneurysms and macular degeneration. In this article, two approaches to blood vessel segmentation are presented. Both of them are based on the evaluation of phase symmetry information using complex logarithmic Gabor wavelets. In the first approach, a phase symmetry filter is combined with the front propagation algorithm fast marching, the second method uses a hysteresis thresholding step. The approaches have shown excellent results for the vessel segmentation on colon polyps. Although they were adapted to structures in retinal fundus imaging, neither eye specific knowledge nor supervised classification methods are used. For high comparability with previous publications in the field, the algorithms are evaluated on the two publicly available image databases DRIVE and STARE. The hysteresis thresholding approach which performs slightly superior achieves an average accuracy of 94.92% (sensitivity: 71.22%, specificity: 98.41%) for the DRIVE and 95, 65% (sensitivity: 71.87%, specificity: 98.34%) for the STARE database. Keywords: Blood vessels, Eye, fundus images, Gabor filters, Retina, Segmentation.

Matrix splitting with symmetry and symmetric tight framelet filter banks with two high-pass filters

The oblique extension principle introduced in Chui et al. (2002), Daubechies et al. (2003) [3,5] is a general procedure to construct tight wavelet frames and their associated filter banks. Symmetric tight framelet filter banks with two high-pass filters have been studied in Han and Mo (2004), Mo and Zhuang (in press), Petukhov (2003) [13,16,17]. Tight framelet filter banks with or without symmetry have been constructed in many papers in the literature. This paper is largely motivated by several results in Han (2010), Han and Mo (2004), Petukhov (2003) [11,13,17] to further study tight wavelet frames and their associated filter banks with symmetry and two high-pass filters. Our study not only leads to a simpler algorithm for the construction of tight framelet filter banks with symmetry and two high-pass filters, but also allows us to obtain a wider class of tight wavelet frames with symmetry which are not available in the current literature. The key ingredient in our investigation is a complete characterization of splitting positive semi-definite 2×2 matrices of Laurent polynomials with symmetry. Several examples are provided to illustrate the results and algorithms in this paper.

Matrix splitting with symmetry and dyadic framelet filter banks over algebraic number fields

Algebraic number fields are of particular interest and play an important role in both mathematics and engineering since an algebraic number field can be viewed as a finite dimensional linear space over the rational number field Q. Algorithms using algebraic number fields can be efficiently implemented involving only integer arithmetics. In this paper, we properly formulate the matrix splitting problem over any general subfield of it C, including an algebraic number field as a special case, and provide a simple necessary and sufficient condition for a 2×2 matrix of Laurent polynomials with symmetry to be able to be factorized by a 2×2 matrix of Laurent polynomials with certain symmetry structure. We propose an effective algorithm on how to obtain the factorization matrix step by step. As an application, we obtain a satisfactory algorithm for constructing dyadic framelet filter banks with the perfect reconstruction property and with symmetry over algebraic number fields. Several examples are provided to illustrate the algorithms proposed in this paper.

Fingerprint reference point detection for image retrieval based on symmetry and variation

Reference point plays an important role in fingerprint identification systems. The reference point is widely used for the fingerprint retrieval in large-scale databases. This paper proposes a novel algorithm for detecting a convex core point as a unique reference point consistently and accurately for all types of fingerprints. In order to detect robust core point candidates, a modified complex filter, called semi-radial symmetry filter, is proposed to detect correctly rotational symmetries of core points. Moreover, a vertical orientation variation feature, called VORIV feature, is proposed to remove spurious core points and concave core points. Therefore, the proposed technique computes the Variation and Symmetry Combined Energy (VSCOME). Then, the reference point is located by searching the global VSCOME maximum. The experimental results on the public database (FVC2004 DB1 set A) show that the proposed technique exhibits a very high robustness and gets the best performance in comparing with other approaches in literature.

Power-Efficient and Cost-Effective 2-D Symmetry Filter Architectures

This paper presents two-dimensional (2-D) VLSI digital filter structures possessing various symmetries in the filter magnitude response. For this purpose, four Type-1 and four Type-2 power-efficient and cost-effective 2-D magnitude symmetry filter architectures possessing diagonal, fourfold rotational, quadrantal, and octagonal symmetries with reduced number of multipliers and one power-efficient and cost-effective multimode 2-D symmetry filter are given. By combining the identities of the four Type-1 symmetry filter structures, the proposed multimode 2-D symmetry filter is capable of providing four different operation modes: diagonal symmetry mode (DSM), fourfold rotational symmetry mode (FRSM), quadrantal symmetry mode (QSM), and octagonal symmetry mode (OSM). The proposed diagonal, fourfold rotational, quadrantal, and octagonal symmetry filter structures can attain power savings of 16.77%, 36.30%, 22.90%, and 37.73% with respect to that of the conventional 2-D filter design without symmetry. On the other hand, the proposed DSM, FRSM, QSM, and OSM modes can reduce power consumption by 11.01%, 31.42%, 17.53%, and 35.26% compared with that of the conventional 2-D filter design. The proposed multimode filter can result in a 63.25% area reduction compared with the sum of the areas of the four individual Type-1 symmetry filter structures.

Theory of tunnel magnetoresistance and spin filter effect in magnetic tunnel junctions

Tunnel magnetoresistance (TMR) and spin filter effect in magnetic tunnel junctions are studied by using numerical simulations based on the linear response theory. In Fe/MgO/Fe junction, TMR is calculated for both clean and disordered systems. Large MR ratio obtained in clean junctions is attributed to the momentum and symmetry filter effect of MgO barrier. It is shown that lattice distortions within MgO and at the interfaces decrease the MR ratio because the disorder weakens the filter effects and causes hybridization between Bloch wave functions having different momenta and symmetries. The spin filter effect in junctions containing a ferromagnetic insulator LaNi0.5Mn0.5O3 is also investigated. It is shown that a large spin filter effect is obtained in LaNiO3/LaNi0.5Mn0.5O3/LaNiO3 junctions although the tunnel barrier height is spin independent.

M-ZDOCK: a grid-based approach for Cn symmetric multimer docking

Computational protein docking is a useful technique for gaining insights into protein interactions. We have developed an algorithm M-ZDOCK for predicting the structure of cyclically symmetric (Cn) multimers based on the structure of an unbound (or partially bound) monomer. Using a grid-based Fast Fourier Transform approach, a space of exclusively symmetric multimers is searched for the best structure. This leads to improvements both in accuracy and running time over the alternative, which is to run a binary docking program ZDOCK and filter the results for near-symmetry. The accuracy is improved because fewer false positives are considered in the search, thus hits are not as easily overlooked. By searching four instead of six degrees of freedom, the required amount of computation is reduced. This program has been tested on several known multimer complexes from the Protein DataBank, including four unbound multimers: three trimers and a pentamer. For all of these cases, M-ZDOCK was able to find at least one hit, whereas only two of the four testcases had hits when using ZDOCK and a symmetry filter. In addition, the running times are 30-40% faster for M-ZDOCK. M-ZDOCK is freely available to academic users at http://zlab.bu.edu/m-zdock/ zhiping@bu.edu http://zlab.bu.edu/m-zdock.

A Simple Method for Modeling Transmembrane Helix Oligomers

We describe an effective procedure for modeling the structures of simple transmembrane helix homo-oligomers. The method differs from many previous approaches in that the only structural constraint we use to help select the correct model is the oligomerization state of the protein. The method involves the following steps: (1) perform 100–250 independent Monte Carlo energy minimizations of helix pairs to produce a large collection of well-packed structures; (2) filter the minimized structures to find those that are consistent with the expected symmetry of the oligomer; (3) cluster the structures that pass the symmetry filter; and (4) select a representative of the most populous cluster as the final prediction. We applied the method to the transmembrane helices of five proteins and compare our results to the available experimental data. Our predictions of glycophorin A, neu, the M2 channel and phospholamban resulted in a single model for each protein that agreed with the experimental results. In the case of erbB-2, however, we obtained three structurally distinct clusters of approximately equal sizes, so it was not possible to identify a clearly favored structure. This may reflect a real heterogeneity of packing modes for erbB-2, which is known to interact with different receptor subunits. Our method should be useful for obtaining structural models of transmembrane domains, improving our understanding of structure/function relationships for particular membrane proteins.

Identification of Sample Preparation Defects in Automated Topological Characterization of Composite Materials

Large Area Automated Microscopy, which involves the capturing and montaging of thousands of digital image frames to create one seamless picture of large-area specimens, is increasingly being used to identify and quantify meso-structural topological features in composite materials. In this work we describe the usage of a geometrical descriptor, namely the symmetry ratio (Sr), to isolate and filter out fiber fragments from optical micrographs of cross-sections of pultruded rods reinforced with continuous carbon fibers. Damaged fibers are present in such images as a result of sample preparation and can easily be mistaken for either ‘‘small’’ fibers or ‘‘misaligned’’ fibers by typical image analysis software. Elimination of such defects removes a small but potentially misleading bimodality from the size histogram of the fiber population.

Automated calibration in vascular X-ray images using the accurate localization of catheter marker bands.

To develop a new automated calibration method for vessel measurements in vascular x-ray images. Radiopaque marker bands mounted equidistantly on a small catheter were acquired in vitro at five image intensifier (II) sizes in x-ray projection images. The positions of the marker centers were detected by using a Hough transform and were computed at subpixel precision by using either a novel, iterative center-of-gravity approach (CGA) or a symmetry filter. Curve-fitting procedures were used to reject false-positive marker detections and to calculate intermarker distances. The calibration factor was calculated from the true marker distance and the average of the measured distances in pixels. Results were compared statistically with a grid calibration method, which was taken as the gold standard. A simulation study was performed to assess the influence of image noise on the CGA method. The iterative CGA method was convergent and faster than the symmetry-based technique. For four II sizes (17, 20, 25, and 31 cm), the results from the CGA method were not significantly different from the results obtained with grid calibration. For the II size of 38 cm, a significant difference (0.3% of the grid calibration factor) was found; however, this was caused by the quantification error in the image data and was not clinically relevant. In general, the performance of the CGA method improved with increasing signal-to-noise ratio. A practical new calibration method for small catheter sizes was developed and validated for quantitative vascular arteriography.

Automated Processing of Two-Dimensional Correlation Spectra

An automated scheme is described which locates the centers of cross peaks in two-dimensional correlation spectra, even under conditions of severe overlap. Double-quantum-filtered correlation (DQ-COSY) spectra have been investigated, but the method is also applicable to TOCSY and NOESY spectra. The search criterion is the intrinsic symmetry (or antisymmetry) of cross-peak multiplets. An initial global search provides the preliminary information to build up a two-dimensional “chemical shift grid.” All genuine cross peaks must be centered at intersections of this grid, a fact that reduces the extent of the subsequent search program enormously. The program recognizes cross peaks by examining the symmetry of signals in a test zone centered at a grid intersection. This “symmetry filter” employs a “lowest value algorithm” to discriminate against overlapping responses from adjacent multiplets. A progressive multiplet subtraction scheme provides further suppression of overlap effects. The processed two-dimensional correlation spectrum represents cross peaks as points at the chemical shift coordinates, with some indication of their relative intensities. Alternatively, the information is presented in the form of a correlation table. The authenticity of a given cross peak is judged by a set of “confidence criteria” expressed as numerical parameters. Experimental results are presented for the 400-MHz double-quantum-filtered COSY spectrum of 4-androsten-3,17-dione, a case where there is severe overlap.

Proton Chemical-Shift Spectra

Three related methods are explored for obtaining high-resolution proton spectra without spin–spin splittings, termed “chemical-shift spectra.” They are based on two-dimensionalJspectroscopy, where theF1dimension is derived by Fourier transformation of spin-echo modulation. The first technique superimposes theJspectrum on its reflection in theF1= 0 axis, creating multiplet patterns in the form of a St. Andrew's cross. The other two techniques purge certain antiphase product-operator terms, either by dispersal in an inhomogeneous effective radiofrequency field oriented at the magic angle (54.7°) or by means of azfilter. In all three cases, the two-dimensional multiplets are separated by means of a symmetry filter and their centers are taken as a measure of the respective chemical shifts. The 400 MHz proton chemical-shift spectrum of 4-androsten-3,17-dione is presented as an illustrative example. Good separation is achieved, even for interpenetrating spin multiplets with near degeneracies in their chemical shifts. Complications due to strong-coupling effects are discussed.