Fast splitting alpha-rooting method of image enhancement: tensor representation.

In the tensor representation, a two-dimensional (2-D) image is represented uniquely by a set of one-dimensional (1-D) signals, so-called splitting-signals, that carry the spectral information of the image at frequency-points of specific sets that cover the whole domain of frequencies. The image enhancement is thus reduced to processing splitting-signals and such process requires a modification of only a few spectral components of the image, for each signal. For instance, the alpha-rooting method of image enhancement can be fulfilled through processing separately a maximum of 3N/2 splitting-signals of an image (N x N), where N is a power of two. In this paper, we propose a fast implementation of the a-rooting method by using one splitting-signal of the tensor representation with respect to the discrete Fourier transform (DFT). The implementation is described in the frequency and spatial domains. As a result, the proposed algorithms for image enhancement use two 1-D N-point DFTs instead of two 2-D N x N-point DFTs in the traditional method of alpha-rooting.     

Efficient Systolic Implementation of DFT Using a Low-Complexity Convolution-Like Formulation

A reduced-complexity algorithm is presented for computation of the discrete Fourier transform, where$N$-point transform is computed from eight number of nearly$(N/8)$-point circular-convolution-like operations. A systolic architecture is also derived for very large-scale integration circuit implementation of the proposed algorithm. The proposed architecture is fully pipelined and contains regular and simple locally connected processing elements. It is devoid of complex control structure and is scalable for higher transform lengths. It is observed that the proposed systolic structure involves either less or nearly the same hardware-complexity compared with the corresponding existing systolic structures. In addition, it offers eight times more throughput and significantly low latency compared with the others.     

VOIR: a volumetric image reconstruction algorithm based on Fouriertechniques for inversion of the 3-D Radon transform

A novel volumetric image reconstruction algorithm known as VOIR is presented for inversion of the 3-D Radon transform or its radial derivative. The algorithm is a direct implementation of the projection slice theorem for plane integrals. It generalizes one of the most successful methods in 2-D Fourier image reconstruction involving concentric-square rasters to 3-D; in VOIR, the spectral data, which is calculated by fast Fourier techniques, lie on concentric cubes and are interpolated by a bilinear method on the sides of these concentric cubes. The algorithm has great computational advantages over filtered-backprojection algorithms; for images of side dimension N, the numerical complexity of VOIR is O(N(3) log N) instead of O(N (4)) for backprojection techniques. An evaluation of the image processing performance is reported by comparison of reconstructed images from simulated cone-beam scans of a contrast and resolution test object. The image processing performance is also characterized by an analysis of the edge response from the reconstructed images.     

Automated 3-D Intraretinal Layer Segmentation of Macular Spectral-Domain Optical Coherence Tomography Images

With the introduction of spectral-domain optical coherence tomography (OCT), much larger image datasets are routinely acquired compared to what was possible using the previous generation of time-domain OCT. Thus, the need for 3-D segmentation methods for processing such data is becoming increasingly important. We report a graph-theoretic segmentation method for the simultaneous segmentation of multiple 3-D surfaces that is guaranteed to be optimal with respect to the cost function and that is directly applicable to the segmentation of 3-D spectral OCT image data. We present two extensions to the general layered graph segmentation method: the ability to incorporate varying feasibility constraints and the ability to incorporate true regional information. Appropriate feasibility constraints and cost functions were learned from a training set of 13 spectral-domain OCT images from 13 subjects. After training, our approach was tested on a test set of 28 images from 14 subjects. An overall mean unsigned border positioning error of $5.69pm 2.41 mu{rm m}$ was achieved when segmenting seven surfaces (six layers) and using the average of the manual tracings of two ophthalmologists as the reference standard. This result is very comparable to the measured interobserver variability of $5.71pm 1.98 mu{rm m}$.      

Realizations of fast 2-D/3-D image filtering and enhancement

This paper proposes a novel algorithm for multidimensional image enhancement based on a fuzzy domain enhancement method, and an implementation of a recursive and separable low-pass filter. Considering a smoothed image as a fuzzy data set, each pixel in an image is processed independently, using fuzzy domain transformation and enhancement of both the dynamic range and the local gray level variations. The algorithm has the advantages of being fast and adaptive, so it can be used in real-time image processing applications and for multidimensional data with low computational cost. It also has the ability to reduce noise and unwanted background that may affect the visualization quality of two-dimensional (2-D)/three-dimensional (3-D) data. Examples for the applications of the algorithm are given for mammograms, ultrasound 3-D images, and photographic images.     

A 3-D Spectral Integral Method (SIM) for Surface Integral Equations

An efficient 3-D spectral integral method (SIM) has been proposed to speed up the method of moments (MOM) calculation of induced currents on a cuboid. This method utilizes the Toeplitz structure in the impedance matrix and the fast Fourier transform to accelerate the MOM solution. It reduces the memory and CPU time per iteration from $O(N^2)$ in the MOM to $O(N^{1.5})$ and $O(N^{1.5}log N)$, respectively. Thus, the SIM can be also used as an efficient radiation boundary condition for the finite element method. Numerical results confirm the effectiveness of this method.      

FEM Design and Modeling of $chi^{(2)} $ Second-Harmonic Enhancement in Circular Photonic Crystal

In this paper, we analyze the enhancement of $chi^{(2)} $ nonlinear process in membrane-type circular photonic crystal (PhC) based on GaAs. This unconventional kind of PhC is well suited for the generation of whispering gallery modes (WGMs) due to the circular symmetric periodic pattern. By using a laser Gaussian beam at 1.55 $ mu{hbox {m}}$ as pump signal, a WGM at 1.55 $ mu{hbox {m}}$ and a second-harmonic (SH) mode at 0.775 $ mu{hbox {m}}$ are obtained. The SH will be generated in the center of the missing-hole microcavity. The periodic pattern and the microcavity are tailored and optimized providing an SH efficiency conversion as high as 50%. We predict the resonances by an accurate 2-D time-domain model including $chi^{(2)}$ nonlinearity and by a 3-D finite-element method. Finally, by using a 3-D membrane configuration, we found a total quality factor of the SH mode of the order of 35 000.      

Significance of image representation for face verification

In this paper we discuss the significance of representation of images for face verification. We consider three different representations, namely, edge gradient, edge orientation and potential field derived from the edge gradient. These representations are examined in the context of face verification using a specific type of correlation filter, called the minimum average correlation energy (MACE) filter. The different representations are derived using one-dimensional (1-D) processing of image. The 1-D processing provides multiple partial evidences for a given face image, one evidence for each direction of the 1-D processing. Separate MACE filters are used for deriving each partial evidence. We propose a method to combine the partial evidences obtained for each representation using an auto-associative neural network (AANN) model, to arrive at a decision for face verification. Results show that the performance of the system using potential field representation is better than that using the edge gradient representation or the edge orientation representation. Also, the potential field representation derived from the edge gradient is observed to be less sensitive to variation in illumination compared to the gray level representation of images.     

On the Computation of the Discrete Cosine Transform

AnN-point discrete Fourier transform (DFT) algorithm can be used to evaluate a discrete cosine transform by a simple rearrangement of the input data. This method is about two times faster compared to the conventional method which uses a2N-point DFT.     

Measurement of SOA Linewidth Enhancement Factor With a Sagnac Fiber Loop

We demonstrate a novel method to measure the linewidth enhancement factor ($alpha$-factor) of the semiconductor optical amplifier (SOA). We derived theoretically the quantitative relationships among the$alpha$-factor, the cross-gain modulation, the cross-phase modulation, and the contrast ratio of an SOA-based Sagnac fiber loop. We found that the$alpha$-factor value can be calculated directly from the maximum power contrast ratio measurement. Our experiment results show that the obtained$alpha$-factor fluctuates within a small range of 5.23 to 6.83 when the bias current varies from 130 to 240 mA. Compared with existing measurement methods, our method is more attractive because of its simple configuration and better stability.     

Simplified square to hexagonal lattice conversion based on 1-D multirate processing

Hexagonal image sampling and processing are theoretically superior to the most commonly used square lattice based sampling and processing, but due to the lack of commercial image sensors, current research mainly relies on virtually hexagonally sampled data through square to hexagonal lattice conversion, which is a typical 2-D interpolation problem. This paper presents a simplified and efficient square to hexagonal lattice conversion method. The method firstly utilizes the separable nature of the interpolation kernel to simplify the original 2-D interpolation into 1-D interpolation along the horizontal direction only, and then it applies the 1-D multirate technique to further simplify the shift-variant 1-D interpolation into shift-invariant 1-D convolutions. Compared with the original 2-D interpolation version, the proposed method becomes both simple and computationally efficient, and it is also suitable for implementation with parallel processing and hardware. Finally, experiments are performed and the results are consistent with the analysis.     

Efficient Hierarchical Motion Estimation Algorithm and Its VLSI Architecture

This paper addresses the development and hardware implementation of an efficient hierarchical motion estimation algorithm, HMEA, using multiresolution frames to reduce the computational complexity. Excellent estimation performance is ensured using an averaging filter to downsample the original image. At the smallest resolution, the least two motion vector candidates are selected using a full-search block matching algorithm. At the middle level, these two candidate motion vectors are employed as the center points for small range local searches. Then, at the original resolution, the final motion vector is obtained by performing a local search around the single candidate from the middle level. HMEA exhibits regular data flow and is suitable for hardware implementation. An efficient VLSI architecture that includes an averaging filter to downsample the image and two 2-D semisystolic processing element arrays to determine the sum of absolute difference in pipeline is also presented. Simulation results indicate that HMEA is more area-efficient and faster than many full-search and multiresolution architectures while maintaining high video quality. This architecture with 59K gates and 1393 bytes of RAM is implemented for a search range of [ $-$16.0, $+$15.5].      

Real-time computation of two-dimensional moments on binary imagesusing image block representation

This work presents a new approach and an algorithm for binary image representation, which is applied for the fast and efficient computation of moments on binary images. This binary image representation scheme is called image block representation, since it represents the image as a set of nonoverlapping rectangular areas. The main purpose of the image block representation process is to provide an efficient binary image representation rather than the compression of the image. The block represented binary image is well suited for fast implementation of various processing and analysis algorithms in a digital computing machine. The two-dimensional (2-D) statistical moments of the image may be used for image processing and analysis applications. A number of powerful shape analysis methods based on statistical moments have been presented, but they suffer from the drawback of high computational cost. The real-time computation of moments in block represented images is achieved by exploiting the rectangular structure of the blocks.     

Strained-SOI n-Channel Transistor With Silicon–Carbon Source/Drain Regions for Carrier Transport Enhancement

A novel 80 nm gate length strained-Si n-channel transistor structure with lattice-mismatched source and drain (S/D) formed on thin-body silicon-on-insulator substrate is reported. The strained transistor features silicon–carbon$(hboxSi_1 - yhboxC_y)$S/D regions, which are pseudomorphically grown by selective epitaxy. The incorporated carbon mole fraction$y$is 0.01. The lattice mismatch between$hboxSi_0.99hboxC_0.01$and Si results in lateral tensile strain and vertical compressive strain in the Si channel region, both contributing to substantial electron mobility enhancement. The implementation of the$hboxSi_0.99hboxC_0.01$stressors provides a substantial drive current$I_ Dsat$enhancement of 11% over a control transistor at a gate length of 80 nm and a width of$simhbox1.1 muhboxm$, while the enhancement for the linear drive current$I_ Dlin$is approximately two times larger. Pulse measurements were also performed to correct for self-heating effects.     

A fundamental theorem of algebra, spectral factorization, and stability of two-dimensional systems

In his doctoral dissertation in 1797, Gauss proved the fundamental theorem of algebra, which states that any one-dimensional (1-D) polynomial of degree n with complex coefficients can be factored into a product of n polynomials of degree 1. Since then, it has been an open problem to factorize a two-dimensional (2-D) polynomial into a product of basic polynomials. Particularly for the last three decades, this problem has become more important in a wide range of signal and image processing such as 2-D filter design and 2-D wavelet analysis. In this paper, a fundamental theorem of algebra for 2-D polynomials is presented. In applications such as 2-D signal and image processing, it is often necessary to find a 2-D spectral factor from a given 2-D autocorrelation function. In this paper, a 2-D spectral factorization method is presented through cepstral analysis. In addition, some algorithms are proposed to factorize a 2-D spectral factor finely. These are applied to deriving stability criteria of 2-D filters and nonseparable 2-D wavelets and to solving partial difference equations and partial differential equations.     

Two-Dimensional Variation Algorithm for Fractal Analysis of Sea SAR Images

This paper proposes a novel algorithm for estimating the fractal dimension of sea synthetic aperture radar (SAR) images. The algorithm is based on the variation method, and it is suitably designed for the analysis of sea SAR images. The SAR image fractal dimension is a feature that provides a measure of the image roughness. Such a feature can play an important role in the classification process for recognizing the presence of anomalies on the sea surface. The innovation aspects of this paper are listed as follows: 1) an extension of the variation method, which was proposed for the fractal analysis of one-dimensional signals, to the case of two-dimensional (2-D) functions; 2) a numerical formulation of the variation method, which is suitable for processing 2-D discrete signals; and 3) an optimization of the algorithm for sea SAR image analysis. The algorithm is tested and validated both on simulated and real ERS-1/2 Precision Image sea SAR images and compared with the classical estimation algorithm based on spectral analysis.     

Three-dimensional cardiac strain estimation using spatio-temporal elastic registration of ultrasound images: a feasibility study

Current ultrasound methods for measuring myocardial strain are often limited to measurements in one or two dimensions. Cardiac motion and deformation however are truly 3-D. With the introduction of matrix transducer technology, 3-D ultrasound imaging of the heart has become feasible but suffers from low temporal and spatial resolution, making 3-D strain estimation challenging. In this paper, it is shown that automatic intensity-based spatio–temporal elastic registration of currently available 3-D volumetric ultrasound data sets can be used to measure the full 3-D strain tensor. The method was validated using simulated 3-D ultrasound data sets of the left ventricle (LV). Three types of data sets were simulated: a normal and symmetric LV with different heart rates, a more realistic asymmetric normal LV and an infarcted LV. The absolute error in the estimated displacement was between $0.47 pm 0.23$ and $1.00 pm 0.59$ mm, depending on heart rate and amount of background noise. The absolute error on the estimated strain was 9%–21% for the radial strain and 1%–4% for the longitudinal and circumferential strains. No large differences were found between the different types of data sets. The shape of the strain curves was estimated properly and the position of the infarcts could be identified correctly. Preliminary results on clinical data taken in vivo from three healthy volunteers and one patient with an apical aneurism confirmed these findings in a qualitative manner as the strain curves obtained with the proposed method have an amplitude and shape similar to what could be expected.      

Semi-Supervised Bilinear Subspace Learning

Recent research has demonstrated the success of tensor based subspace learning in both unsupervised and supervised configurations (e.g., 2-D PCA, 2-D LDA, and DATER). In this correspondence, we present a new semi-supervised subspace learning algorithm by integrating the tensor representation and the complementary information conveyed by unlabeled data. Conventional semi-supervised algorithms mostly impose a regularization term based on the data representation in the original feature space. Instead, we utilize graph Laplacian regularization based on the low-dimensional feature space. An iterative algorithm, referred to as adaptive regularization based semi-supervised discriminant analysis with tensor representation (ARSDA/T), is also developed to compute the solution. In addition to handling tensor data, a vector-based variant (ARSDA/V) is also presented, in which the tensor data are converted into vectors before subspace learning. Comprehensive experiments on the CMU PIE and YALE-B databases demonstrate that ARSDA/T brings significant improvement in face recognition accuracy over both conventional supervised and semi-supervised subspace learning algorithms.     

Fast Parallel Approach for 2-D DHT-Based Real-Valued Discrete Gabor Transform

Two-dimensional fast Gabor transform algorithms are useful for real-time applications due to the high computational complexity of the traditional 2-D complex-valued discrete Gabor transform (CDGT). This paper presents two block time-recursive algorithms for 2-D DHT-based real-valued discrete Gabor transform (RDGT) and its inverse transform and develops a fast parallel approach for the implementation of the two algorithms. The computational complexity of the proposed parallel approach is analyzed and compared with that of the existing 2-D CDGT algorithms. The results indicate that the proposed parallel approach is attractive for real time image processing.      

Nonlinear anisotropic filtering of MRI data

In contrast to acquisition-based noise reduction methods a postprocess based on anisotropic diffusion is proposed. Extensions of this technique support 3-D and multiecho magnetic resonance imaging (MRI), incorporating higher spatial and spectral dimensions. The procedure overcomes the major drawbacks of conventional filter methods, namely the blurring of object boundaries and the suppression of fine structural details. The simplicity of the filter algorithm permits an efficient implementation, even on small workstations. The efficient noise reduction and sharpening of object boundaries are demonstrated by applying this image processing technique to 2-D and 3-D spin echo and gradient echo MR data. The potential advantages for MRI, diagnosis, and computerized analysis are discussed in detail.