Color-scale morphological filters with multiple structuring elements

With the wide use of color in many areas, the interest on the color perception and processing has been growing rapidly. An important topic in color image processing is the development of efficient tools capable of filtering images without blurring them and without changing their original chromatic contents. In this paper, a new technique reducing noise of color image is developed. A class of color-scale morphological operations is introduced, which extend mathematical morphology to color image processing, representing a color image as a vector function. The correlation between color components is utilized to perform noise removal. Color-scale morphological niters with multiple structuring elements (CSMF-MSEs) are proposed. Their properties are discussed and proved. Experimental results show that CSMF-MSEs are suitable and powerful to eliminate noise and preserve edges in color image because of efficient utilization of inherent correlation between color components, and they perform better than vector med     

Decomposition of morphological structuring elements with integer linear programming

A method is proposed for decomposing morphological structuring elements based on integer linear programming. A decomposition problem is formulated into a set of linear constraints, and an optimal decomposition is a solution to the constraints, obtained by the cutting-plane simplex algorithm. The method has several advantages. It provides a systematic way of decomposing arbitrarily shaped structuring elements. For convex images, factors can be of any size, not restricted to 3 /spl times/ 3; the candidate set can be freely assigned by the user; and the optimality criteria can be flexible.     

Efficient 2-D based algorithms for WLS designs of 2-D FIR filters with arbitrary weighting functions

The impulse response coefficients of a two-dimensional (2-D) finite impulse response (FIR) filter naturally constitute a matrix. It has been shown by several researchers that, two-dimension (2-D) based algorithms that retain the natural matrix form of the 2-D filter’s coefficients are computationally much more efficient than the conventional one-dimension (1-D) based algorithms that rearrange the coefficient matrix into a vector. In this paper, two 2-D based algorithms are presented for the weighted least squares (WLS) design of quadrantally symmetric 2-D FIR filters with arbitrary weighting functions. Both algorithms are based on matrix iterative techniques with guaranteed convergence, and they solve the WLS design problems accurately and efficiently. The convergence rate, solution accuracy and design time of these proposed algorithms are demonstrated and compared with existing algorithms through two design examples.     

Efficient implementation of accurate geometric transformations for 2-D and 3-D image processing

This paper proposes the use of a polynomial interpolator structure (based on Horner's scheme) which is efficiently realizable in hardware, for high-quality geometric transformation of two- and three-dimensional images. Polynomial-based interpolators such as cubic B-splines and optimal interpolators of shortest support are shown to be exactly implementable in the Horner structure framework. This structure suggests a hardware/software partition which can lead to efficient implementations for multidimensional interpolation.     

一种全方位多角度自适应形态滤波器及其算法

根据形态滤波器的结构元特性,结合形态开—闭(闭—开)组合运算及自适应算法,建立了一种能有效去除复杂纹理图像中的各种噪声,并较好的保持图像细节的方法。实验证明,这种全方位多角度自适应形态滤波器与现有的中值滤波器、全方位结构元形态闭—开最小、开—闭最大滤波器等非线性滤波器相比较有更好的降噪性能及细节保护能力,扩展了形态滤波器在滤除高斯噪声方面的应用,提高了形态滤波器的适应性。     

A fast implementation of 3-D binary morphological transformations

This paper proposes a fast algorithm for implementing the basic operation of Minkowski addition for the special case of binary three-dimensional (3-D) images, using 3-D structuring elements of arbitrary size and shape. The application of the proposed algorithm for all the other morphological transformations is straightforward, as they can all be expressed in terms of Minkowski addition. The efficiency of the algorithm is analyzed and some experimental results of its application are presented. As shown, the efficiency of the algorithm increases with the size of the structuring element.     

Efficient mode analysis with edge elements and 3-D adaptiverefinement

Efficient mode analysis of 3-D inhomogeneously loaded cavity resonators of arbitrary shape by the finite edge element method is presented in this paper. Two weak formulations involving field vectors E and H are derived from a Galerkin weighted scheme resulting in a sparse symmetric generalized eigenvalue problem, the solution of which is obtained by a sparse eigenvalue technique. Edge elements with divergence free shape functions guarantee the continuity of the tangential components of the field variables E or H, but not of their normal components, across element interfaces in contrast with node based elements that impose full continuity. The discontinuity of the normal component of D or B, present in the numerical model, is proposed as an error estimator suitable for adaptive mesh refinement of 3-D tetrahedral meshes with edge elements. Application to a dielectrically loaded cavity is given with full documentation and by way of illustration     

Fast 2-D distance transformations

The performance of a number of image processing methods depends on the output quality of a distance transformation (DT) process. Most of the fast DT methodologies are not accurate, whereas other error-free DT algorithms are not very fast. In this paper, a novel, fast, simple, and error-free DT algorithm is presented. By recording the relative x- and y-coordinates of the examined image pixels, an optimal algorithm can be developed to achieve the DT of an image correctly and efficiently in constant time without any iteration. Furthermore, the proposed method is general since it can be used by any kind of distance function, leading to accurate image DTs.     

Automatic 3-D grayscale volume matching and shape analysis.

Recently, shape matching in three dimensions (3-D) has been gaining importance in a wide variety of fields such as computer graphics, computer vision, medicine, and biology, with applications such as object recognition, medical diagnosis, and quantitative morphological analysis of biological operations. Automatic shape matching techniques developed in the field of computer graphics handle object surfaces, but ignore intensities of inner voxels. In biology and medical imaging, voxel intensities obtained by computed tomography (CT), magnetic resonance imagery (MRI), and confocal microscopes are important to determine point correspondences. Nevertheless, most biomedical volume matching techniques require human interactions, and automatic methods assume matched objects to have very similar shapes so as to avoid combinatorial explosions of point. This article is aimed at decreasing the gap between the two fields. The proposed method automatically finds dense point correspondences between two grayscale volumes; i.e., finds a correspondent in the second volume for every voxel in the first volume, based on the voxel intensities. Mutiresolutional pyramids are introduced to reduce computational load and handle highly plastic objects. We calculate the average shape of a set of similar objects and give a measure of plasticity to compare them. Matching results can also be used to generate intermediate volumes for morphing. We use various data to validate the effectiveness of our method: we calculate the average shape and plasticity of a set of fly brain cells, and we also match a human skull and an orangutan skull.     

A generalized discrete morphological skeleton transform with multiple structuring elements for the extraction of structural shape components

A common problem shared by several leading morphological shape representation algorithms is that there is much overlapping among the representative disks of the same size. A shape component represented by a group of connected disk centers sometimes uses many heavily overlapping representative disks to represent a relatively simple shape part. A shape component may also contain a large number of representative disks that form a complicated structure. We introduce a generalized discrete morphological skeleton transform that uses eight structuring elements to generate skeleton subsets so that no two skeletal points from the same skeleton subset are adjacent to each other. Each skeletal point represents a shape part that is in general an octagon with four pairs of parallel opposing sides. The number of representative points needed to represent a given shape is significantly lower than that in the standard skeleton transform. A collection of shape components needed to build a structural representation is easily derived from the generalized skeleton transform. Each shape component covers a significant area of the given shape and severe overlapping is avoided. The given shape can also be accurately approximated using a small number of shape components.     

Efficient compact 2-D time-domain method with weighted Laguerre polynomials

An efficient time-domain method based on a compact two-dimensional (2-D) finite-difference time-domain (FDTD) method combined with weighted Laguerre polynomials has been proposed to analyze the propagation properties of uniform transmission lines. Starting from Maxwell's differential equations corresponding to the compact 2-D FDTD method, we use the orthonormality of weighted Laguerre polynomials and Galerkin's testing procedure to eliminate the time variable. Thus, an implicit relation, which results in a marching-on-in-degree scheme, can be obtained. To verify the accuracy and efficiency of the hybrid method, we compare the results with those from the conventional compact 2-D FDTD and compact 2-D alternating-direction-implicit (ADI) FDTD methods. The hybrid method improves the computational efficiency notably, especially for complex problems with fine structure details that are restricted by stability constrains in the FDTD method.     

Efficient architectures for 1-D and 2-D lifting-based wavelet transforms

The lifting scheme reduces the computational complexity of the discrete wavelet transform (DWT) by factoring the wavelet filters into cascades of simple lifting steps that process the input samples in pairs. We propose four compact and efficient hardware architectures for implementing lifting-based DWTs, namely, one-dimensional (1-D) and two-dimensional (2-D) versions of what we call recursive and dual scan architectures. The 1-D recursive architecture exploits interdependencies among the wavelet coefficients by interleaving, on alternate clock cycles using the same datapath hardware, the calculation of higher order coefficients along with that of the first-stage coefficients. The resulting hardware utilization exceeds 90% in the typical case of a five-stage 1-D DWT operating on 1024 samples. The 1-D dual scan architecture achieves 100% datapath hardware utilization by processing two independent data streams together using shared functional blocks. The recursive and dual scan architectures can be readily extended to the 2-D case. The 2-D recursive architecture is roughly 25% faster than conventional implementations, and it requires a buffer that stores only a few rows of the data array instead of a fixed fraction (typically 25% or more) of the entire array. The 2-D dual scan architecture processes the column and row transforms simultaneously, and the memory buffer size is comparable to existing architectures.     

Efficient built-in redundancy analysis for embedded memories with 2-D redundancy

A novel redundant mechanism is proposed for embedded memories in this paper. Redundant rows and columns are added into the memory array as in the conventional approaches. However, the redundant rows and columns are divided into row blocks and column blocks, respectively. The reconfiguration is performed at the row (column) block level instead of the conventional row (column) level. Based on the proposed redundant mechanism, we first show that the complexity of the redundancy allocation problem is NP-complete. Thereafter, an extended local repair-most (ELRM) algorithm suitable for built-in implementation is proposed. The complexity of the ELRM algorithm is O(N), where N denotes the number of memory cells. According to the simulation results, the hardware overhead for implementing this algorithm is below 0.17% for a 1024/spl times/2048-b SRAM. Due to the efficient usage of the redundant elements, the manufacturing yield, repair rate, and reliability can be improved significantly.     

FMM算法用于二维复杂散射体的RCS计算

利用快速多极子算法(FMM)计算任意形状二维电大尺寸导体加介质体目标的电磁散射，介质体为镶嵌在电大尺寸金属体上的有耗介质。建立金属一介质体的混合积分方程，用共轭梯度法和场量叠代的方法计算散射场，在叠代过程中用快速多极子方法，大大降低计算时间和减小内存要求。数据结果表明该方法的准确和高效。     

Rate-Distortion Efficient Piecewise Planar 3-D Scene Representation From 2-D Images

In any practical application of the 2-D-to-3-D conversion that involves storage and transmission, representation efficiency has an undisputable importance that is not reflected in the attention the topic received. In order to address this problem, a novel algorithm, which yields efficient 3-D representations in the rate distortion sense, is proposed. The algorithm utilizes two views of a scene to build a mesh-based representation incrementally, via adding new vertices, while minimizing a distortion measure. The experimental results indicate that, in scenes that can be approximated by planes, the proposed algorithm is superior to the dense depth map and, in some practical situations, to the block motion vector-based representations in the rate-distortion sense.      

Efficient algorithm for 2-D arithmetic Fourier transform

This article presents an efficient algorithm for the two-dimensional (2-D) arithmetic Fourier transform (AFT) based on the Mobius inversion formula of odd number series. It requires fewer multiplications and has less complexity over previous algorithms. In addition, a technique is proposed to carry out the on-axis Fourier coefficients. A parallel VLSI architecture is developed for the new algorithm     

Efficient morphological shape representation with overlapping diskcomponents

This paper proposes a new morphological shape representation algorithm, in which a two-dimensional (2-D) binary shape is represented as a union of certain disks contained in the given shape. The representative disks of different sizes may overlap. But excessive overlapping between them is avoided. The algorithm combines the advantages of the morphological skeleton transform (MST) and the morphological shape decomposition (MSD). The representative disks have simple and well-defined mathematical characterizations. The algorithm is simple and efficient to implement. The experimental results show that the number of representative disks used by our algorithm is significant lower than that used by the MSD. The overlapping level between the representative disks is much lower than that of the MST. A simple procedure can be used to combine the representative disks into more meaningful shape components. These shape components seem to correspond better to the natural shape parts than those generated by the MSD. It is also possible to build a good approximation for a given shape using only a small number of major components.     

Efficient design of digital filters for 2-D and 3-D depth migration

Two- and three-dimensional (2-D and 3-D) depth migration can be performed using 1-D and 2-D extrapolation digital filters, respectively. The depth extrapolation is done, one frequency at a time, by convolving the seismic wavefield with a complex-valued, frequency- and velocity-dependent, digital filter. This process requires the design of a complete set of extrapolation filters: one filter for each possible frequency-velocity pair. Instead of independently designing the frequency- and velocity-dependent filters, an efficient procedure is introduced for designing a complete set of 1-D and 2-D extrapolation filters using transformations. The problem of designing a desired set of migration filters is thus reduced to the design of a single 1-D filter, which is then mapped to produce all the desired 1-D or 2-D migration filters. The new design procedure has the additional advantage that both the 1-D and 2-D migration filters can be realized efficiently and need not have their coefficients precomputed or tabulated     

Efficient arbitrary sampling rate conversion with recursivecalculation of coefficients

In this paper, we present a novel algorithm for sampling rate conversion by an arbitrary factor. Theoretically, sampling rate conversion of a discrete-time (DT) sequence can be performed by converting the sequence to a series of continuous-time (CT) impulses. This series of impulses is filtered with a CT lowpass filter, and the output is then sampled at the desired rate. If the CT filter is chosen to have a rational transfer function, then this system can be simulated using a DT algorithm for which both computation and memory requirements are low. The DT implementation is comprised of a parallel structure, where each branch consists of a time-varying filter with one or two taps, followed by a fixed recursive filter operating at the output sampling rate. The coefficients of the time-varying filters are calculated recursively. This eliminates the need to store a large table of coefficients, as is commonly done     

Efficient algorithms for computing the 2-D hexagonal Fouriertransforms

In this paper, representations of the two-dimensional (2-D) signals are presented that reduce the computation of 2-D discrete hexagonal Fourier transforms (2-D DHFTs). The representations are based on the concept of the covering that reveals the mathematical structure of the transforms. Specifically, a set of unitary paired transforms is derived that splits the 2-D DHFT into a number of smaller one-dimensional (1-D) DFTs. Examples for the 8×4 and 16×8 hexagonal lattices are described in detail. The number of multiplications required for computing the 8×4- and 16×8-point DHFTs are equal 20 and 136, respectively. In the general N⩾8 case, the number of multiplications required to compute the 2N×N-point DHFT by the paired transforms equals N² (log N-1)+N