Wen-Ming Yan

The complex Householder transform

The Householder (1968) transform is very useful in matrix computations and signal processing. A straightforward derivation for a complex Householder transform is given. It needs fewer complex operations when compared with the previous results by Venkaiah et al. (1993) and Xia and Suter (see Digital Signal Process., vol.5, p.116-17, 1995). We also investigate applying our result to the derivation of a hyperbolic Householder transform.

A fast algorithm for solving special tridiagonal systems

In this paper, a fast algorithm for solving the special tridiagonal system is presented. This special tridiagonal system is a symmetric diagonally dominant and Toeplitz system of linear equations. The error analysis is also given. Our algorithm is quite competitive with the Gaussian elimination, cyclic reduction, specialLU factorization, reversed triangular factorization, and Toeplitz factorization methods. In addition, our result can be applied to solve the near-Toeplitz tridiagonal system. Some examples demonstrate the good efficiency and stability of our algorithm.ZusammenfassungIn dieser Arbeit wird ein schneller Algorithmus zur Lösung symmetrischer, diagonaldominanter tridiagonaler Töpflitz-Systeme vorgestellt. Auch eine Fehleranalyse liegt vor. Der Algorithmus ist den folgenden Verfahren mindestens gleichwertig: Gauss-Elimination, zyklische Reduktion, spezielleLU-Faktorisierung, umgekehrte Faktorisierung, Töplitz-Faktorisierung. Außerdem kann unser Vorgehen zur Lösung in tridiagonalen fast-Töplitz-Systemen verwendet werden. Einige Beispiele zeigen die Effizienz und Stabilität unseres Algorithmus.

A hybrid gray image representation using spatial- and DCT-based approach with application to moment computation

In this paper, a novel hybrid gray image representation using spatial- and DCT-based approach is presented. In the first phase, according to the bintree decomposition principle under the specified error, an S-tree spatial data structure (SDS) is used to represent the decomposed bintree of the input gray image. In the constructed S-tree SDS, the leaves are partitioned into two types, namely the homogeneous leaves and the nonhomogeneous leaves. The homogeneous leaf is used to represent one rectangular or square homogeneous subimage with smooth, i.e., low frequency, content and the nonhomogeneous leaf is used to represent one nonhomogeneous subimage with nonsmooth, i.e., high frequency, content. In the second phase, each nonhomogeneous leaf is encoded by the DCT-based coding scheme for reducing the memory requirement. Based on some real gray images, experimental results show that our proposed gray image representation over the previously published S-tree- and shading-based SDS has about 63.08% memory-saving improvement ratio in average. Finally, we investigate the computational benefit when computing moments on our proposed gray image representation directly.

Distortion reduction for histogram modification-based reversible data hiding

Abstract The histogram modification (HM) method proposed by Ni et al. is very efficient for reversible data hiding (RDH). Besides the excellent execution-time performance, Ni et al.’s HM-based RDH (HMRDH) method has a high PSNR lower bound of marked images. In this short communication, an observation on Ni et al.’s HM-based RDH (HMRDH) method is pointed out that the distortion of the marked image from Ni et al.’s method is dependent on the number of 1’s in the watermark. From this observation, we first present a watermark complement scheme to reduce the distortion occurred in Ni et al.’s HMRDH method. Later, combinatorial analysis for average distortion ratio of the proposed scheme is provided. This analysis motivates us to present a block-based complement scheme to improve the distortion reduction further. The tradeoff between the distortion and the number of partitioned blocks is also investigated. Taking nine well-known trademarks as the test watermarks and two cover images with different types of content, experimental results demonstrated the distortion reduction and higher PSNR lower bound advantages of the proposed block-based watermark complement scheme.

New memory- and computation-efficient hough transform for detecting lines

The slope-intercept Hough transform (SIHT) is one of the two types of line-detection methods. However, the disadvantage of the SIHT is its low memory utilization, say 50%. Based on the affine transformation, this paper presents a new method to improve the memory utilization of the SIHT from 50% to 100%. According to the proposed affine transformation, we first present a basic SIHT-based algorithm for detecting lines. Instead of concerning floating-point operations in the basic SIHT-based algorithm, an improved SIHT-based algorithm, which mainly concerns integer operations, is presented. Besides the memory utilization advantage, experimental results reveal that the improved SIHT-based algorithm has more than 60% execution time improvement ratio when compared to the basic SIHT-based algorithm and has more than 33% execution time improvement ratio when compared to another type of line-detection methods, such as the (r,θ)-based HT algorithm and its variant. The detailed complexity analyses for all the related algorithms are also investigated and we show that the time complexity required in the improved SIHT-based algorithm is the least.

On the number of spanning trees of a multi-complete/star related graph

Abstract This paper derives a closed formula for the number of spanning trees of a multi-complete/star related graph G=K n −K m (a 1 ,a 2 ,…,a l ;b 1 ,b 2 ,…,b m−l ) , where K m (a 1 ,a 2 ,…,a l ;b 1 ,b 2 ,…,b m−l ) consists of l complete graphs and m−l star graphs such that the i th complete graph has a i +1 nodes; the j th star graph has b j +1 nodes, and further, the related m roots are connected together to form a complete graph. The proposed results extend previous results to a larger graph class. In addition, we provide a general maximization theorem for the multi-star graph.

A formula for the number of spanning trees of a multi-star related graph

Abstract Using a new labeling technique and matrix computations, this paper derives a closed formula for the number of spanning trees of a multi-star related graph G = K n − K m ( a 1 , a 2 ,…, a m ), where K m ( a 1 , a 2 ,…, a m ) consists of m star graphs such that the i th one has a root node connected to a i leaves, and further, the m roots are connected together to form a complete graph. This result generalizes the previous result by Nikolopoulos and Rondogiannis (1998) which is limited to m = 2, 3, 4.

New joint demosaicing and arbitrary-ratio resizing algorithm for color filter array based on DCT approach

This paper presents a new joint demosaicing and arbitrary-ratio resizing algorithm for mosaic images. By using the adaptive heterogeneity projection masks and Sobel- and luminance estimation-based (SL-based) masks, more accurate edge information is extracted first. Next, the fully populated green color plane is constructed by using the edge-sensing approach and color difference idea. Instead of interpolating the R and B color planes directly, the green-red color difference plane and green-blue color difference plane are therefore interpolated in order to reduce the estimation error. Next, based on the discrete cosine transform (DCT) technique, the above three constructed planes are resized to the arbitrary sized ones. Finally, the resized red and blue color planes are constructed by using the three resized planes, and then the arbitrary sized full color image is obtained. To the best of our knowledge, this is the first time that such a joint demosaicing and arbitrary-ratio resizing algorithm for mosaic images is presented. Based on twenty-four popular testing mosaic images, the proposed resizing algorithm has better image quality performance when compared with three native algorithms which are the combinations of three well-know demosaicing methods and one existing resizing method. Thus, the proposed algorithm can be used in consumer electronic products, such as digital cameras and digital camcorders, to provide the quality-efficient arbitrary-ratio resizing effect.

Efficient algorithms for 3-D polygonal approximation based on LISE criterion

Abstract Given a polygonal curve P in three-dimensional (3-D) space, the polygonal approximation (PA) problem in this research is to find a polygon P′ to approximate P either with the minimal polygonal segments under a given error or, conversely, with the minimal error under a specified number of segments allowable. The former PA problem is called the PA-# problem; the latter PA problem is called the PA-e problem. Given a 3-D P with n nodes, under the local integral square error criterion, this paper first presents an O(n2)-time algorithm for solving the PA-# problem using O(n) space. Then we present an O(n 2 log n) -time algorithm for solving the PA-e using O(n2) space. Finally, a sampling technique is employed to reduce the memory requirement from O(n2) to O(n). Some experiments are carried out to confirm the theoretical analysis.

A parallel solver for circulant block-tridiagonal systems

Abstract Generalizing Muller and Scheerers method which is used to parallelize the tridiagonal solvers, this paper presents a parallel method for solving the circulant block-tridiagonal systems. The applications of our result to solve the block-tridiagonal systems, the banded systems, and the circulant tridiagonal systems (for example, solving the closed B-spline curve fitting) are also addressed.