Jim Z. C. Lai

A fast VQ codebook generation algorithm using codeword displacement

In this paper, we present a fast codebook generation algorithm called CGAUCD (Codebook Generation Algorithm Using Codeword Displacement) by making use of the codeword displacement between successive partition processes. By implementing a fast search algorithm named MFAUPI (Modified Fast Algorithm Using Projection and Inequality) for VQ encoding in the partition step of CGAUCD, the codebook generation time can be further reduced significantly. Using MFAUPI, the computing time of CGAUCD can be reduced by a factor of 4.7-7.6. Compared to Generalized Lloyd Algorithm (GLA), our proposed method can reduce the codebook generation time by a factor of 35.9-121.2. Compared to the best codebook generation algorithm to our knowledge, our approach can further reduce the corresponding computing time by 26.0-32.8%. It is noted that our proposed algorithm can generate the same codebook as that produced by the GLA. The superiority of our method is more remarkable when a larger codebook is generated.

A fast k-means clustering algorithm using cluster center displacement

In this paper, we present a fast k-means clustering algorithm (FKMCUCD) using the displacements of cluster centers to reject unlikely candidates for a data point. The computing time of our proposed algorithm increases linearly with the data dimension d, whereas the computational complexity of major available kd-tree based algorithms increases exponentially with the value of d. Theoretical analysis shows that our method can reduce the computational complexity of full search by a factor of SF and SF is independent of vector dimension. The experimental results show that compared to full search, our proposed method can reduce computational complexity by a factor of 1.37-4.39 using the data set from six real images. Compared with the filtering algorithm, which is among the available best algorithms of k-means clustering, our algorithm can effectively reduce the computing time. It is noted that our proposed algorithm can generate the same clusters as that produced by hard k-means clustering. The superiority of our method is more remarkable when a larger data set with higher dimension is used.

Artifact reduction of JPEG coded images using mean-removed classified vector quantization

Image compression techniques are frequently applied to reduce the network bandwidth and storage space. In the case of higher compression ratios, annoying artifacts may be generated and they degrade the perceptual quality of compressed images. This paper modified mean-removed classified vector quantization (MRCVQ) to reduce the artifacts of JPEG coded images. This algorithm consists of four phases: mean removal, encoding, decoding, and mean restoration. The mean removal phase removes the mean values of compressed image blocks. The encoding procedure needs a codebook for the encoder, which transforms a mean-removed compressed image to a set of codeword-indices. The decoding phase requires a different codebook for the decoder, which enhances a mean-removed compressed image from a set of codeword-indices. Finally, the mean values are restored in the mean restoration phase. The experimental results show that the proposed approach can remove effectively the artifacts caused by high compression and improve the perceptual quality significantly. Compared to the existing methods, our approach usually has the much better performance in terms of computing time, storage space and PSNR.

Fast-searching algorithm for vector quantization using projection and triangular inequality

In this paper, a new and fast-searching algorithm for vector quantization is presented. Two inequalities, one used for terminating the searching process and the other used to delete impossible codewords, are presented to reduce the distortion computations. Our algorithm makes use of a vectors features (mean value, edge strength, and texture strength) to reject many unlikely codewords that cannot be rejected by other available approaches. Experimental results show that our algorithm is superior to other algorithms in terms of computing time and the number of distortion calculations. Compared with available approaches, our method can reduce the computing time and the number of distortion computations significantly. Compared with the best method of reducing distortion computation, our algorithm can further reduce the number of distortion calculations by 29% to 58.4%. Compared with the best encoding algorithm for vector quantization, our approach also further reduces the computing time by 8% to 47.7%.

Inverse error-diffusion using classified vector quantization

This correspondence extends and modifies classified vector quantization (CVQ) to solve the problem of inverse halftoning. The proposed process consists of two phases: the encoding phase and decoding phase. The encoding procedure needs a codebook for the encoder which transforms a halftoned image to a set of codeword-indices. The decoding process also requires a different codebook for the decoder which reconstructs a gray-scale image from a set of codeword-indices. Using CVQ, the reconstructed gray-scale image is stored in compressed form and no further compression may be required. This is different from the existing algorithms, which reconstructed a halftoned image in an uncompressed form. The bit rate of encoding a reconstructed image is about 0.51 b/pixel.

Fast global k-means clustering using cluster membership and inequality

In this paper, we present a fast global k-means clustering algorithm by making use of the cluster membership and geometrical information of a data point. This algorithm is referred to as MFGKM. The algorithm uses a set of inequalities developed in this paper to determine a starting point for the jth cluster center of global k-means clustering. Adopting multiple cluster center selection (MCS) for MFGKM, we also develop another clustering algorithm called MFGKM+MCS. MCS determines more than one starting point for each step of cluster split; while the available fast and modified global k-means clustering algorithms select one starting point for each cluster split. Our proposed method MFGKM can obtain the least distortion; while MFGKM+MCS may give the least computing time. Compared to the modified global k-means clustering algorithm, our method MFGKM can reduce the computing time and number of distance calculations by a factor of 3.78-5.55 and 21.13-31.41, respectively, with the average distortion reduction of 5,487 for the Statlog data set. Compared to the fast global k-means clustering algorithm, our method MFGKM+MCS can reduce the computing time by a factor of 5.78-8.70 with the average reduction of distortion of 30,564 using the same data set. The performances of our proposed methods are more remarkable when a data set with higher dimension is divided into more clusters.

Fast k-nearest-neighbor search based on projection and triangular inequality

In this paper, a novel algorithm for finding k points that are closest to a query point is presented. Some inequalities are used to delete impossible data points and reduce distance computations. Our algorithm makes use of a data points feature to reject unlikely candidates for a query point and can eliminate many of the unlikely data points, which cannot be rejected by other available algorithms. Experimental results show that our algorithm is superior to other methods in terms of computing time and the number of distance calculations in most cases and is more remarkable, if a larger data set with higher dimension is used. Compared with available approaches, our method can reduce the computing time and number of distance calculations significantly.

Improvement of the k-means clustering filtering algorithm

In this paper, we present a modified filtering algorithm (MFA) by making use of center variations to speed up clustering process. Our method first divides clusters into static and active groups. We use the information of cluster displacements to reject unlikely cluster centers for all nodes in the kd-tree. We reduce the computational complexity of filtering algorithm (FA) through finding candidates for each node mainly from the set of active cluster centers. Two conditions for determining the set of candidate cluster centers for each node from active clusters are developed. Our approach is different from the major available algorithm, which passes no information from one stage of iteration to the next. Theoretical analysis shows that our method can reduce the computational complexity, in terms of the number of distance calculations, of FA at each stage of iteration by a factor of FC/AC, where FC and AC are the numbers of total clusters and active clusters, respectively. Compared with the FA, our algorithm can effectively reduce the computing time and number of distance calculations. It is noted that our proposed algorithm can generate the same clusters as that produced by hard k-means clustering. The superiority of our method is more remarkable when a larger data set with higher dimension is used.

Rough clustering using generalized fuzzy clustering algorithm

In this paper, we present a rough k-means clustering algorithm based on minimizing the dissimilarity, which is defined in terms of the squared Euclidean distances between data points and their closest cluster centers. This approach is referred to as generalized rough fuzzy k-means (GRFKM) algorithm. The proposed method solves the divergence problem of available approaches, where the cluster centers may not be converged to their final positions, and reduces the number of user-defined parameters. The presented method is shown to be converged experimentally. Compared to available rough k-means clustering algorithms, the proposed method provides less computing time. Unlike available approaches, the convergence of the proposed method is independent of the used threshold value. Moreover, it yields better clustering results than RFKM for the handwritten digits data set, landsat satellite data set and synthetic data set, in terms of validity indices. Compared to MRKM and RFKM, GRFKM can reduce the value of Xie-Beni index using the handwritten digits data set, where a lower Xie-Beni index value implies the better clustering quality. The proposed method can be applied to handle real life situations needing reasoning with uncertainty.

Fast Search Algorithms for VQ Codebook Generation

Abstract In this paper, we propose two fast codebook generation algorithms by making use of the information in the iterative process. Comparing to the conventional full search method (the LBG algorithm), the Fast Codebook Generation Algorithm (FCGA) reduces the CPU time by a factor of 2.49 to 6.16 for real images. Compared to FCGA the Maximum Set Algorithm (MSA), which is designed for the large codebook, gives the worse performance in general for our simulations. However, the Maximum Set Algorithm (MSA) still gives a better performance than that of the LBG algorithm and reduces the CPU time by a factor of 1.63 to 2.67. Both methods presented in this paper outperform the DSBS method developed by Huang and Harris. Compared to the LBG algorithm, the DSBS method reduced the codebook generation time by a factor of 1.5–2. It is noted that both FCGA and MSA give the same codebook as that produced by the LBG algorithm. Finally, some experimental results for several training sets with different types and sizes are listed.