Color correction for drone images, which are captured by unmanned aerial vehicles, is an essential task in drone-image based intelligent applications. Different from existing methods, in this paper, we propose an effective error compensation-based fusion algorithm for drone-image color correction. In our first novelty, an image feature matching method is performed on all image pairs to determine their matched feature point pairs and the overlapping areas. To correct color for each target pixel in the overlapping area, we propose an error compensation-based fusion method. The proposed fusion method combines the joint bilateral interpolation (JBI), which works on the color differences of the matched feature point pairs in the overlapping area, and the histogram equalization (HE), which works on the whole source and target pixels in the overlapping area, such that the overall errors caused by JBI and HE can be minimized. In our second novelty, to better correct color for each target pixel in the non-overlapping area, a boundary reference interval-based fusion method is proposed by using the color differences on the boundary and the color-corrected target sub-region in the overlapping area. Based on seven challenging datasets, comprehensive experiments have been carried out. In terms of thorough quality metrics, the experimental data demonstrate the substantial quantitative and qualitative quality improvements of our algorithm when compared to state-of-the-art methods. The source code of our algorithm is available at https://github.com/ivpml84079/EC-Based-Color-Correction.git.

Color correction for multiview images is a fundamental yet challenging task to generate a color-consistent composite image and has important applications in remote sensing and 3-D vision. In this article, we propose an effective fusion algorithm for multiview color correction using a graph-based adaptive minimum weight-first-then-larger outdegree (AMWLO) strategy to select the next target image. Initially, the given multiview images are stitched using an existing image stitching method. First, we take a modified color distance (MCD) metric to estimate the residual of the overlapped region of each image pair as the weight of the edge. After constructing the graph model of the given multiview images, an AMWLO approach is proposed to select the first target image to be performed for color correction. Then, integrating the histogram equalization (HE) and the joint bilateral interpolation (JBI), the proposed fusion-based method is used to correct the color for the selected target image. After that, the weights between the color-corrected target image and its overlapped images are updated. The above AMWLO-based target image selection, color correction for the selected target image, and edge weight update are repeated until the color correction for all multiview images is completed. To better evaluate the quality performance of the color-corrected stitched multiview images, some modified quality assessments are proposed by taking the overlapping area factor into account. Based on large-scale testing multiview image datasets, the comprehensive experimental results demonstrated the quantitative and qualitative quality merits of our algorithm relative to the state-of-the-art methods.

The most widely used color filter array (CFA) pattern in commercial digital color cameras is the Bayer pattern, and the captured image is called the Bayer CFA image, in which each pixel contains only one color value and each image consists of 25% red, 50% green and 25% blue color values. The chroma 4:2:2 or 4:2:0 subsampling of Bayer CFA images is a necessary process prior to compression. According to the block-distortion minimization principle, in this paper, we propose an effective gradient descent-based chroma subsampling (GDCS) method for Bayer CFA images. Based on the test Bayer CFA images collected from the Kodak and IMAX datasets, experimental results demonstrated that in high efficiency video coding, our GDCS method has better quality and quality-bitrate tradeoff performance of the reconstructed images when compared with the existing chroma subsampling methods.

In this paper, we propose an effective novel content-aware chroma reconstruction (CACR) method for screen content images (SCIs). After receiving the decoded downsampled YUV image on the client side, our fast chroma-copy approach reconstructs the missing chroma pixels in the flat regions of SCI. Then, for non-flat regions, a non-flat region-based winner-first voting (NRWV) strategy is proposed to identify the chroma subsampling scheme used on the server side prior to compression. Further, an effective adaptive hybrid approach is proposed to reconstruct each missing chroma pixel in the non-flat region by fusing the two reconstructed results, one from our modified NRWV-based chroma subsampling-binding and luma-guided chroma reconstruction scheme, which favors the sharp edges in SCI, as well as the other from the bicubic interpolation scheme, which favors blurred and continuous-tone textures. Further, based on the identified chroma subsampling scheme, a geometry alignment-based error compensation approach is proposed to enhance the reconstructed chroma image. Based on typical test SCIs and JCT-VC screen content videos, comprehensive experiments are carried out in HEVC-16.17 to demonstrate that in terms of quality, visual effect, and quality-bitrate tradeoff of the reconstructed SCIs, our CACR method significantly outperforms the existing state-of-the-art methods.

In asymmetric resolution stereoscopic video coding (ARSVC), a stereoscopic video consists of one full-sized leftview video sequence and the synchronized quarter-sized rightview video sequence for achieving a bitrate reduction effect by the encoder. Prior to displaying 3D scenes on the screen, it is necessary to upsample the decoded downsampled right-view video sequence at the client side. In this paper, we propose an effective adaptive upsampling method for ARSVC. First, we employ the resolution- and texture-consistency (RTC) consideration in the conventional Wiener filter-based interpolation scheme, called RTCWF, to enhance the upsampling accuracy in the spatial domain. Second, we propose a linear regression-based interview prediction (LRIP) scheme with residual compensation (RC), called LRIPRC, to increase the upsampling accuracy in the interview domain. Third, we propose an adaptive fusion-based approach to integrate RTCWF and LRIPRC, called RTCWFLRIPRC, to maximize the quality improvement of the upsampled image. Based on seven typical test stereoscopic video sequences, in 3D-HEVC, the experimental results demonstrated that in terms of six well-known quality metrics and execution time requirements, our RTCWF-LRIPRC method outperforms the state-of-the-art upsampling methods for ARSVC.

In this paper, we propose a novel and effective hybrid method, which joins the conventional chroma subsampling and the distortion-minimization-based luma modification together, to improve the quality of the reconstructed RGB fullcolor image. Assume the input RGB full-color image has been transformed to a YUV image, prior to compression. For each 2×2 UV block, one 4:2:0 subsampling is applied to determine the one subsampled U and V components, Us and Vs. Based on Us, Vs, and the corresponding 2×2 original RGB block, a main theorem is provided to determine the ideally modified 2×2 luma block in constant time such that the color peak signalto-noise ratio (CPSNR) quality distortion between the original 2×2 RGB block and the reconstructed 2×2 RGB block can be minimized in a globally optimal sense. Furthermore, the proposed hybrid method and the delivered theorem are adjusted to tackle the digital time delay integration images and the Bayer mosaic images whose Bayer CFA structure has been widely used in modern commercial digital cameras. Based on the IMAX, Kodak, and screen content test image sets, the experimental results demonstrate that in high efficiency video coding, the proposed hybrid method has substantial quality improvement, in terms of the CPSNR quality, visual effect, CPSNR-bitrate trade-off, and Bjøntegaard delta PSNR performance, of the reconstructed RGB images when compared with existing chroma subsampling schemes.

In this paper, we propose a novel adaptive chroma subsampling-binding and luma-guided (ASBLG) chroma reconstruction method for screen content images (SCIs). After receiving the decoded luma and subsampled chroma image from the decoder, a fast winner-first voting strategy is proposed to identify the used chroma subsampling scheme prior to compression. Then, the decoded luma image is subsampled as the identified subsampling scheme was performed on the chroma image such that we are able to conclude an accurate correlation between the subsampled decoded luma image and the decoded subsampled chroma image. Accordingly, an adaptive sliding window-based and luma-guided chroma reconstruction method is proposed. The related computational complexity analysis is also provided. We take two quality metrics, the color peak signal-to-noise ratio (CPSNR) of the reconstructed chroma images and SCIs and the gradient-based structure similarity index (CGSS) of the reconstructed SCIs to evaluate the quality performance. Let the proposed chroma reconstruction method be denoted as `ASBLG'. Based on 26 typical test SCIs and 6 JCT-VC test screen content video sequences (SCVs), several experiments show that on average, the CPSNR gains of all the reconstructed UV images by 4:2:0(A)-ASBLG, SCIs by 4:2:0(MPEG-B)-ASBLG, and SCVs by 4:2:0(A)-ASBLG are 2.1, 1.87, and 1.87 dB, respectively, when compared with that of the other combinations. Specifically, in terms of CPSNR and CGSS, CSBILINEAR-ASBLG for the test SCIs and CSBICUBIC-ASBLG for the test SCVs outperform the existing state-of-the-art comparative combinations, where CSBILINEAR and CSBICUBIC denote the luma-aware based chroma subsampling schemes by Wang et al.

With the advance of coding and network technology, the multiview video (MVV) system has received growing attention in the 3-D TV market since it can provide consumers with more realistic scenes from different viewpoints. In the MVV system, each video sequence consists of one color-map video and one depth video to be encoded and the depth-image-based rendering technique is often used to create/synthesize virtual views for different viewpoints. To attain the same quality of virtual views, encoding depth videos in a fast and bitrate-saving manner is crucial. Based on the depth no-synthesis-error model developed by Zhao et al., this paper proposes a new intra-/inter-prediction scheme first and then a fast quadtree structure determination scheme for encoding depth videos in 3-D High Efficiency Video Coding (3D-HEVC). The first proposed scheme has bitrate-saving merit because for each coding unit, each depth value is modified to approach the predicted intra-/inter-depth value as closely as possible, but without causing any synthesis errors in the resultant virtual views. The second proposed scheme has the merit of low computational cost because it can terminate the quadtree structure determination for coding tree units as early as possible. Based on four typical test video sequences, the empirical results demonstrate that on average, our proposed encoding method for depth videos has 16.3% bitrate and 13.8% encoding-time improvement ratios when compared with the traditional method in 3D-HEVC test model, while preserving the quality of the rendered virtual views. In addition, our proposed method outperforms that of Lee et al. in terms of the required bitrate and encoding time.

To save manufacturing cost, most color digital video cameras employ a single-sensor technology with a red-green- blue (RGB) color filter array (CFA) to capture real-world scenes. Due to only one primary color measured at each pixel location, the captured videos are usually referred to as the mosaic videos. For the purposes of economical storage and transmission, it is very important to achieve a good tradeoff between the quality and bitrate when compressing mosaic videos with different RGB-CFA structures. In this paper, based on mathematical optimization technique, a novel chroma subsampling strategy is presented for compressing mosaic videos with arbitrary RGB-CFA structures in H.264/AVC and High Efficiency Video Coding (HEVC). For each 2 × 2 YUV block to be subsampled with 4:2:0 format, the proposed strategy determines the proper sampled U and V components by minimizing, prior to compression, the quality distortion between the original colocated mosaic block and the mosaic block conversed from the current subsampled YUV block. Through the mathematical optimization formulated in the proposed strategy, the significance of the sampled U and V components for reconstructing R, G, and B pixels can be simultaneously taken into consideration. The experimental results demonstrate that the proposed chroma subsampling strategy has the best quality and bitrate tradeoff at a similar execution time requirement for compressing mosaic videos with arbitrary RGB-CFA structures in H.264/AVC and HEVC compared with the state-of-the-art ones by Chen et al. and Yang et al. as well as the three commonly used ones.

In asymmetric resolution stereoscopic video coding (ARSVC), to reduce the bitrate required for bandwidth-limited channels, each downsampled right-view frame is a quarter the size of the corresponding left-view frame and will be upsampled to the original size by the decoder. In this paper, two upsampling methods for ARSVC are proposed. The first proposed method integrates the traditional Wiener filter-based method and the interview prediction scheme by incorporating the information from the similarity between the left-view and right-view frames. By compensating for the prediction errors, the second proposed method further improves the quality of the upsampled images obtained by the first proposed method, especially in the sequences with heavy irregular textures.

In this paper, we propose a universal chroma subsampling strategy for compressing mosaic video sequences with arbitrary red-green-blue (RGB) color filter arrays (CFAs), which are widely used in the single sensor imaging pipeline, in H.264/AVC. We first develop a modified universal demosaicing scheme, which specifically recovers the G component in the color difference domain, to recover the missing color components in the input mosaic image frames. Then, based on the transform between the RGB and the YUV color spaces, the proposed universal subsampling strategy automatically samples, by considering the significance of the U and V components for reconstructing R and B pixels, the proper U and V chroma components according to the corresponding mosaic structure. To the best of our knowledge, this is the first universal chroma subsampling strategy designed specifically for mosaic video sequences with arbitrary RGB-CFAs. Experimental results on mosaic video sequences with seven common types of the RGB-CFAs demonstrate that the proposed universal chroma subsampling strategy is superior to the conventional strategy of H.264/AVC. Moreover, integrating the proposed universal demosaicing scheme and the chroma subsampling strategy can deliver better video sequence quality.

Error concealment plays an important role in robust video transmission. Recently, Chen and Leung presented an efficient data hiding-based (DH-based) approach to recover corrupted macroblocks from the intra-frame of an H.264/AVC sequence, but it suffers from the quality degradation problem. Since the quantized discrete cosine transform coefficients of an H.264/AVC sequence tend to form a Laplace distribution, we therefore propose a reversible DH-based approach for intra-frame error concealment based on this characteristic. Our design is able to achieve no quality degradation. Experimental results demonstrate that the quality of recovered video sequences obtained by our approach is indeed superior to that of the DH-based method. In addition, the quality advantage of our approach is illustrated when compared with the previous five related methods.

Recently, Tsai presented an efficient algorithm which uses the ratio value of the hue over the intensity to construct the ratio map for detecting shadows of color aerial images. Instead of only using the global thresholding process in Tsai's algorithm, this paper presents a novel successive thresholding scheme (STS) to detect shadows more accurately. In our proposed STS, the modified ratio map, which is obtained by applying the exponential function to the ratio map proposed by Tsai, is presented to stretch the gap between the ratio values of shadow and nonshadow pixels. By performing the global thresholding process on the modified ratio map, a coarse-shadow map is constructed to classify the input color aerial image into the candidate shadow pixels and the nonshadow pixels. In order to detect the true shadow pixels from the candidate shadow pixels, the connected component process is first applied to the candidate shadow pixels for grouping the candidate shadow regions. For each candidate shadow region, the local thresholding process is performed iteratively to extract the true shadow pixels from the candidate shadow region. Finally, for the remaining candidate shadow regions, a fine-shadow determination process is applied to identify whether each remaining candidate shadow pixel is the true shadow pixel or not. Under six testing images, experimental results show that, for the first three testing images, both Tsai's and our proposed algorithms have better detection performance than that of the algorithm of Huang et al., and the shadow detection accuracy of our proposed STS-based algorithm is comparable to Tsai's algorithm. For the other three testing images, which contain some low brightness objects, our proposed algorithm has better shadow detection accuracy when compared with the previous two shadow detection algorithms proposed by Huang et al. and Tsai.

Without demosaicing processing, this paper first proposes a new approach to extract more accurate gradient/edge information on mosaic images directly. Next, based on spectral-spatial correlation, a novel adaptive heterogeneity-projection with proper mask size for each pixel is presented. Combining the extracted gradient/edge information and the adaptive heterogeneity-projection values, a new edge-sensing demosaicing algorithm is presented. Based on 24 popular testing images, experimental results demonstrated that our proposed high-quality demosaicing algorithm has the best image quality performance when compared with several recently published algorithms.

Recently, several efficient context-based arithmetic coding algorithms have been developed successfully for lossless compression of error-diffused images. In this paper, we first present a novel block- and texture-based approach to train the multiple-template according to the most representative texture features. Based on the trained multiple template, we next present an efficient texture- and multiple-template-based (TM-based) algorithm for lossless compression of error-diffused images. In our proposed TM-based algorithm, the input image is divided into many blocks and for each block, the best template is adaptively selected from the multiple-template based on the texture feature of that block. Under 20 testing error-diffused images and the personal computer with Intel Celeron 2.8-GHz CPU, experimental results demonstrate that with a little encoding time degradation, 0.365 s (0.901 s) on average, the compression improvement ratio of our proposed TM-based algorithm over the joint bilevel image group (JBIG) standard [over the previous block arithmetic coding for image compression (BACIC) algorithm proposed by Reavy and Boncelet is 24%] (19.4%). Under the same condition, the compression improvement ratio of our proposed algorithm over the previous algorithm by Lee and Park is 17.6% and still only has a little encoding time degradation (0.775 s on average). In addition, the encoding time required in the previous free tree-based algorithm is 109.131 s on average while our proposed algorithm takes 0.995 s; the average compression ratio of our proposed TM-based algorithm, 1.60, is quite competitive to that of the free tree-based algorithm, 1.62.

The inverse halftoning algorithm is used to reconstruct a gray image from an input halftone image. Based on the recently published lookup table (LUT) technique, this paper presents a novel edge-based LUT method for inverse halftoning which improves the quality of the reconstructed gray image. The proposed method first uses the LUT-based inverse halftoning method as a preprocessing step to transform the given halftone image to a base gray image, and then the edges are extracted and classified from the base gray image. According to these classified edges, a novel edge-based LUT is built up to reconstruct the gray image. Based on a set of 30 real training images with both low-and high-frequency contents, experimental results demonstrated that the proposed method achieves a better image quality when compared to the currently published two methods, by Chang et al. and Meşe and Vaidyanathan.

We propose a new scheme for compressing on image set by building its minimal-cost prediction structure. Existing prediction-based video coding methods can be easily extended and incorporated into this scheme to achieve higher compression efficiency. According to this prediction structure, we also develop a progressive transmission approach for interactive object movie (OM) browsing.

Decomposing a query window into maximal quadtree blocks is a fundamental problem in quadtree-based spatial database. Recently, Proietti presented the first optimal algorithm for solving this problem. Given a query window of size n/sub 1//spl times/n/sub 2/, Proietti's algorithm takes O(n/sub 1/) time, where n/sub 1/=max(n/sub 1/, n/sub 2/). Based on a strip-splitting approach, we present a new optimal algorithm for solving the same problem. Experimental results reveal that our proposed algorithm is quite competitive with Proietti's algorithm.

According to the observation on the distribution of motion differentials among the motion vector of any block and those of its four neighboring blocks from six real video sequences, this paper presents a new predictive search area approach for fast block motion estimation. Employing our proposed simple predictive search area approach into the full search (FS) algorithm, our improved FS algorithm leads to 93.83% average execution-time improvement ratio, but only has a small estimation accuracy degradation. We also investigate the advantages of computation and estimation accuracy of our improved FS algorithm when compared to the edge-based search algorithm of Chan and Siu; experimental results reveal that our improved FS algorithm has 74.33% average execution-time improvement ratio and has a higher estimation accuracy. Finally, we further compare the performance among our improved FS algorithm, the three-step search algorithm, and the block-based gradient descent search algorithm.

An adaptive search order (ASO) algorithm is presented to speed up the block motion estimation in digital video coding. According to the motion trend, a table of the adaptive search order is defined. For each searching iteration, a better search order is derived and then the best matched block can be found in the early search stage. Some experimental results demonstrate the computational advantage of the proposed improved algorithm when compared to previous algorithms, such as the full search algorithm, the successive elimination algorithm, the block sum pyramid algorithm, and the multilevel successive elimination algorithm.

Using bincodes to represent binary images is a storage-saving encoding scheme. Finding neighbors is one of the most important operations in spatial data structures. This paper presents an efficient parallel algorithm for solving the problem of neighbor-finding for a bincode-based binary image. Given a set of the bincodes of n blocks, the neighbor-finding algorithm can be accomplished in O(1)-time on an n1/2 × n1/2 × n1/2 reconfigurable mesh. Under the same time bound, i.e. constant time, the number of processors used in the proposed parallel algorithm is O(n3/2) and is less than that of the previous fastest one on a mesh with multiple broadcasting buses [1] which needs O(n2) processors.

It has been shown that using bincodes (BCs) to represent binary images is storage-saving and easy to be manipulated. Given a set of BCs, this paper presents improved codes, namely, the modified BCs (MBCs) to represent binary images. We first transform the given BCs into a set of logical expressions, then an improved encoding scheme is employed to reduce the storage space required for representing these logical expressions, thus obtaining the MBCs. Given twenty different types of real images, experimental results show that the proposed MBCs has 25% to 28% improvement when compared to BCs. By adopting the level-compact scheme on MBCs, storage space can be reduced further. It is shown that in some cases the storage-saving improvement is more than 50%. Some image manipulations, such as computing geometrical properties and set operations, on the MBCs are also investigated.

Vector quantization (VQ) technique is a well known method in image compression. Employing Winograd's (1968) identity, this article presents a simple improved method in order to cut the computation time in the full search method for VQ nearly 50%. Some experiments are carried out to confirm the theoretical analysis.

Distasi et al. (see ibid., vol.45, p.1095-1100, 1997), presented a storage-saving image compression method called the B-tree triangular coding (BTTC) method. Based on the modified S-tree data structure and the Gouraud shading method, this paper presents an improved image compression method railed the S-tree compression (STC) method. Experimental results illustrate that the bit rates and the image quality of the proposed STC method are quite competitive with the BTTC method, Due to the simple geometrical decomposition in the STC method, the ratio of the execution time or the proposed method over the BTTC method is less than 1/2.

Based on the space-filling approach, this paper presents a fast algorithm for window query on compressed images. Given a query window of size n1xn2, the proposed algorithm takes O(n1logT+P) time to perform the window query, where n1=max(n1, n2) and TxT is the image size; P is the number of outputted codes. The proposed algorithm improves the naive algorithm, which needs O(n1n2logT+P) time, significantly. Some experimentations are carried out to demonstrate the computational advantage of the proposed algorithm. From the experimental results, it is observed that the proposed algorithm has about 72-98% time improvement when compared to the naive algorithm.

Based on the breadth-first search manner and the level-compression technique, this article first presents a new array data structure to represent the classical Huffman (1952) tree. Then, the decoding algorithm is given. Both the memory and the decoding time required in the proposed method are less than those of previous methods. Some experimentations are carried out to demonstrate the advantages of the proposed method. In fact, the proposed algorithm can be applied to the canonical Huffman tree.

In this paper, we first present a variation of the 2-dimensional run-encoding, called the run-length Morton code encoding scheme, for compressing binary images, then we present efficient algorithms for manipulating set operations and performing conversions between the proposed encoding scheme and some well-known spatial data structures. The time complexities of set operations are linearly proportional to the size (number) of the run-length Morton codes and the time complexities of conversions are linearly proportional to the number of the nodes in the corresponding quadtree/bintree with respect to the run-length Morton codes.

Given a pattern of length m and a text of length n, commonly m≪n, this paper presents a randomized parallel algorithm for pattern matching in O(n1/10) (=O(n1/10+(n−m)1/10)) time on a newly proposed n3/5×n2/5 modular meshconnected computers with multiple buses. Furthermore, the time bound of our parallel algorithm can be reduced to O(n1/11) if fewer processors are used.

A simple vectorized method for calculating a moving sum is developed. Our proposed method is suitable for register-to-register vector computers and entails much less redundant floating-point operations than the vectorized algorithm of Mossberg (1987). We demonstrate the performance of our vectorized algorithm on the CRAY X-MP EA/116se supercomputer.>

The mesh-connected computer with multiple buses (MC-CMB) is a well-known parallel organization, providing broadcast facilities in each row and each column. In this paper, we propose a 2D generalized MCCMB (2-GMCCMB) for the purpose of increasing the efficiency of executing some important applications of prefix computations such as solving Linear recurrences and tridiagonaI systems, etc. A k/sub 1/n/sub 1spl times/k/sub 1/n/sub 2/ 2-GMCCMB is constructed from a k/sub 1/n/sub 1spl times/k/sub 1/n/sub 2/ mesh organization by enhancing the power of each disjoint n/sub 1spl times/n/sub 2/ submesh with multiple buses (sub-2-MCCMB). Given n data, a prefix computation can be performed in O(n/sup 1/10/) time on an n/sup 3/5spl times/n/sup 2/5/ 2-GMCCMB, where each disjoint sub-2-MCCMB is of size n/sup 1/2spl times/n/sup 3/10/. This time bound is faster than the previous time bound of O(n/sup 1/8/) for the same computation on an n/sup 5/8spl times/n/sup 3/8/ 2-MCCMB. Furthermore, the time bound of our parallel prefix algorithm can be further reduced to O(n/sup 1/11/) if fewer processors are used. Our result can be extended to the d-dimensional GMCCMB, giving a time bound of O(n/sup 1/(d2(d)+d)/) for any constant d; here, we omit the constant factors. This time bound is less than the previous time bound of O(n/sup 1/(d2(d))/) on the d-dimensional MCCMB.>

Embedding one parallel architecture into another is very important in the area of parallel processing because parallel architectures can vary widely. Given a pyramid architecture of (4/sup N/-1)/3 nodes and height N, this paper presents a mapping method to embed the pyramid architecture into a 2/sup N-1-k//spl times/2/sup N-1-k//spl times/(4/sup k+1/+2)/3 mesh for 0/spl les/k/spl les/N-1. Our method has dilation max{4/sup k/, 2/sup N-2-k/} and expansion 1+2/(4k+1). When setting k=(N-2)/3, the pyramid can be embedded into a 2/sup (2N-1//3)/spl times/2/sup (2N-1//3)/spl times/[4/sup (N+1//3)+2]/3 mesh, and it has dilation and expansion 1+2/[4/sup (N+1//3)]. This result has can optimal expansion when N is sufficiently large and is superior to the previous mapping methods in terms of the same gauges.

The authors present a novel and fast vectorized algorithm for B-spline curve fitting. They demonstrate the good performance of their algorithm on the CRAY X-MP EA/16se supercomputer, given a set of random points.>

The average complexity for searching a record in a sorted file of records that are stored on a tape is analyzed for four search algorithms, namely, sequential search, binary search, Fibonacci search, and a modified version of Fibonacci search. The theoretical results are consistent with the recent simulation results by S. Nishihara and N. Nishino (1987). The results show that sequential search, Fibonacci search, and modified Fibonacci search are all better than binary search on a tape.>

We show how to transform the B-spline curve and surface fitting problems into suffix computations of continued fractions. Then a parallel substitution scheme is introduced to compute the suffix values on a newly proposed mesh-of-unshuffle network. The derived parallel algorithm allows the curve interpolation through n points to be solved in O(logn) time using Θ(n/log n processors and allows the surface interpolation through m × n points to be solved in O(log m log n) time using Θ(mn/(log m log n)) processors. Both interpolation algorithms are cost-optimal for their respective problems. Besides, the surface fitting problem can be even faster solved in O(log m + log n) time if Θ(mn) processors are used in the network.