nils-herrmann/clean_scirepeval huggingface dataset:
Discrete Fractional Fourier Transform Based on New Nearly Tridiagonal Commuting Matrices

Based on discrete Hermite-Gaussian-like functions, a discrete fractional Fourier transform (DFRFT), which provides sample approximations of the continuous fractional Fourier transform, was defined and investigated recently. In this paper, we propose a new nearly tridiagonal matrix, which commutes with the discrete Fourier transform (DFT) matrix. The eigenvectors of the new nearly tridiagonal matrix are shown to be DFT eigenvectors, which are more similar to the continuous Hermite-Gaussian functions than those developed before. Rigorous discussions on the relations between the eigendecomposition of the newly proposed nearly tridiagonal matrix and the DFT matrix are described. Furthermore, by appropriately combining two linearly independent matrices that both commute with the DFT matrix, we develop a method to obtain DFT eigenvectors even more similar to the continuous Hermite-Gaussian functions (HGFs). Then, new versions of DFRFT produce their transform outputs closer to the samples of the continuous fractional Fourier transform, and their applications are described. Related computer experiments are performed to illustrate the validity of the works in this paper
Banknote reconstruction from fragments using quadratic programming and SIFT points

Due to a variety of accidents, banknotes may be broken into several fragments. These fragments are usually stained, burned, partially lost, and twisted, which makes banknote reconstruction a hard problem. Since the fragments are always not intact, the traditional edge and texture based fragment assembling methods cannot be applied here. In this paper, we develop a framework for banknote reconstruction. We applied the techniques of SIFT point matching, RANSAC, and feature-based alignment. Moreover, convex quadratic optimization based on maximizing the reconstructed area and avoiding overlapping is adopted. Several simulations are given to demonstrate the effectiveness of our framework.
Improved Efficiency on Adaptive Arithmetic Coding for Data Compression Using Range-Adjusting Scheme, Increasingly Adjusting Step, and Mutual-Learning Scheme

Context-based adaptive arithmetic coding (CAAC) has high coding efficiency and is adopted by the majority of advanced compression algorithms. In this paper, five new techniques are proposed to further improve the performance of CAAC. They make the frequency table (the table used to estimate the probability distribution of data according to the past input) of CAAC converge to the true probability distribution rapidly and hence improve the coding efficiency. Instead of varying only one entry of the frequency table, the proposed range-adjusting scheme adjusts the entries near to the current input value together. With the proposed mutual-learning scheme, the frequency tables of the contexts highly correlated to the current context are also adjusted. The proposed increasingly adjusting step scheme applies a greater adjusting step for recent data. The proposed adaptive initialization scheme uses a proper model to initialize the frequency table. Moreover, a local frequency table is generated according to local information. We perform several simulations on edge-directed prediction-based lossless image compression, coefficient encoding in JPEG, bit plane coding in JPEG 2000, and motion vector residue coding in video compression. All simulations confirm that the proposed techniques can reduce the bit rate and are beneficial for data compression.
Coefficient-truncated higher-order commuting matrices of the discrete fourier transform

Recently, Candan introduced higher order DFT-commuting matrices whose eigenvectors are accurate approximations to the continuous Hermite-Gaussian functions (HGFs). However, the highest order 2k of the O(h2k) NtimesN DFT-commuting matrices proposed by Candan is restricted by 2k+1lesN. In this paper, we remove that restriction of order upper bound by developing a coefficient truncation technique to construct arbitrary-order DFT-commuting matrices. Exploiting that coefficient truncation technique, we also develop a method to construct n-diagonal arbitrary-order DFT-commuting matrices, whose number of nonzero diagonal bands n can be prespecified at will. Results of computer experiments show that the Hermite-Gaussian-like (HGL) eigenvectors of the new DFT-commuting matrices proposed in this paper outperform those of Candan's.
Shape-adaptive image compression using lossy shape coding, SA-prediction, and SA-deblocking

As the annoying blocking or ghost artifacts tend to appear in the conventional compression approaches either in the JPEG or JPEG2000 standards at low bitrate, the concept of the object-oriented image compression is proposed. This kind of methods is able to retain the image structural boundaries and therefore has relatively good visual qualities even in high compression ratios. In this paper, we propose a shape-adaptive image compression scheme employing an efficient lossy contour compression algorithm to encode the region information, which is usually the main overhead data in such systems. In addition, the prediction and deblocking techniques commonly used in novel compression approaches are also applied with the proposed shape-adaptive versions. Simulation results suggest that the proposed compression system is able to provide compressed images with much better visual qualities and more reasonable degradation forms compared to other prevailing methods.
The integer transforms analogous to discrete trigonometric transforms

The integer transform (such as the Walsh transform) is the discrete transform that all the entries of the transform matrix are integer. It is much easier to implement because the real number multiplication operations can be avoided, but the performance is usually worse. On the other hand, the noninteger transform, such as the DFT and DCT, has a good performance, but real number multiplication is required. W derive the integer transforms analogous to some popular noninteger transforms. These integer transforms retain most of the performance quality of the original transform, but the implementation is much simpler. Especially, for the two-dimensional (2-D) block transform in image/video, the saving can be huge using integer operations. In 1989, Cham had derived the integer cosine transform. Here, we will derive the integer sine, Hartley, and Fourier transforms. We also introduce the general method to derive the integer transform from some noninteger transform. Besides, the integer transform derived by Cham still requires real number multiplication for the inverse transform. We modify the integer transform introduced by Cham and introduce the complete integer transform. It requires no real number multiplication operation, no matter what the forward or inverse transform. The integer transform we derive would be more efficient than the original transform. For example, for the 8-point DFT and IDFT, there are in total four real numbers and eight fixed-point multiplication operations required, but for the forward and inverse 8-point complete integer Fourier transforms, there are totally 20 fixed-point multiplication operations required. However, for the integer transform, the implementation is simpler, and many of the properties of the original transform are kept.
Less buffer sized efficienct compression algorithm based on column DCTs, Row DWTs, and predictive coding

Although JPEG2000 is powerful for image compression, since it requires a large buffer size, it is not as popular as JPEG. In industry, less buffer size requirement is an important issue in image compression because in many embedded systems and mobile devices, such as cell phones, TV, and digital cameras, the buffer sizes are usually very small. A large buffer size means large space requirement and high hardware cost. In this paper, a new compression method that is the hybrid of the discrete cosine transform and the discrete wavelet transform is proposed. The proposed algorithm combines the advantages of JPEG and JPEG2000 and adopts predictive coding techniques. Its buffer size requirement is the same as that of JPEG but the compression ability is much higher.
Coarse-to-fine temporal optimization for video retargeting based on seam carving

In this paper, a new video retargeting method based on temporal information and seam carving is presented. Two video energy functions, motion weight prediction and pixel-based optimization, are proposed to take the temporal information into account and make dynamic programming available during the process of retargeting. The motion weight prediction exploits both the block-based motion estimation and Gaussian masks to predict the coarse location of seams in the current frame and reduce the search range of dynamic programming. The pixel-based optimization then utilizes the concept of pixel-based optical flow to explore better temporal relations between the current frame and previous frames in the reduced search range. The experimental results show that combining these two video energy functions as well as dynamic programming, the proposed method could achieve content-aware and temporal smoothing retargeting results with less computational complexity.
Collagen image compression using the JPEG-based predictive lossless coding scheme

Collagen second harmonic generation (SHG) images are helpful for the diagnosis of cancer and diabetes. In this paper, we develop the JPEG-based predictive lossless image coding (JPLIC) algorithm to encode SHG images. The main difference between collagen SHG images and other images is that they have very irregular texture and the correlations among adjacent pixels are very low. Therefore, conventional lossless compression algorithms, including JPEG-LS and CALIC, which are based on predicting current pixel values from neighbors, may not be suitable for collagen SHG image compression. Therefore, instead of applying adjacent pixels, the proposed algorithm predicts pixel values by JPEG. After prediction, we use adaptive arithmetic coding together with context modeling to encode the residue. Simulations show that the proposed JPLIC algorithm has better performance than other lossless compression methods for collagen SHG images. Moreover, the proposed algorithm is also suitable for nearly lossless image compression and noise-like image compression.
Quadtree classified vector quantization based image retrieval scheme

With the fast development of multimedia, it is crucial to find the way to search image database effectively. The vector quantization (VQ) based image retrieval method is popular in recent years. In this paper, we propose the quadtree classified vector quantization (QCVQ) scheme to improve the VQ method by exploiting the visual importance of image blocks and using the edge information to describe the content of each block efficiently. Moreover, we also apply the adaptive block size. The simulation results show that, compared with the previous image retrieval algorithms using VQ and chromaticity moments (CM), our proposed scheme has obviously better average retrieval rate and higher average precision.
Two-Dimensional Orthogonal DCT Expansion in Trapezoid and Triangular Blocks and Modified JPEG Image Compression

In the conventional JPEG algorithm, an image is divided into eight by eight blocks and then the 2-D DCT is applied to encode each block. In this paper, we find that, in addition to rectangular blocks, the 2-D DCT is also orthogonal in the trapezoid and triangular blocks. Therefore, instead of eight by eight blocks, we can generalize the JPEG algorithm and divide an image into trapezoid and triangular blocks according to the shapes of objects and achieve higher compression ratio. Compared with the existing shape adaptive compression algorithms, as we do not try to match the shape of each object exactly, the number of bytes used for encoding the edges can be less and the error caused from the high frequency component at the boundary can be avoided. The simulations show that, when the bit rate is fixed, our proposed algorithm can achieve higher PSNR than the JPEG algorithm and other shape adaptive algorithms. Furthermore, in addition to the 2-D DCT, we can also use our proposed method to generate the 2-D complete and orthogonal sine basis, Hartley basis, Walsh basis, and discrete polynomial basis in a trapezoid or a triangular block.
Efficient implementation of quaternion Fourier transform, convolution, and correlation by 2-D complex FFT

The concepts of quaternion Fourier transform (QFT), quaternion convolution (QCV), and quaternion correlation, which are based on quaternion algebra, have been found to be useful for color image processing. However, the necessary computational algorithms and their complexity still need some attention. We develop efficient algorithms for QFT, QCV, and quaternion correlation. The conventional complex two-dimensional (2-D) Fourier transform (FT) is used to implement these quaternion operations very efficiently. With these algorithms, we only need two complex 2-D FTs to implement a QFT, six complex 2-D FTs to implement a one-side QCV or a quaternion correlation and 12 complex 2-D FTs to implement a two-side QCV, and the efficiency of these quaternion operations is much improved. Meanwhile, we also discuss two additional topics. The first one is about how to use QFT and QCV for quaternion linear time-invariant (QLTI) system analysis. This topic is important for quaternion filter design and color image processing. Besides, we also develop the spectrum-product QCV. It is an improvement of the conventional form of QCV. For any arbitrary input functions, it always corresponds to the product operation in the frequency domain. It is very useful for quaternion filter design.
End-point preserved stroke extraction

The stroke is a very important feature for a character and is helpful for word recognition and handwriting identification. Although thinning algorithms can be applied for stroke extraction, they always suffer from the problems of bifurcation and disconnection. Moreover, since the end points of strokes cannot be preserved by thinning, the stroke length cannot be accurately determined and the start and the end parts of a stroke, which are useful for identifying the writing habit of a person, are hard to be extracted explicitly. In this paper, we proposed a very accurate stroke extraction algorithm which can well preserve the ends of strokes. Simulations on some Chinese characters show that the proposed algorithm is reliable and can precisely extract the strokes of characters.
Nonlocal context modeling and adaptive prediction for lossless image coding

Properly designed context models can increase the compression gain. In this paper, we propose a new lossless image coding scheme with two proposed algorithms: nonlocal context modeling and adaptive prediction (NCMAP). Since structural self-similarity often exists in natural images, we use the probability to measure the similarity between the powers of prediction errors for the pixels to be coded. Furthermore, the spatial distance and the intensity range are also considered for context generation. Moreover, a prediction scheme that adaptively combines the weighted edge-directed prediction (WEDP) and the nonlocal predictor (NLP) is also proposed. With the proposed context generating and prediction strategies, better compression performances can be achieved. Simulations show that the proposed scheme outperforms existing methods for lossless image compression.
A new definition of continuous fractional Hartley transform

This paper is concerned with the definition of the continuous fractional Hartley transform. First, a general theory of the linear fractional transform is presented to provide a systematic procedure to define the fractional version of any well-known linear transforms. Then, the results of general theory are used to derive the definitions of the fractional Fourier transform (FRFT) and fractional Hartley transform (FRHT) which satisfy the boundary conditions and additive property simultaneously. Next, an important relationship between FRFT and FRHT is described. Finally, a numerical example is illustrated to demonstrate the transform results of the delta function of FRHT.
Analysis of Attenuation Measurements in Ocean Sediments Using Normal Incidence Chirp Sonar

An analysis of chirp sonar signals backscattered from ocean sediments is presented in this paper to estimate sound attenuation in ocean sediments. The theory of applying a matched filter to linear frequency modulation chirp signals for generating time compressed pulses (CPs) is described and implemented. After the matched filter technique was applied, the signal-to-noise ratio (SNR) of the CP was enhanced. However, a smearing effect resulting from the convolution operation diminished the advantage of the improved SNR. The chirp signal processing algorithm is described and applied to a sample data set collected from an area with a variety of different sediments offshore northeastern Taiwan. For the exploration of signal features, time-frequency analysis is employed to reveal the characteristics of chirp signals presented in the joint time-frequency domain. Based on the spectral ratio method, ocean sediment attenuation properties are compared to those obtained from core samples analyzed in the laboratory. The observed attenuation coefficient was lower than those of some of the previous studies, but it was still within the reported data range. Factors that could contribute to the uncertainty are discussed.
Advanced one-bit transform algorithm with edge enhancement and representative feature extraction for low-complexity and accurate motion estimation

Motion estimation is an essential procedure in video coding and object tracing, but it always has a high computational load. Some low bit-depth motion estimation methods, such as one/two-bit transform or gray coding based methods, have lower complexity. However, one-bit transform based methods are sensitive to noise, whereas two-bit transform and gray coding methods use many bit planes or operations to perform motion estimation. In this paper, we select features with high representative by two means. First, we present an improved one-bit transform with pre-processing techniques. Second, an adaptive matching criterion was introduced to pick out features with higher representative. Moreover, a fast search algorithm is also proposed to reduce the searching cost. The experimental results show that the proposed algorithm outperforms other methods both in matching accuracy and in computation efficiency.
Salient Region Detection Improved by Principle Component Analysis and Boundary Information

Salient region detection is useful for several image-processing applications, such as adaptive compression, object recognition, image retrieval, filter design, and image retargeting. A novel method to determine the salient regions of images is proposed in this paper. The L0 smoothing filter and principle component analysis (PCA) play important roles in our framework. The L0 filter is extremely helpful in characterizing fundamental image constituents, i.e., salient edges, and can simultaneously diminish insignificant details, thus producing more accurate boundary information for background merging and boundary scoring. PCA can reduce computational complexity as well as attenuate noise and translation errors. A local-global contrast is then used to calculate the distinction. Finally, image segmentation is used to achieve full-resolution saliency maps. The proposed method is compared with other state-of-the-art saliency detection methods and shown to yield higher precision-recall rates and F-measures.
Blur kernel estimation using normalized color-line priors

This paper proposes a single-image blur kernel estimation algorithm that utilizes the normalized color-line prior to restore sharp edges without altering edge structures or enhancing noise. The proposed prior is derived from the color-line model, which has been successfully applied to non-blind deconvolution and many computer vision problems. In this paper, we show that the original color-line prior is not effective for blur kernel estimation and propose a normalized color-line prior which can better enhance edge contrasts. By optimizing the proposed prior, our method gradually enhances the sharpness of the intermediate patches without using heuristic filters or external patch priors. The intermediate patches can then guide the estimation of the blur kernel. A comprehensive evaluation on a large image deblurring dataset shows that our algorithm achieves the state-of-the-art results.
Asymmetric fourier descriptor of non-closed segments

The Fourier descriptor is an efficient and effective way to describe a closed boundary. However, for a non-closed segment, since the two non-adjacent end points result in signal discontinuity, after eliminating the high-frequency part, the reconstructed segment has large error near the two ends. In this paper, we propose a warping method to connect the two ends and perform odd-symmetric extension to smooth the warped segment around them. With these modifications, the high-frequency components near the two ends can be much reduced and we can obtain the reconstructed segment with accurate end-point locations even when only the low frequency coefficients are preserved. This method could also be used for a closed boundary with a pre-segmentation process, and the experimental result shows that with the same boundary compression rate, our method has better reconstruction quality than directly extracting Fourier descriptors on the closed boundary.
Fast morphology algorithm with parallel processing structures

Morphology, including erosion and dilation, is important for many image processing applications, such as shape analysis, pattern recognition, denoising, and segmentation. In this paper, an efficient way to perform erosion and dilation operations is proposed. Since the proposed algorithm deals with each row and column separately, it can be implemented in a parallel processing structure, which can significantly reduce the computation time. Moreover, recursive structures can also be adopted in the proposed algorithm. In addition to less computation time, the memory requirement of the proposed algorithm is also very less. The proposed algorithm is suitable for any structuring element of the symmetric and convex form. When using different structuring element, only a very small part of the structure should be adjusted. The proposed algorithm can much improve the efficiency of morphology and is suitable for both software and hardware implementation.
2D quaternion Fourier spectral analysis and its applications

Hypercomplex Fourier transforms based on quaternions have been used for gray and color image processing. In this paper, we present the relations between the quaternion Fourier spectral coefficients. Using these relations, we can separate the scalar and vector part of quaternion image for frequency domain and find the constraints of the Fourier spectral coefficients which the quaternion Fourier transform of these spectral coefficients will have zero scalar part. In addition, we can calculate the DQFT of four real images, or the DQFT of two complex images by only one DQFT and we can design a color cosine image from frequency domain. Finally, we discuss the property of the DQFT of a causal image.