Pyramid Data Structure Research Articles

Time Series Prediction Based on Multi-Scale Feature Extraction

Time series data are prevalent in the real world, particularly playing a crucial role in key domains such as meteorology, electricity, and finance. Comprising observations at historical time points, these data, when subjected to in-depth analysis and modeling, enable researchers to predict future trends and patterns, providing support for decision making. In current research, especially in the analysis of long time series, effectively extracting and integrating long-term dependencies with short-term features remains a significant challenge. Long-term dependencies refer to the correlation between data points spaced far apart in a time series, while short-term features focus on more recent changes. Understanding and combining these two features correctly are crucial for constructing accurate and reliable predictive models. To efficiently extract and integrate long-term dependencies and short-term features in long time series, this paper proposes a pyramid attention structure model based on multi-scale feature extraction, referred to as the MSFformer model. Initially, a coarser-scale construction module is designed to obtain coarse-grained information. A pyramid data structure is constructed through feature convolution, with the bottom layer representing the original data and each subsequent layer containing feature information extracted across different time step lengths. As a result, nodes higher up in the pyramid integrate information from more time points, such as every Monday or the beginning of each month, while nodes lower down retain their individual information. Additionally, a Skip-PAM is introduced, where a node only calculates attention with its neighboring nodes, parent node, and child nodes, effectively reducing the model’s time complexity to some extent. Notably, the child nodes refer to nodes selected from the next layer by skipping specific time steps. In this study, we not only propose an innovative time series prediction model but also validate the effectiveness of these methods through a series of comprehensive experiments. To comprehensively evaluate the performance of the designed model, we conducted comparative experiments with baseline models, ablation experiments, and hyperparameter studies. The experimental results demonstrate that the MSFformer model improves by 35.87% and 42.6% on the MAE and MSE indicators, respectively, compared to traditional Transformer models. These results highlight the outstanding performance of our proposed deep learning model in handling complex time series data, particularly in capturing long-term dependencies and integrating short-term features.

π-means: Granular Approach towards Interactive Data Exploration

In this paper, we examine the possibility of employing the idea of progressive-inductive (π) aggregation in the k-means algorithm. We base our work on the interactive visualization framework called Skydive which is a tightly coupled system that combines data aggregation and visual aggregation for smooth user interaction. It is based on an aggregate pyramid data structure (π-cube), allowing a visualization client to quickly filter the data. Skydive was designed for interactive data visualization in terms of expressiveness and efficiency. Therefore, the underlying data structure enabled access to data on desired levels of granularity. In this paper, we utilize this concept to speed up the process of clustering proposing π-means - a modified version of the k-means algorithm. This will allow us to explore further possible applications of π-cube towards interactive data exploration.

Multilevel mesh adaptivity for discrete ordinates transport calculation with spatial-moment-ratio indicators

It is difficult to control discretization errors and reduce computational cost at the same time for multi-scale neutron transport problems, and the adaptive mesh refinement technique is one of the powerful and effective methods for high-resolution transport calculation. We propose a multilevel mesh adaptivity algorithm and develop a discrete ordinates calculation framework on 3-D Cartesian meshes. Data management and transport sweep are optimized based on the multilevel pyramid data structure containing pointer-type and array-type variables. A new spatial-moment-ratio error indicator is derived to measure the leading term of distribution functions and to drive the local mesh refinement. The numerical properties of spatial moment factors are better than the normalized gradient of angular flux. Compared with uniform refinement, our adaptivity algorithm reaches the same accuracy level with a computational cost saving of 60%-80% for heterogeneous problems.

Time Conserving Multi-Label Classification System by Incorporating Pyramid Data Structure

Data classification is one of the evergreen research areas of data analysis. Numerous data classification approaches exist in the literature and most of the classification systems are based on binary and multi-class classification. Multi-label classification system attempts to suggest multiple labels for a single entity. However, it is complex to attain a better multi-label classification system. Taking this as a challenge, this work proposes a multi-label classification system, which extracts the features of both entities and labels. The relationship between them are organised in the pyramid data structure. As the features are organized effectively, the interrelated labels are present in the same tier. This feature makes it simple for suggesting multiple labels for a single entity. The performance of this work is analysed over three different datasets and compared against existing approaches in terms of precision, recall, accuracy and time consumption.

Adaptive multi-resolution method for compressible multi-phase flows with sharp interface model and pyramid data structure

In this work, we present a block-based multi-resolution method coupled with a sharp interface model (MR-SIM) for the high-resolution simulation of multi-phase flows, where data structure and adaptive multi-resolution approach are tailored to achieve high computational efficiency. The method updates the dynamic topological data structure according to two separate procedures: (i) tracking of the interface position, and (ii) MR analysis on each individual phase. High efficiency is achieved by employing a storage-and-operation-splitting pyramid data structure, in which any two adjacent blocks partially overlap while the overlapping parts share the same data in memory. The non-overlapping data are distributed into fine-grained data packages and stored within a memory pool. The proposed narrow-band technique for the level-set-based interface method also increases the computational and memory efficiency greatly by restricting all interface-relevant data and operations to a neighborhood of the interface. A broad set of test simulations is carried out to demonstrate the potential and performance of the MR-SIM approach.

Robust ellipse detection based on hierarchical image pyramid and Hough transform

In this research we propose a fast and robust ellipse detection algorithm based on a multipass Hough transform and an image pyramid data structure. The algorithm starts with an exhaustive search on a low-resolution image in the image pyramid using elliptical Hough transform. Then the image resolution is iteratively increased while the candidate ellipses with higher resolution are updated at each step until the original image resolution is reached. After removing the detected ellipses, the Hough transform is repeatedly applied in multiple passes to search for remaining ellipses, and terminates when no more ellipses are found. This approach significantly reduces the false positive error of ellipse detection as compared with the conventional randomized Hough transform method. The analysis shows that the computing complexity of this algorithm is Θ(n(5/2)), and thus the computation time and memory requirement are significantly reduced. The developed algorithm was tested with images containing various numbers of ellipses. The effects of noise-to-signal ratio combined with various ellipse sizes on the detection accuracy were analyzed and discussed. Experimental results revealed that the algorithm is robust to noise. The average detection accuracies were all above 90% for images with less than seven ellipses, and slightly decreased to about 80% for images with more ellipses. The average false positive error was less than 2%.

Edge Adaptive Hierarchical Interpolation for Lossless and Progressive Image Transmission

Based on the quincunx sub-sampling grid, the New Interleaved Hierarchical INTerpolation (NIHINT) method is recognized as a superior pyramid data structure for the lossless and progressive coding of natural images. In this paper, we propose a new image interpolation algorithm, Edge Adaptive Hierarchical INTerpolation (EAHINT), for a further reduction in the entropy of interpolation errors. We compute the local variance of the causal context to model the strength of a local edge around a target pixel and then apply three statistical decision rules to classify the local edge into a strong edge, a weak edge, or a medium edge. According to these local edge types, we apply an interpolation method to the target pixel using a one-directional interpolator for a strong edge, a multi-directional adaptive weighting interpolator for a medium edge, or a non-directional static weighting linear interpolator for a weak edge. Experimental results show that the proposed algorithm achieves a better compression bit rate than the NIHINT method for lossless image coding. It is shown that the compression bit rate is much better for images that are rich in directional edges and textures. Our algorithm also shows better rate-distortion performance and visual quality for progressive image transmission.

A study on medical image registration by mutual information with pyramid data structure

The registration method based on mutual information is currently a popular technique for medical image registration, but the computation of the mutual information is complex and the registration speed is slow. In this work, a new slice accumulation pyramid (SAP) data structure was proposed to expedite the registration process. A numerical comparative study between the new data structure and the existing wavelet pyramid (WP) data structure was given, and the results confirmed that the new pyramid data structure was superior to the WP in both the calculation efficiency and the optimizing performance. Finally, SAP was applied to remove the artifacts between CT and MRI data sets, and the results showed the validation of SAP to registration of mulmodality images.

Recursive computation method for fast encoding of vector quantization based on 2-pixel-merging sum pyramid data structure

Vector quantization (VQ) is a popular signal compression method. In the framework of VQ, fast search method is one of the key issues because it is the time bottleneck for VQ applications. In order to speed up VQ encoding process, how to construct some lower dimensional feature vectors for a k-dimensional original vector so as to measure the distortion between any vectors lightly becomes important. To reduce the dimension for approximately representing a k-dimensional vector, the multi-resolution concept is a natural consideration. By introducing a pyramid data structure, the multi-resolution concept used in fast VQ encoding includes two aspects, which are (1) a multi-resolution distortion check method and (2) a multi-resolution distortion computation method. Some fast search methods that are based on a 4-pixel-merging (4-PM) mean pyramid data structure [Lin, S.J., Chung, K.L., Chang, L.C. 2001. An improved search algorithm for vector quantization using mean pyramid structure. Pattern Recognition Lett. 22 (3/4) 373] and a 2-pixel-merging (2-PM) sum pyramid data structure [Pan, Z., Kotani, K., Ohmi, T. 2004. An improved fast encoding algorithm for vector quantization using 2-pixel-merging sum pyramid data structure. Pattern Recognition Lett. 25 (3) 459] have already been proposed. Both of them realized the multi-resolution concept by using a multi-resolution distortion check method. However, both of them ignored the multi-resolution distortion computation method, which can also be guaranteed by the multi-resolution concept if a recursive computation way is introduced. In principle, a multi-resolution distortion computation method can completely reuse the obtained computation result that is already executed at a lower resolution level so that no waste to it will occur at all. This paper aims at improving the search efficiency of the previous work [Pan, Z., Kotani, K., Ohmi, T. 2004. An improved fast encoding algorithm for vector quantization using 2-pixel-merging sum pyramid data structure. Pattern Recognition Lett. 25 (3) 459] further by introducing a multi-resolution distortion computation method into multi-resolution distortion check method so that about half of its computational cost can be reduced mathematically. Experimental results confirmed the proposed method outperforms the previous works obviously.

Thresholding technique with adaptive window selection for uneven lighting image

By adaptively selecting image window size based on the pyramid data structure manipulation of Lorentz information measure, a new technique for image thresholding is proposed. The advantage of this technique is its effectiveness in eliminating both uneven lighting disturbance and ghost objects. When applied to Otsu’s thresholding approach, it can provide accurate result under uneven lighting disturbance while using Otsu’s method alone cannot. Experimental results show the effectiveness of this method.

ViBE: A Compressed Video Database Structured for Active Browsing and Search

In this paper, we describe a unique new paradigm for video database management known as ViBE (video indexing and browsing environment). ViBE is a browseable/searchable paradigm for organizing video data containing a large number of sequences. The system first segments video sequences into shots by using a new feature vector known as the Generalized Trace obtained from the DC-sequence of the compressed data. Each video shot is then represented by a hierarchical structure known as the shot tree. The shots are then classified into pseudo-semantic classes that describe the shot content. Finally, the results are presented to the user in an active browsing environment using a similarity pyramid data structure. The similarity pyramid allows the user to view the video database at various levels of detail. The user can also define semantic classes and reorganize the browsing environment based on relevance feedback. We describe how ViBE performs on a database of MPEG sequences.

An improved fast encoding algorithm for vector quantization using 2-pixel-merging sum pyramid data structure

Vector quantization (VQ) is an asymmetric coding method and the winner search in encoding process is extremely time-consuming. This property of VQ constrains its practical applications very much. Based on the sum pyramid data structure of a vector, a fast encoding algorithm with PSNR equivalent to full search is proposed in this paper to improve the results that have been given in [Pattern Recognition Lett. 22(3/4) (2001) 373]. Three major modifications are made. Because sum can be computed accurately using integer operation, mismatched winners due to roundoff error of taking the mean can be overcome firstly by using sum instead of the mean. Secondly, since sum is computed by 2-pixel-merging other than 4-pixel-merging way, more levels can be constructed in a sum pyramid so that the rejection to current codeword can be realized easier. Finally, codebook is off-line rearranged by sorted real sums directly, and the lower and upper bound for promising codeword class are updated dynamically to narrow search scope further once a better-matched codeword has been found during winner search process. For the same four 512 × 512, 256-level standard test images, experimental results show that the proposed algorithm outperforms the method used in [Pattern Recognition Lett. 22(3/4) (2001) 373] in the meaning of total equivalent distance computation being reduced obviously.

A Web-based Technique to Generate and Visualize 3D Scenes from Global to Local Views

Global terrain visualization is a very challenging subject. Adopted a client/server architecture for complex, dynamic and distributed 3D scenes, based on hypertext transfer protocol and oriented object methods, a virtual scene for the earth which merges satellite and aerial imagery with DEM data using the Earth itself as an interface is built. Database organization functions in the server, data transfer and real-time display mechanisms are discussed in this paper; then pyramid data structure and wallet analysis principles are introduced to simplified data. How to construct high efficient indexes and algorithms of operating 3D landscape on the browser are also discussed. Finally an experiment is performed using different levels of detail data.

An improved fast encoding algorithm for vector quantization

AbstractIn the current information age, people have to access various information. With the popularization of the Internet in all kinds of information fields and the development of communication technology, more and more information has to be processed in high speed. Data compression is one of the techniques in information data processing applications and spreading images. The objective of data compression is to reduce data rate for transmission and storage. Vector quantization (VQ) is a very powerful method for data compression. One of the key problems for the basic VQ method, i.e., full search algorithm, is that it is computationally intensive and is difficult for real time processing. Many fast encoding algorithms have been developed for this reason. In this paper, we present a reasonable half‐L2‐norm pyramid data structure and a new method of searching and processing codewords to significantly speed up the searching process especially for high dimensional vectors and codebook with large size; reduce the actual requirement for memory, which is preferred in hardware implementation system, e.g., SOC (system‐on‐chip); and produce the same encoded image quality as full search algorithm. Simulation results show that the proposed method outperforms some existing related fast encoding algorithms.

A progressively predictive image pyramid for efficient lossless coding

A low entropy pyramidal image data structure suited for lossless coding and progressive transmission is proposed in this work. The new coder, called the progressively predictive pyramid (PPP) is based on the well-known Laplacian pyramid. By introducing inter-resolution predictors into the original Laplacian pyramid, we show that the entropy level in the original pyramid can be reduced significantly. To take full advantage of progressive transmission, a scheme is introduced to create the predictor adaptively, thus eliminating the need to transmit the predictor and reducing the coding overheads. A method for designing the predictor is presented. Numerical results show that PPP is superior to traditional approaches to pyramid generation in the sense that the pyramids generated by PPP always have significantly lower entropy values.

球面六角形画像ピラミッドを用いた球面投影による全方位画像処理

Pyramid- and tree-type structures manipulate hierarchical and multi-resolution representations of data and are used in many image processing applications. However, it has been thought that it is difficult to deal with a spherical image by use of a pyramidal data structure. Because, connectedness of such structure is far weaker than a normal square tessellation.In this paper, we propose a new data structure for spherical image processing on an omni-directional view that is a spherical hexagonal image pyramid. It is composed of hexagonal pixels on a regular polyhedron. Using this data structure, we can represent an omni-directional view in a complete spherical image. And we performed an experiment to extract great circles in a spherical image and to estimate coordinate systems using vanishing points as one of omni-directional image processing applications.

Layered image coding using the DCT pyramid

A block-based subband image coder that exploits the ability to perform decimation in the discrete cosine transform (DCT) domain to effect a pyramidal data structure is described. The proposed "DCT pyramid" has a distinct feature of improved image rendition properties without the associated blocking artifacts at low bit-rates.

Pyramid Structure Using Projection for Progressive Image Transmission

In this paper, we propose a progressive image transmission technique using hierarchical pyramid data structure which is constructed based on the projection data of an image. To construct the hierarchical Gaussian pyramid, we first divide an image into 4 × 4 nonoverlapping subblocks and generate the projection data of each subblock along the horizontal, vertical, diagonal, and antidiagonal directions. Among four images reconstructed by backprojecting the projection data along each direction, the image giving the minimum distortion is subsampled to construct the Gaussian image. The Gaussian pyramid is recursively generated by the proposed algorithm and the resulting Gaussian images preserve well-edge information. Based on the projection concept, a new encoding technique of the lowest Laplacian plane is also presented. Computer simulation with several test images shows that the quantitative performance of the proposed progressive image transmission technique using projection is similar to that of the conventional methods with its transmission bit rate reduced by 0.1-0.2 bit per pixel (bpp). Its subjective performance is also better because of the edge-preserving property of a projection operation.

Fuzzy pyramid-based invariant object recognition

A new fuzzy-decision-based invariant pattern recognition method for object recognition is presented. Blending the well-known image pyramid data structure with fuzzy mathematics, the new method sets out to show how fuzzy concepts, such as membership grade, are used in fuzzifying the features and building up a fuzzy feature pyramid. This is supported by a new segmentation technique using annular and sector windows inspired by the human visual system. A fuzzy pyramid technique is then naturally introduced to make the recognition decision. This new fuzzy decision approach is shown to have all the essential invariant properties and robustness against noise and uncertainty. The recognition system was applied to the problem of tool recognition and good results were obtained. A comparative study reveals many important advantages of our method over other techniques.

Progressive image transmission using a prefilter and a modified difference pyramid structure

Abstract Pyramid data structures have played an important role in progressive image transmission. Over the years, the reduced difference pyramid (RDP) has been found to be one of the best data structure. The RDP takes the differences between the neighboring nodes at the same level. The new modified difference pyramid (MDP) data structure, developed in this paper, takes the differences between successive levels. Simulation results show that both the bit rate and the complexity of the receiver for the MDP structure are lower than those for the RDP structure at the same quality. An MDP coding process which incorporates a prefilter is also proposed in this paper. Simulation results show it can provide good quality (in a subjective sense) reconstructed images at a lower bit rate than the unfiltered scheme can. Also, acceptable intermediate images are interpolated via the repetition method and via the cubic convolution method to get images which are the same size as the original. Results are compared.