Piecewise Linear Transformation Research Articles

A lightweight dual-attention network for tomato leaf disease identification.

Tomato disease image recognition plays a crucial role in agricultural production. Today, while machine vision methods based on deep learning have achieved some success in disease recognition, they still face several challenges. These include issues such as imbalanced datasets, unclear disease features, small inter-class differences, and large intra-class variations. To address these challenges, this paper proposes a method for classifying and recognizing tomato leaf diseases based on machine vision. First, to enhance the disease feature details in images, a piecewise linear transformation method is used for image enhancement, and oversampling is employed to expand the dataset, compensating for the imbalanced dataset. Next, this paper introduces a convolutional block with a dual attention mechanism called DAC Block, which is used to construct a lightweight model named LDAMNet. The DAC Block innovatively uses Hybrid Channel Attention (HCA) and Coordinate Attention (CSA) to process channel information and spatial information of input images respectively, enhancing the model's feature extraction capabilities. Additionally, this paper proposes a Robust Cross-Entropy (RCE) loss function that is robust to noisy labels, aimed at reducing the impact of noisy labels on the LDAMNet model during training. Experimental results show that this method achieves an average recognition accuracy of 98.71% on the tomato disease dataset, effectively retaining disease information in images and capturing disease areas. Furthermore, the method also demonstrates strong recognition capabilities on rice crop disease datasets, indicating good generalization performance and the ability to function effectively in disease recognition across different crops. The research findings of this paper provide new ideas and methods for the field of crop disease recognition. However, future research needs to further optimize the model's structure andcomputational efficiency, and validate its application effects in more practical scenarios.

Implementation of Adaptive Coding Approach Based on Periodic Walsh Piecewise-Linear Transform for Digital Grayscale Image

Implementation of Adaptive Coding Approach Based on Periodic Walsh Piecewise-Linear Transform for Digital Grayscale Image

Integrable symplectic maps with a polygon tessellation

Identifying integrable dynamics remains a formidable challenge, and despite centuries of research, only a handful of examples are known to date. In this article, we explore a distinct form of area-preserving (symplectic) mappings derived from the stroboscopic Poincaré cross section of a kicked rotator—an oscillator subjected to an external force periodically switched on in short pulses. The significance of this class of problems extends to various applications in physics and mathematics, including particle accelerators, crystallography, and studies of chaos. Notably, Suris's theorem constrains the integrability within this category of mappings, outlining potential scenarios with analytic invariants of motion. In this paper, we challenge the assumption of the analyticity of the invariant by exploring piecewise linear transformations on a torus (T2) and associated systems on the plane (R2), incorporating arithmetic quasiperiodicity and discontinuities. Introducing a new automated technique, we discovered previously unknown scenarios featuring polygonal invariants that form perfect tessellations and, moreover, fibrations of the plane or torus. This work reveals a novel category of planar tilings characterized by discrete symmetries that emerge from the invertibility of transformations and are intrinsically linked to the presence of integrability. Our algorithm relies on the analysis of the Poincaré rotation number and its piecewise monotonic nature for integrable cases, contrasting with the noisy behavior in the case of chaos, thereby allowing for clear separation. Some of the newly discovered systems exhibit the peculiar behavior of “integrable diffusion,” characterized by infinite and quasirandom hopping between tiles while being confined to a set of invariant segments. Finally, through the implementation of a smoothening procedure, all mappings can be generalized to quasi-integrable scenarios with suppressed volume occupied by chaotic trajectories, thereby opening doors to potential practical applications. Published by the American Physical Society 2024

A novel piecewise linear transformation to moderate regional boundary effect on Real-Time regional ionospheric map (RT-RIM)

RT-RIM with high accuracy and dense spatiotemporal resolution of the ionospheric total electron content is crucial to diverse real-time GNSS applications. However, the uneven ionospheric pierce points distribution and boundary effect severely restrict the RT-RIM accuracy. We dedicate to the rapid and straightforward method to address the limited accuracy issue caused by the two crucial challenges. A novel piecewise linear transformation-adjusted spherical cap harmonic (PLT-ASCH) method is proposed to moderate the localized accuracy decrease in various latitudes areas for both active and stable ionospheric conditions. Especially, in the active ionospheric condition, the RMS improvements referring to IGS products are about 38.85%, 17.04%, 16.73% in Europe and 53.12%, 4.36%, 4.35% in South America, comparing to the inverse distance weighting, ASCH, and adjusted spherical harmonics adding Kriging methods. Moreover, the RMS improvements referring to differential slant TEC are about 48.11%, 16.53%, 16.99% in Europe and 61.01%, 4.87%, 4.33% in South America.

Shopping trip recommendations: A novel deep learning-enhanced global planning approach

Brick-and-mortar shopping malls are embracing Artificial Intelligence (AI) technology and recommender systems to enhance the shopping experience and boost mall revenue. Echoing this trend, we formulate a new shopping trip recommendation problem, which aims to recommend a shopping trip (i.e., a list of stores) that matches customer preferences and has appropriate trip lengths. To solve this problem, we develop a novel deep learning-enhanced global planning (DeepGP) approach featuring three methodological novelties. First, we introduce a new shopping intensity term based on deep neural networks to capture the variation of trip lengths specific to different shopping contexts. Second, we innovatively formulate the learning and optimization objectives in a consistent form by balancing the shopping choice likelihood and the shopping intensity likelihood, thus resolving the inconsistency issue encountered by prior global planning methods. Third, to overcome the computational challenge caused by the nonlinear shopping intensity term, we design a new exact and efficient solution technique based on piecewise linear transformations. Using a real-world offline shopping dataset, we empirically demonstrate the superior performances of our approach compared to representative benchmarks in offering more accurate and relevant shopping trip recommendations. Through a simulation, we show the capacity of our approach to attract and balance customer traffic in practical deployments. Overall, our research highlights the efficacy of combining shopping choices and shopping intensity in a consistent learning and optimization framework for offline shopping trip recommendations.

Piecewise Linear Transformation – Propagating Aleatoric Uncertainty in Neural Networks

Real-world data typically exhibit aleatoric uncertainty which has to be considered during data-driven decision-making to assess the confidence of the decision provided by machine learning models. To propagate aleatoric uncertainty represented by probability distributions (PDs) through neural networks (NNs), both sampling-based and function approximation-based methods have been proposed. However, these methods suffer from significant approximation errors and are not able to accurately represent predictive uncertainty in the NN output. In this paper, we present a novel method, Piecewise Linear Transformation (PLT), for propagating PDs through NNs with piecewise linear activation functions (e.g., ReLU NNs). PLT does not require sampling or specific assumptions about the PDs. Instead, it harnesses the piecewise linear structure of such NNs to determine the propagated PD in the output space. In this way, PLT supports the accurate quantification of predictive uncertainty based on the criterion exactness of the propagated PD. We assess this exactness in theory by showing error bounds for our propagated PD. Further, our experimental evaluation validates that PLT outperforms competing methods on publicly available real-world classification and regression datasets regarding exactness. Thus, the PDs propagated by PLT allow to assess the uncertainty of the provided decisions, offering valuable support.

Frame set for Gabor systems with Haar window

We describe the full structure of the frame set for the Gabor system G(g;α,β):={e−2πimβ⋅g(⋅−nα):m,n∈Z} with the window being the Haar function g=−χ[−1/2,0)+χ[0,1/2). This is the first compactly supported window function for which the frame set is represented explicitly.The strategy of this paper is to introduce the piecewise linear transformation M on the unit circle, and to provide a complete characterization of structures for its (symmetric) maximal invariant sets. This transformation is related to the famous three gap theorem of Steinhaus which may be of independent interest. Furthermore, a classical criterion on Gabor frames is improved, which allows us to establish a necessary and sufficient condition for the Gabor system G(g;α,β) to be a frame, i.e., the symmetric invariant set of the transformation M is empty.

The Complexity of Iterated Reversible Computation

We study a class of functional problems reducible to computing $f^{(n)}(x)$ for inputs $n$ and $x$, where $f$ is a polynomial-time bijection. As we prove, the definition is robust against variations in the type of reduction used in its definition, and in whether we require $f$ to have a polynomial-time inverse or to be computible by a reversible logic circuit. These problems are characterized by the complexity class $\mathsf{FP}^{\mathsf{PSPACE}}$, and include natural $\mathsf{FP}^{\mathsf{PSPACE}}$-complete problems in circuit complexity, cellular automata, graph algorithms, and the dynamical systems described by piecewise-linear transformations.

Mixing apples and oranges: Assessing ecological status and its confidence from multiple and diverse indicators

Ecosystem responses to increasing human pressures are complex and diverse, affecting organisms across all trophic levels. This has prompted the development of methods that integrate information across many indicators for environmental management. Legislative frameworks such as the European Water Framework Directive (WFD), specifically prescribe that integrated assessme nt (IA) of ecological status must consider indicators representing various biological and supporting quality elements. We present a general approach for an IA system based on a piece-wise linear transformation of indicator distributions to a standardized scale, allowing for integrating information from multiple and diverse indicators through a policy-dependent aggregation scheme. Uncertainties associated with monitoring data used for calculating indicators and their propagation throughout the integration scheme allow for confidence assessment at all levels of the hierarchical integration. Specific pressures leading to ecological impact can be identified through the most impaired indicators in the hierarchical and transparent aggregation scheme. The IA and its confidence are facilitated though the development of an online tool that accesses information from monitoring databases and presents the outcome at all levels of the assessment, ensuring consistency and transparency in the calculations for all potential stakeholders. We demonstrate the versality and applicability of the approach using indicators and aggregation principles from the Swedish national guidelines for assessing ecological status of rivers, lakes and coastal waters according to the WFD. Although the approach and the tool were developed specifically for the WFD ecological status assessment in Sweden, the generality of the approach implies that it can easily be adapted to the WFD assessment methods of other countries as well as other policies, where an integrated assessment is required.

Comparing and contrasting choice model and machine learning techniques in the context of vehicle ownership decisions

In recent years, planners have started considering Machine Learning (ML) techniques as an alternative to discrete choice models (CM). ML techniques are primarily data-driven and typically achieve better prediction accuracy compared to CM. However, it is hypothesized that since the ML techniques do not have the strong grounding to economic theory as the CMs, they may not perform well in contexts that are radically different from the ‘training’ scenario. It is also hypothesized that the relative prediction performance may be affected by the metrics used for comparing the models. This research aims to test these two hypotheses empirically by modelling vehicle ownership choices using household survey data from Dhaka, Bangladesh collected in 2004, 2010 and 2019. The performances of CM (multinomial logit) and ML techniques (neural networks and gradient boosting trees) have been compared using log-likelihood and mean absolute percentage error of market shares. The results indicate that the multinomial logit model (MNL) with a piecewise linear transformation of the household income, has the best performance in terms of log-likelihood and mean absolute percentage error of market shares. This is followed by Neural Networks (NN) and Gradient Boosting Trees (GBT). The results thus provide empirical evidence that the ML techniques do not consistently outperform CM. Moreover, the difference in the performance of the models further increases if the prediction scenario is substantially different. This reinforces the hypothesis that CMs, with their behavioural underpinning, are better suited for long-term forecasting than data-driven ML approaches, especially if the population and network attributes are expected to change substantially. These findings will be useful for planners and policy makers in the selection of the appropriate tool for forecasting travel demand.

An unsupervised learning-based generalization of Data Envelopment Analysis

In this paper, we introduce an unsupervised machine learning method for production frontier estimation. This new approach satisfies fundamental properties of microeconomics, such as convexity and free disposability (shape constraints). The new method generalizes Data Envelopment Analysis (DEA) through the adaptation of One-Class Support Vector Machines with piecewise linear transformation mapping. The new technique aims to reduce the overfitting problem occurring in DEA. How to measure technical inefficiency through the directional distance function is also introduced. Finally, we evaluate the performance of the new technique via a computational experience, showing that the mean squared error in the estimation of the frontier is up to 83% better than the standard DEA in certain scenarios.

Application of vibration compensation based on image processing in track displacement monitoring

Abstract The track state detection is of great significance to timely understand the operation state of track and find track defects and prevent operation accidents. This article initially analyzes the key technologies of track detection system and then proposes an image detection technology and image processing method for analyzing track detection at home and abroad, thus putting forward the scheme of track detection using image processing. The characteristics of onsite track images are analyzed, and a track state detection system based on track image preprocessing, image position correction, image defect comparison, and track section size measurement is designed in this article. Further in this article, a study of image linear transformation, noise filtering, defect recognition, and edge detection in track image processing is applied. Furthermore, a robust piecewise linear transformation is designed using the combination of image threshold transformation and image gray transformation. It reduces the loss of detailed information in the process of image processing. The center point of track bright band is determined by the image region segmentation method, which effectively reduces the error of image track measurement and improves the measurement accuracy.

Outlier removal and feature point pairs optimization for piecewise linear transformation in the co-registration of very high-resolution optical remote sensing imagery

Co-registration of very high-resolution images is a challenging and essential preprocessing step in remote sensing image analysis. Piecewise linear (PL) transformation has been shown to accurately handle the registration of very high-resolution images with various local deformations. However, the PL transformation has strict requirements on the structure of the local triangulated irregular network (TIN) and the position accuracy of feature point pairs (FPPs). Existing outlier removal methods barely consider the local TIN structure of FPPs, thus failing to meet the requirements of the PL transformation. Moreover, the inevitably remaining outliers lead to lower local registration accuracy. This paper proposes an outlier removal method and an FPPs optimization method to improve the registration accuracy of the PL transformation. First, we developed a triangle-area representation ratio of the triangulated irregular network (TIN-TARR) descriptor to identify the outliers. Then, we divided these outliers into three types and removed them iteratively. Finally, we further optimized the FPPs by maximizing the similarity between the fixed and the registered images to improve the registration accuracy of the PL transformation. The proposed method was validated using three pairs of TripleSat-2 images with a spatial resolution of 3.2 m, one pair of WorldView-2 images with a spatial resolution of 1.6 m, and one pair of aerial images with a spatial resolution of 0.3 m. The results demonstrated that: (1) The obvious deformations in each registered image were eliminated after the outlier removal using TIN-TARR. (2) The FPPs optimization significantly improved the registration accuracy of the PL transformation. The average registration errors in five tests were 0.542, 0.389, 0.456, 0.420, and 0.592 pixels, respectively. (3) Different similarity metrics had various effects on the FPPs optimization, and structural similarity was the most effective measurement. (4) The proposed co-registration framework presented better registration accuracy than three state-of-the-art methods, especially in images with land cover changes and shadows.

Generalized Continuous Piecewise Linear Companding Transform Design for PAPR Reduction in OFDM Systems

Linear companding transform (LCT) is one of the most attractive schemes to deal with the inherent problem of high peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems, due to its effectiveness and low complexity. In this paper, a generalized continuous piecewise linear companding (CPLC) transform is proposed. The companding and decompanding functions of the proposed scheme consist of multiple continuous linear segments, and the total number of segments is generalized to be any integer not less than four. These linear segments can provide much adaptability for function shaping, leading to high flexibility for performance tradeoffs among PAPR reduction, bit error rate (BER), out-of-band (OOB) rejection and algorithmic complexity. The continuity of the companding function helps to reduce OOB radiations. Several optimization problems with different targets under the constraint condition of constant average power are constructed. Permissible ranges of key parameters, relationships among these parameters and their influence on algorithmic performance are analyzed. Parameter selecting strategies are also provided. In addition, an iterative receiving method is designed to reduce system BER effectively at the receiver. Simulation results validate the performance superiorities of the proposed scheme to that of other typical companding schemes.

A data variability index: Quantifying complexity of models and analyzing adversarial data

In system modeling arises a fundamental question about the level of difficulty one may encounter when designing a model on a basis of some training data. In this study, we advocate that such level of difficulty inherently depends upon the variability of the available function (data). If for a pair of input data which exhibits small differences, the differences of the corresponding outputs are substantial then building a model in the presence of such data becomes more challenging than in cases of data where the differences in the output data are far more limited. Dwelling on this observation, we introduce a variability index quantifying the nature of data in terms of variability observed in input and output data, respectively. The proposed index is model-neutral (model agnostic), namely describes and quantifies the modeling challenge implied by the data irrespectively of the specific model to be constructed. In case of functions, we show that the Lipschitz constant plays a similar role as the variability index computed for experimental data. An original way of reducing values of the variability index through a nonlinear transformation of original data completed by a fuzzy rule-based model is introduced. It is shown that such rule-based architecture gives rise to a piecewise linear transformation (multipoint linear approximation) exhibiting required contraction-dilation characteristics. The optimization of this transformation is carried out with the use of a Particle Swarm Optimization algorithm. We also demonstrate that the index can be used to quantify a concept of adversarial data. Along this line, we introduce a granular characterization of adversarial feature of individual data points. A series of experiments is provided to offer a thorough illustration and detailed insight into the nature and a thorough characterization of publicly available data.

Analysis of image-to-image registration performance of multitemporal KOMPSAT-3∙3A imagery with respect to convergence angle

ABSTRACT Unlike numerous studies on the impact of a convergence angle between two stereo images, its effects on image-to-image registration have not been extensively investigated. In this study, we analysed the impact of the magnitude of the convergence angles of very-high-resolution (VHR) satellite image pairs on registration accuracy with respect to the two-dimensional (2D) geometric alignment. To perform image-to-image registration, we used an iterative process to extract a large number of well-distributed conjugate points (CPs) by combining area- and feature-based matching approaches. To evaluate the proposed method’s ability to extract CPs and demonstrate the relationship between the registration performance and the magnitude of the convergence angles, we conducted experiments using KOMPSAT-3 and KOMPSAT-3A satellite images acquired over Daejeon, South Korea. A total of 18 satellite images were used to generate 153 image pairs with different convergence angles. Two transformation models, affine and piecewise linear transformations, were used independently to warp a target image to a reference image, and their performances were compared. An analysis of the affine transformation with respect to the size of the convergence angles revealed that a larger convergence angle between images resulted in lower accuracy of the registration performance. This result differs from the convergence angle condition required in stereo images to extract accurate 3D information. However, the piecewise linear transformation achieved a reliable registration performance regardless of the magnitude of the convergence angles.

A pointer meter reading recognition method based on improved ORB algorithm for substation inspection robot

Currently, pointer meters in substations are read manually, which causes a waste of human resources. To realize automatic reading of such meters, an accurate method for recognizing and reading of pointer meters was proposed for the inspection robot in substation. The new method consists of three steps. Step 1: the image is preprocessed with grayscale, noise reduction and piecewise linear grayscale transformation. Step 2: the Gaussian scale space is used to enhance the scale invariace of the ORB algorithm. Meanwhile, the RANSAC algorithm is used to screen the matching point pairs, which improves the accuracy of the feature pointer matching. Step 3: the Hough transform algorithm is utilized to fit the pointer. Finally, the reading result is obtained according to the angle method and the prior information of the pointer meter. The proposed approach can recognize and read the meter accurately. It has high reliability and engineering application value.

Quasi-Periodic Phase Coding for Long-Depth-Range 3-D Measurements of Moving Objects

Fringe projection profilometry (FPP) requires an auxiliary projection sequence or spatial landmark to remove phase ambiguity, thereby severely limiting the measurement speed or depth range for moving objects. In this article, we propose a novel quasi-periodic phase coding method for long-depth-range 3-D measurements of moving objects without temporal or spatial limitations. This article mainly focuses on the construction of the encoding schema for quasi-periodic fringe patterns and the execution of the phase decoding framework for long-depth-range 3-D measurements of moving surfaces. First, a set of stripes with similar periods is designed on the basis of a preset equivalent period, and the various combinations of these stripes constitute quasi-periodic fringe patterns. Second, we present a progressive phase recovery strategy for decoding quasi-periodic fringe images, in which the wrapped phase is converted first into a continuous phase distribution and then into the absolute phase. In this strategy, the absolute phase map is effectively screened via the piecewise linear transformation from the quasi-periodic phase to the equivalent phase. Compared with the existing FPP methods, the proposed method avoids the low-frame-rate constraint and the need for landmark configuration. Simulation and experimental results verify that the proposed method is applicable for dynamic 3-D measurements of moving objects over a large-depth range.

Point Pairs Optimization for Piecewise Linear Transformation of Multimodal Remote Sensing Images by the Similarity of Log-Gabor Features

The registration of multimodal remote sensing (MMRS) images often suffers from local deformations and obvious nonlinear radiometric differences. Piecewise linear (PL) transformation handles local deformations well but requires a stricter position accuracy of feature point pairs (FPPs). After outlier removal, the inevitably remaining outliers lead to lower local registration accuracy. To fix this issue, we propose a new similarity metric <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MSOLG_SSIM</i> , which combines the multi-scale and multi-orientation Log-Gabor features with structural similarity. The metric is then used to optimize the FPPs by maximizing the similarity between the fixed and the registered images to improve the registration accuracy of the PL transformation. Experimental results based on eight pairs of MMRS images demonstrated the robustness of the proposed similarity metric and the effectiveness of the FPPs optimization method. The code of the proposed method can be downloaded from https://github.com/HoucaiGuo/FPPs-Optimization-Multimodal.

Learning Relaxed Neighborhood Consistency for Feature Matching

Feature matching is a critical prerequisite in many applications of remote sensing, and its aim is to establish reliable correspondences between two sets of features. Existing attempts typically involve estimating the underlying image transformations to remove false matches in putative matches. However, the image transformation could vary with different application scenarios, which means that using a predefined geometrical model may lead to inferior matching accuracy, especially if the image transformation is nonrigid. This article casts the mismatch removal into a neighborhood consistency evaluation problem under a customized learning framework. With only seven training image pairs involving approximately 8000 putative matches, our method can handle different types of images or transformation models (affine, homography, piecewise-linear transformation, and others). Extensive experiments on feature matching and image registration are conducted to demonstrate the superiority of our method over the eight state-of-the-art competitors.