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hessian matrix-aware comprehensive post-training quantization for vision transformers

JOURNAL OF ELECTRONIC IMAGING 2025年第1期34卷

作者： Zhang, Weixing Tian, Zhuang Lin, Nan Yang, Cong Chen, Yongxia Zhengzhou Univ Sch Cyber Sci & Engn Zhengzhou Peoples R China

In recent years, vision transformers (ViTs) have made significant breakthroughs in computer vision and have demonstrated great potential in large-scale models. However, the quantization methods for convolutional neural network models do not perform well on ViTs models, leading to a significant decrease in accuracy when applied to ViTs models. We extend the quantization parameter optimization method based on the hessian matrix and apply it to the quantization of the LayerNorm module in ViT models. This approach reduces the impact of quantization on task accuracy for the LayerNorm module and enables more comprehensive quantization of ViT models. To achieve fast quantization of ViTs models, we propose a quantization framework specifically designed for ViTs models: hessian matrix-aware post-training quantization for vision transformers (HAPTQ). The experimental results on various models and datasets demonstrate that our HAPTQ method, after quantizing the LayerNorm module of various ViT models, can achieve lossless quantization (with an accuracy drop of less than 1%) in ImageNet classification tasks. Specifically, the HAPTQ method achieves 85.81% top-1 accuracy on the ViT-L model.

关键词： model quantization post-training quantization image classification hessian matrix vision transformer

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Multi-line laser stripe centerline extraction methods for reflective metal surfaces using deep learning and hessian matrix

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MEASUREMENT SCIENCE AND TECHNOLOGY 2025年第6期36卷 065403-065403页

作者： Peng, Tao Gu, Anqi Zhang, Zhijiang Shanghai Univ Sch Commun & Informat Engn Shangda Rd 99 Shanghai Peoples R China

Accurately extracting the center of laser stripes remains a challenge in industrial measurement, where precision and noise robustness must be balanced. On highly reflective metal surfaces, low surface roughness often leads to overexposed regions in laser stripe images. This results in uneven stripe width distribution and asylight intensity profiles, complicating center extraction. In this paper, we propose a novel method for laser stripe extraction from images of reflective metal surfaces, leveraging deep learning and multi-scale Gaussian kernels. First, an improved YOLOv8 network detects regions of interest (ROIs) containing laser lines and determines stripe cross-section widths. Next, a multi-scale Gaussian template, derived from the stripe width, is convolved with the ROI to construct a multi-scale hessian matrix. Using the hessian matrix, the normal direction of the laser line is calculated, along which a second-order Taylor expansion is performed to locate the subpixel center point. To enhance robustness, non-maximum suppression and a stripe energy distribution model are applied to eliminate noise points, optimizing the center coordinates. The entire algorithm is implemented with parallel acceleration, enabling high-precision and noise-robust subpixel center extraction. We validate the proposed method on both synthetic and real-world images. The experiments show that under different noise conditions, the deviation of the central point pixel remains within 0.09 pixels. Compared to traditional Steger's method, our approach improves subpixel localization accuracy by up to 45.80%, effectively improving the sensor's measurement performance.

关键词： deep learning hessian matrix multi-scale Gaussian kernel laser centerline extraction

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Asymptotic estimate of solutions in a 4th-order parabolic equation with the Frobenius norm of a hessian matrix

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CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES 2025年第1期68卷 91-108页

作者： Li, Ke Liu, Bingchen Dou, Jiaxin China Univ Petr Coll Sci Qingdao Peoples R China

This paper deals with a 4th-order parabolic equation involving the Frobenius norm of a hessian matrix, subject to the Neumann boundary conditions. Some threshold results for blow-up or global or extinction solutions are obtained through classifying the initial energy and the Nehari energy. The bounds of blow-up time, decay estimates, and extinction rates are studied, respectively

关键词： 4th-order parabolic equation hessian matrix global existence blow-up time extinction rate

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High-Accuracy Spectral Measurement of Stimulated-Brillouin-Scattering Lidar Based on hessian matrix and Steger Algorithm

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REMOTE SENSING 2023年第6期15卷 1511-1511页

作者： Liu, Zhiqiang Sun, Jie Zhang, Xianda Zeng, Zhi Xu, Yupeng Luo, Ningning He, Xingdao Shi, Jiulin Nanchang Hangkong Univ Jiangxi Prov Key Lab Optoelect Informat Sci & Tech Nanchang 330063 Peoples R China Nanchang Hangkong Univ Key Lab Nondestruct Test Minist Educ Nanchang 330063 Peoples R China Nanchang Hangkong Univ Natl Engn Lab Nondestruct Testing & Optoelect Sens Nanchang 330063 Peoples R China

The measurement accuracy of Brillouin scattering spectra is crucial for ocean remote sensing by Brillouin scattering lidar. Due to the limited resolution of ICCD cameras, the traditional processing methods remain at the pixel or partial sub-pixel level, which cannot meet the requirements of high-performance lidar. In this paper, to extract the frequency shift with high precision from stimulated Brillouin scattering (SBS) lidar, a novel spectral processing method with sub-pixel recognition accuracy is proposed based on the hessian matrix and Steger algorithm combined with the least square fitting method. Firstly, the hessian matrix and Frangi filter are used for signal denoising. Then, the center points of SBS spectra at the sub-pixel level are extracted using the Steger algorithm and are connected and classified according to the signal type. On that basis, the frequency shifts of Brillouin scattering are calculated by using the center and radii of interference spectra after through fitting by the least squares method. Finally, the water temperatures are inverted by using the frequency shifts of Brillouin scattering. The results show that the processing method proposed in this paper can accurately calculate the frequency shift of Brillouin scattering. The measured errors of frequency shift are generally at an order of MHz, and the inversion accuracy of water temperature can be as low as 0.14 degrees C. This work is essential to the application for remote sensing the seawater parameters by using the Brillouin lidar technique.

关键词： Brillouin lidar spectral measurement hessian matrix Steger algorithm

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A novel adaptive Kriging method combining hessian matrix and an efficient F-scoreβ-based stopping criterion for structural reliability analysis

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STRUCTURES 2023年 58卷

作者： Li, Jingkui Gao, Yiling Wu, Xinxing Deng, Yansen Shenyang Aerosp Univ Civil Aviat Coll Shenyang 110136 Peoples R China

Reliability analysis of complex structures or highly nonlinear performance functions generate an enormous computational burden and affects computational efficiency. It is crucial to accurately assess structural reliability. However, current methods do not meet the accuracy and efficiency requirements as the complexity and nonlinearity of the model gradually increase. To address these problems, a novel active learning Kriging method combined with a hessian matrix was proposed for efficient structural reliability analysis. The predicted mean of the Kriging model was used as an element of the hessian matrix to describe the degree of nonlinearity of the model. Based on the fact that the iterative process is greatly influenced dramatically by the sample points in proximity to the limit state surface (LSS), a candidate sample pool (CSP) is generated, where the sample points located in the vicinity of the LSS with a larger curvature are chosen to add to the design of experiments (DoE). A stopping criterion about F-score(beta) based on the number of the misclassified points is proposed to judge the model fitting effect, which can be used to effectively identify the LSS. Two mathematical cases and two finite element cases were used to illustrate the high accuracy and efficiency of the method, which a novel manner of the nonlinear reliability calculation is provided.

关键词： Structure reliability Active learning method Kriging model hessian matrix Stopping criterion F-score

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Modification of the Confidence Bar Algorithm Based on Approximations of the Main Diagonal of the hessian matrix for Solving Optimal Control Problems

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AUTOMATION AND REMOTE CONTROL 2022年第10期83卷 1590-1599页

作者： Gornov, A. Yu. Anikin, A. S. Zarodnyuk, T. S. Sorokovikov, P. S. Russian Acad Sci Matrosov Inst Syst Dynam & Control Theory Siberian Branch Irkutsk 664033 Russia

The paper proposes an approach to the study of the standard optimal control problem based on the use of reduction to a finite-dimensional optimization problem with subsequent use of approximation of the main diagonal of the hessian. The results of computational experiments on solving auxiliary optimization problems for separable, quasiseparable, and Rosenbrock-Skokov functions are presented.

关键词： confidence bar algorithm quasiseparable function hessian matrix optimal control problem

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Dim and Small Target Detection Based on Improved hessian matrix and F-Norm Collaborative Filtering

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REMOTE SENSING 2022年第18期14卷 4490-4490页

作者： Fan, Xiangsuo Li, Juliu Chen, Huajin Min, Lei Li, Feng Guangxi Univ Sci & Technol Sch Automat Liuzhou 545006 Peoples R China Guangxi Univ Sci & Technol Sch Elect Engn Liuzhou 545006 Peoples R China Chinese Acad Sci Inst Opt & Elect Chengdu 610209 Peoples R China

In order to effectively improve the dim and small target detection ability of photoelectric detection system to solve the high false rate issue under complex clouds scene in background modeling, a novelty hessian matrix and F-norm collaborative filtering is proposed in this paper. Considering the influence of edge noise, we propose an improved hessian matrix background modeling (IHMM) algorithm, where a local saliency function for adaptive representation of the local gradient difference between the target and background region is constructed to suppress the background and preserve the target. Because the target energy is still weak after the background modeling, a new local multi-scale gradient maximum (LMGM) energy-enhancement model is constructed to enhance the target signal, and with the help of LMGM, the target's energy significant growth and the target's recognition are clearer. Thus, based on the above preprocessing, using the motion correlation of the target between frames, this paper proposes an innovative collaborative filtering model combining F-norm and Pasteur coefficient (FNPC) to obtain the real target in sequence images. In this paper, we selected six scenes of the target size of 2 x 2 to 3 x 3 and with complex clouds and ground edge contour to finish experimental verification. By comparing with 10 algorithms, the background modeling indicators SSIM, SNR, and IC of the IHMM model are greater than 0.9999, 47.4750 dB, and 12.1008 dB, respectively. In addition, the target energy-enhancement effect of LMGM model reaches 17.9850 dB in six scenes, and when the false alarm rate is 0.01%, the detection rate of the FNPC model reaches 100% in all scenes. It shows that the algorithm proposed in this paper has excellent performance in dim and small target detection.

关键词： hessian matrix F-norm background modeling energy enhancement dim and small target detection

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A High-Speed Centerline Extraction Method for Multiple Laser Stripe based on hessian matrix

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Procedia Computer Science 2024年 250卷 235-243页

作者： Juntian Shi Weichao Guo Xinjun Sheng State Key Laboratory of Mechanical System and Vibration School of Mechanical Engineering Shanghai Jiao Tong University Shanghai 200240 China Meta Robotics Institute Shanghai Jiao Tong University Shanghai 200240 China

Laser centerline extraction is a critical step in the machine vision-aided measurement process, especially in the field of aerospace drilling and riveting. We propose a novel and efficient algorithm for the extraction of multiple laser centerlines, which consists of three major parts: laser linewidth estimation, ROI (Region of Interest) extraction, and precise positioning. In the linewidth estimation part, a method based on second-order moment is used to estimate the linewidth, and the scanning frame to linewidth ratio is adopted as the convergence condition to achieve a stable estimation result. In the ROI extraction part, we use a scanning frame to perform raster scanning on the entire image, and calculate the feature function threshold based on the sampling and grayscale volume method to complete ROI extraction. In the precise positioning part, we employ an improved method based on the hessian matrix to reduce computation time, and use a λ filtering method to eliminate noise. Finally, the K-means method is used to classify the center points belonging to different laser centerlines, and RANSAC is utilized to perform line fitting. The final results demonstrate that the proposed algorithm has certain improvements in accuracy and also exhibits high computational efficiency.

关键词： Manufacturing Laser centerline extraction hessian matrix

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Detection of microaneurysms and hemorrhages based on improved hessian matrix

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INTERNATIONAL JOURNAL OF COMPUTER ASSISTED RADIOLOGY AND SURGERY 2021年第6期16卷 883-894页

作者： Yang, Linying Yan, Shiju Xie, Yuanzhi Univ Shanghai Sci & Technol Sch Med Instrument & Food Engn Shanghai 200093 Peoples R China

Purpose Knowing the early lesion detection of fundus images is very important to prevent blindness, and accurate lesion segmentation can provide doctors with diagnostic evidence. This study proposes a method based on improved hessian matrix eigenvalue analysis to detect microaneurysms and hemorrhages in the fundus images of diabetic patients. Methods A two-step method including identification of lesion candidate regions and classification of candidate regions is adopted. In the first step, the method of eigenvalue analysis based on the improved hessian matrix was applied to enhance the image preprocessed. A dual-threshold method was used for segmentation. Then, blood vessels were gradually removed to obtain the lesion candidate regions. In the second step, all candidates were classified into three categories: microaneurysms, hemorrhages and the others. Results The proposed method has achieved a better performance compared with the existing algorithms on accuracy rates. The classification accuracy rates of microaneurysms and hemorrhages obtained by using our method were 94.4% and 94.0%, respectively, while the classification accuracy rates obtained by using Frangi's filter based on the hessian matrix to enhance the image were 90.9% and 92.1%. Conclusion This study demonstrated a methodology for enhancing images by using eigenvalue analysis based on the improved hessian matrix and segmentation by using double thresholds. The proposed method is beneficial to improve the detection accuracy of microaneurysms and hemorrhages in fundus images.

关键词： Fundus images Hemorrhages Microaneurysms hessian matrix Image enhancement

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Mixed-precision Quantization with Dynamical hessian matrix for Object Detection Network

Mixed-precision Quantization with Dynamical Hessian Matrix f...

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IEEE International Conference on Visual Communications and Image Processing (VCIP) - Visual Communications in the Era of AI and Limited Resources

作者： Yang, Zerui Fei, Wen Dai, Wenrui Li, Chenglin Zou, Junni Xiong, Hongkai Shanghai Jiao Tong Univ Sch Elect Informat & Elect Engn Shanghai Peoples R China

ISBN: (纸本)9781728185514

Mixed-precision quantization with adaptive bitwidth allocation for neural network has achieved higher compression rate and accuracy in classification task. However, it has not been well explored for object detection networks. In this paper, we propose a novel mixed-precision quantization scheme with dynamical hessian matrix for object detection networks. We iteratively select a layer with the lowest sensitivity based on the hessian matrix and downgrade its precision to reach the required compression ratio. The L-BFGS algorithm is utilized for updating the hessian matrix in each quantization iteration. Moreover, we specifically design the loss function for objection detection networks by jointly considering the quantization effects on classification and regression loss. Experimental results on RetinaNet and Faster R-CNN show that the proposed DHMQ achieves state-of-the-art performance for quantized object detectors.

关键词： Network quantization object detection bitwidth allocation hessian matrix L-BFGS

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