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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2025, Vol. 42 ›› Issue (5): 974-982.doi: 10.3969/j.issn.1005-3085.2025.05.013cstr: 32411.14.cjem.CN61-1269/O1.2025.05.013

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自表示显著性物体检测模型矩阵优化问题的迭代算法

黄威铭1,  段雪峰2   

  1. 1. 广西国际商务职业技术学院人文教育学院，南宁 530007
    2. 桂林电子科技大学数学与计算科学学院，桂林 541004
  • 收稿日期:2022-09-26 接受日期:2025-03-07 出版日期:2025-10-15 发布日期:2025-12-15
  • 通讯作者: 段雪峰 E-mail: duanxuefeng@guet.edu.cn
  • 基金资助:
    国家自然科学基金 (12361079; 12201149; 62462018; 12261026)；广西自然科学基金 (2023GXNSFAA026067; 2024GXNSFAA010521).

Iterative Algorithm for Matrix Optimization Problem in Salient Object Detection Model

HUANG Weiming1,  DUAN Xuefeng2   

  1. 1. College of Humanities and Education, Guangxi International Business Vocational College, Nanning 530007

    2. School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004


  • Received:2022-09-26 Accepted:2025-03-07 Online:2025-10-15 Published:2025-12-15
  • Contact: X. Duan. E-mail address: duanxuefeng@guet.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (12361079; 12201149; 62462018; 12261026); the Natural Science Foundation of Guangxi (2023GXNSFAA026067; 2024GXNSFAA010521).

摘要：

为了提高图像显著性物体检测的准确度，分辨率与计算效率，利用图像背景空间与图像空间之间的关系，结合Schatten-$p$范数和$l_{2,1}$范数构造了新的显著性物体检测模型。与基于核范数的低秩逼近的传统显著性物体检测模型相比，新模型考虑了图像特征空间与背景空间之间的关系，并且Schatten-$p$范数相对于核范数，在数值比例上能更好地逼近低秩函数。针对新模型的矩阵优化问题，设计不动点迭代算法对模型进行求解，在4个显著性物体检测模型的标准数据集进行可行性验证，并和4种常用的算法进行对比实验，实验结果验证了该算法具有较高的计算效率和准确度。

关键词: 显著性物体检测, 低秩逼近, Schatten-$p$范数, $l_{2,1}$范数, 不动点迭代

Abstract:

In order to improve the accuracy, resolution and computational efficiency of image salient object detection, a new salient object detection model is constructed by combining Schatten-$p$ norm and $l_{2,1}$-norm by using the relationship between image background space and image space. Compared with the traditional saliency object detection model based on the low-rank approximation of the nuclear norm, the new model considers the relationship between the image feature space and the background space, and the Schatten-$p$ norm can be better approximated by the low-rank function on numerical proportional than nuclear norm. For the matrix optimization problem of the new model, a fixed-point iterative algorithm is designed for solving the problem, and the feasibility is verified on the standard data sets of four salient object detection models, and the comparison experiments with four commonly used algorithms are also carried out. The experimental results verify that the algorithm has high computational efficiency and accuracy.

Key words: salient object detection, low rank approximation, Schatten-$p$ norm, $l_{2,1}$-norm, fixed point iteration

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