基于 CA-SIFT 的图像特征两级匹配算法

中国民航大学学报 ›› 2025, Vol. 43 ›› Issue (2): 73-82.

基于 CA-SIFT 的图像特征两级匹配算法

中国民航大学天津市智能信号与图像处理重点实验室，天津 300300

收稿日期:2023-03-29 修回日期:2023-05-22 出版日期:2025-05-14 发布日期:2025-05-14
作者简介:焦卫东（1973— ），男，陕西咸阳人，教授，博士，研究方向为 Clifford 代数、图像处理.
基金资助:
国家重点基础研究发展计划项目（2020YFB1600101）

Two-level matching algorithm for image features based on CA-SIFT

Tianjin Key Laboratory for Advanced Signal Processing, CAUC, Tianjin 300300, China

Received:2023-03-29 Revised:2023-05-22 Online:2025-05-14 Published:2025-05-14

摘要/Abstract

摘要：

针对欧氏空间尺度不变特征变换（SIFT，scale invariant feature transform）算法在彩色图像匹配过程中丢失

图像光谱信息、匹配精度低、计算量大等问题，利用 Clifford 代数（CA，Clifford algebra）对多维空间的表达能

力提出一种基于 CA-SIFT 的图像匹配算法。首先，将图像转换到 CA 空间表示，同时保留图像空间和光谱信

息，通过共形几何代数内积运算构造度量函数，提高特征点搜索效率，在 CA 空间中检测特征点；其次，采用图

像特征两级匹配策略，即将 CA-SIFT 特征描述向量转换为哈希编码，由暴力匹配得到粗匹配结果；最后，采

用网格运动统计（GMS，grid-based motion statistics）方法完成精匹配。实验结果表明：本文算法性能优于

SIFT 算法，提取的特征点对数量最多提升近 54%；图像匹配方面，平均匹配精度达到 98%以上，实现了高

精度、适用于多数场景的图像匹配方法。

关键词:

特征匹配, Clifford 代数, 特征检测, 内积, 网格运动统计

Abstract:

To address the problems of loss of image spectral information, low matching accuracy and large computational effort in the process of color image matching by the scale invariant feature transform (SIFT) algorithm in Euclidean

space, an image matching algorithm based on CA-SIFT is proposed using the expressiveness of Clifford algebra

(CA) for multidimensional space. Firstly, the image is transformed to CA space representation, while retaining the

image space and spectral information, and the metric function is constructed by the inner product operation of the

conformal geometric algebra to improve the efficiency of feature point search and detect feature points in CA space.

Secondly, a two-stage image feature matching strategy is adopted, the CA-SIFT feature description vector is converted into a hash code, and the coarse matching results are obtained by brute force matching. Finally, a gridbased motion statistics (GMS) method is used to complete the fine matching. The experimental results show that the

proposed algorithm outperforms the SIFT algorithm, and the number of extracted feature point pairs is improved

nearly 54%. In terms of image matching, the average matching accuracy reaches over 98%, achieving a highly accurate and applicable image matching method for most scenes.

Key words:

feature matching, Clifford algebra, feature extraction, inner product, grid-based motion statistics (GMS)

中图分类号:

TP391.41

焦卫东, 焦一哲.

基于 CA-SIFT 的图像特征两级匹配算法

[J]. 中国民航大学学报, 2025, 43(2): 73-82.

JIAO Weidong, JIAO Yizhe.

Two-level matching algorithm for image features based on CA-SIFT

[J]. Journal of Civil Aviation University of China, 2025, 43(2): 73-82.

参考文献 10

[1]	李宇杰, 李煊鹏, 张为公．基于视觉的三维目标检测算法研究综述
[J]	．计算机工程与应用, 2020, 56(1): 11-24．
	[2]
	LOWE D G． Distinctive image features from scale-invariant keypoints
	． International Journal of Computer Vision, 2004, 60(2): 91-110．
	[3]
	MIKOLAJCZYK K, SCHMID C． A performance evaluation of local descriptors[J]． IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005, 27(10): 1615-1630．
	[4]
	BAY H, TUYTELAARS T, VAN GOOL L． SURF: speeded up robust fea－
	tures[M]//Computer Vision-ECCV 2006．Berlin, Heidelberg: Springer
	Berlin Heidelberg, 2006: 404-417．
	[5]
	LIU X Z, TIAN Z, LENG C C, et al． Remote sensing image registration
	based on KICA-SIFT descriptors[C]//2010 Seventh International Con－
	ference on Fuzzy Systems and Knowledge Discovery, August 10 -12,
	2010, Yantai, China．IEEE, 2010: 278-282．
[6]	李丹, 孙海涛, 王海莉．一种改进的 SIFT 图像立体匹配算法[J]．西
	南交通大学学报, 2015, 50(3): 490-496．
[7]	贾雯晓, 张贵仓, 汪亮亮, 等．基于 SIFT 和改进的 RANSAC 图像配
	准算法[J]．计算机工程与应用, 2018, 54(2): 203-207．
	[8]
	BIAN J W, LIN W Y, LIU Y, et al． GMS: Grid-based motion statistics
	for fast, ultra-robust feature correspondence[J]． International Journal of
	Computer Vision, 2020, 128(6): 1580-1593．
	[9]
	LABUNETS V． Clifford algebras as unified language for image process－
	ing and pattern recognition[C]//Computational Noncommutative Algebra
	and Applications, Dordrecht: Springer Netherlands, 2004: 197-225．
[10]	BULOW T, FELSBERG M, SOMMER G． Non-commutative hyper com-

	plex Fourier transforms of multidimensional signals[M]//Geometric Computing with Clifford Algebras． Berlin, Heidelberg: Springer Berlin Heidelberg, 2001: 187-207．


	[11] 李洪波．共形几何代数: 几何代数的新理论和计算框架[J]．计算机辅


	助设计与图形学学报, 2005, 17(11): 3-13．


	[12] LI Y S, LIU W M, LI X T, et al． GA-SIFT: a new scale invariant feature


	transform for multispectral image using geometric algebra[J]． Information


	Sciences, 2014, 281: 559-572．


	[13] PHAM M T, DO P H, TACHIBANA K． Feature extraction for classification method using principal component based on conformal geometric


	algebra [C]//2016 International Joint Conference on Neural Networks


	(IJCNN), July 24-29, 2016, Vancouver, BC, Canada． IEEE, 2016: 4112-


	4117．


	[14] 华亮, 程天宇, 顾菊平, 等．基于 ROI 及 Clifford 代数相对不变量


	的 3D 医学图像配准[J]．图学学报, 2017, 38(1): 90-96．


	[15] WANG R, LIANG M X, HE Y M, et al． A normalized adaptive filtering


	algorithm based on geometric algebra[J]． IEEE Access, 2020, 8: 92861-


	92874．


	[16] 崔文弢, 焦卫东, 庞艳丽．基于几何代数的 SVS-NLMS 点云配准算


	法[J]．红外与激光工程, 2021, 50(12): 562-571．


	[17] 刘丙槐．基于共形几何代数的机器人运动仿真开发[D]．北京: 北方


	工业大学, 2018．


	[18] DATAR M, IMMORLICA N, INDYK P, et al． Locality-sensitive hash－


	ing scheme based on p-stable distributions[C]//Twentieth Annual Sym－


	posium on Computational Geometry, June 8-11, 2004, Brooklyn, New


	York, USA． ACM, 2004: 253-262．


	[19] MA L, LI H F, YU K P． Fast iris localization algorithm on noisy images


	based on conformal geometric algebra[J]． Digital Signal Processing, 2020,


	100: 102682．


	[20] LEUTENEGGER S, CHLI M, SIEGWART R Y． BRISK: Binary Robust


	invariant scalable keypoints[C]//2011 International Conference on Com－


	puterVision,November 6-13, 2011, Barcelona, Spain． IEEE, 2011: 2548-


	2555．


	[21] ALCANTARILLA P, NUEVO P, BARTOLI A. Fast explicit diffusion for


	accelerated features in nonlinear scale spaces[C]//British Machine Vi－


	sion Conference (BMVC) 2013. Bristol: British Machine Vision Associa－


	tion, 2013: 13.1-13.11.


	[22] TRAN Q H, CHIN T J, CARNEIRO G, et al． In defence of RANSAC for


	outlier rejection in deformable registration[M]//Computer Vision- ECCV


	2012． Berlin, Heidelberg: Springer Berlin Heidelberg, 2012: 274-287．