| 摘要: |
| Radon变换是一种用于形状分析的非常有用的数学工具.它是一种无损变换，利用该变换，可以方便地抽取到目标形状结构的重要视觉特征.但因为该变换含有目标的大小、位置和方向信息，所以并不能将其直接用于目标形状的识别任务.现有的基于Radon变换的形状分析方法虽然通过各种途径消除这些信息，以保证抽取的形状特征的不变性，但这些操作也损失了大量有用的形状信息，使得描述的精度有限.为解决该问题，提出了一种λ-变换的数学工具.该变换利用平行直线的相对位置关系（用一个属于区间[0，1]的变量r来表达）和它们对形状函数的积分，构造了一个变量r和直线的方向角变量θ的二维函数，用于形状的描述和差异性度量.从理论上分析了λ-变换满足对平移、缩放的不变性，以及对旋转变换仅使其在θ维发生平移的特性，也从理论上分析了λ-变换对Radon变换信息的保持特性，而这种保持特性使得该变换比其他基于Radon变换的形状描述子具有更高的描述精度.λ-变换的有效性和相较于其他同类方法的优越性，通过几组常用形状图像检索实验得到验证. |
| 关键词: Radon变换 图像分析 形状描述 目标识别 图像检索 |
| DOI：10.13328/j.cnki.jos.005314 |
| 分类号: |
| 基金项目:国家自然科学基金（61372158）；江苏省自然科学基金（BK20141487）；江苏省科技计划（产学研合作前瞻性联合研究）（BY2016009-03）；江苏省高校优秀科技创新团队（2017-15）；江苏省高校优势学科建设工程资助项目（PAPD） |
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| λ-Transform:A Mathematical Tool for Accurate Shape Description |
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WANG Bin1,2
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1.School of Information Engineering, Nanjing University of Finance and Economics, Nanjing 210023, China;2.Key Laboratory of Electronic Business(Nanjing University of Finance and Economics), Nanjing 210023, China
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| Abstract: |
| Radon transform is a useful mathematical tool for shape analysis. It is a lossless transform and makes the extraction of structural shape features become very easy. However it cannot be directly applied to shape recognition due to its sensitivity to translation, scaling and rotation of the shape. The existing Radon transform based methods have had many attempts to remove the information of size, position and orientation of the shape from the Radon transform. However in these methods, the invariant features are achieved at the expense of useful shape features. To address this issue, a novel mathematical tool termed λ-transform is proposed for shape description.The λ-transform utilizes the relative position information between the parallel lines(encoded in a variable r∈[0,1]) and their integrals over the shape to construct a 2D function of the variable r and the direction angle θ of the line for shape description. This study theoretically proves that λ-transform is invariant to the translation and scaling and a rotation only makes it shift along the θ direction. It also theoretically concludes that λ-transform can effectively preserve the useful information of Radon transform. These desirable characteristic make λ-transform outperform the other Radon based methods for shape recognition. Tests on the proposed λ-transform are carried out on several commonly used shape image datasets, and the experimental results indicate it achieves better performance over other Radon based shape descriptors. |
| Key words: Radon transform image analysis shape description object recognition image retrieval |
