论文标题
网格组平面中的签名欧元定理
Signature-inverse Theorem in Mesh Group-planes
论文作者
论文摘要
这是第二张关于基础关节不变的数字版本的数字版本的纸张。签名定理及其反向保证差分不变符号曲线的任何应用在视觉对象的不变识别中。我们首先显示了曲率截面和签名逆定理的无效性，这意味着非统一的网格可能具有相同的关节不变数值曲率或签名。然后，通过在欧几里得和仿射案例中分别对三分和五点普通网格进行分类，我们会根据相关的关节不变签名来寻找条件，从而使这些定理正确。此外，我们提出主机定理，为封闭的普通网格提供更简单的签名与内定理。
This is the second paper devoted to the numerical version of Signature-inverse Theorem in terms of the underlying joint invariants. Signature Theorem and its Inverse guarantee any application of differential invariant signature curves to the invariant recognition of visual objects. We first show the invalidity of Curvature-inverse and Signature inverse theorems, meaning non-congruent meshes may have the same joint invariant numerical curvature or signature. Then by classifying three and five point ordinary meshes respectively in the Euclidean and affine cases, we look for conditions in terms of the associated joint invariant signatures which make these theorems correct. Additionally, we bring forward The Host Theorem to provide a simpler version of Signature-inverse Theorem for closed ordinary meshes.
