论文标题
自动分类可变形形状
Automatic classification of deformable shapes
论文作者
论文摘要
令$ \ mathcal {d} $为平滑的3D曲面数据集，将分区分为不相交的类$ \ mathit {cl} _J $，$ j = 1，\ ldots，k $。我们展示了如何将优化的差异登记应用于大量对$ s，s'\ in \ mathcal {d} $如何提供描述性特征向量，以在$ \ mathcal {d} $上实现自动分类，并在$ \ mathbbbbbbbb in nird by Intig by Intignation classate classifiers上实现自动分类。为了提高自动分类的准确性，我们通过对$ s，s'\ in \ mathit {cl} _j $之间的平滑表面的差异插值来丰富最小的类$ \ mathit {cl} _j $。我们还通过平滑差异的随机流$ f_t：\ mathbb {r}^3 \ to \ mathbb {r}^3 $实现了表面$ s \ s $ s \ in \ mathit {cl} _j $ in \ mathit {cl} _j $ in \ mathit {cl} _j $ in \ mathit {cl} _j $ in \ mathit {cl} _j $ in \ mathit {cl} _j $ in \ in \ mathit {cl} _j $。最后，我们在离散二尖瓣表面的心脏病学数据库上测试自动分类方法。
Let $\mathcal{D}$ be a dataset of smooth 3D-surfaces, partitioned into disjoint classes $\mathit{CL}_j$, $j= 1, \ldots, k$. We show how optimized diffeomorphic registration applied to large numbers of pairs $S,S' \in \mathcal{D}$ can provide descriptive feature vectors to implement automatic classification on $\mathcal{D}$, and generate classifiers invariant by rigid motions in $\mathbb{R}^3$. To enhance accuracy of automatic classification, we enrich the smallest classes $\mathit{CL}_j$ by diffeomorphic interpolation of smooth surfaces between pairs $S,S' \in \mathit{CL}_j$. We also implement small random perturbations of surfaces $S\in \mathit{CL}_j$ by random flows of smooth diffeomorphisms $F_t:\mathbb{R}^3 \to \mathbb{R}^3$. Finally, we test our automatic classification methods on a cardiology data base of discretized mitral valve surfaces.
