Tae-Young Heo, Joon Myoung Lee, Myung Hun Woo, Hyeongseok Lee, Min Ho Cho
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引用次数: 0
摘要
形状分析广泛应用于计算机视觉、医学和生物研究等多个领域。分析图像中物体的形状所面临的一个挑战是其对保形变换的不变性。为了测量两个不同形状之间的距离或差异,我们使用了平方根速度函数(SRVF)表示法和弹性度量。由于形状在非线性空间中本身就是高维的,因此我们在平均形状处采用了切线空间,并在线性化空间上采用了几个主成分(PC)。我们提出了基于逻辑回归的分类方法,使用这些 PC 和切向量以及弹性网惩罚。然后,我们将其与其他基于模型的形状分类方法进行了性能比较,并将其应用于流域中藻类的形状以及由 von Mises-Fisher 分布混合生成的模拟数据。
Logistic regression models for elastic shape of curves based on tangent representations
Shape analysis is widely used in many application areas such as computer vision, medical and biological studies. One challenge to analyze the shape of an object in an image is its invariant property to shape-preserving transformations. To measure the distance or dissimilarity between two different shapes, we worked with the square-root velocity function (SRVF) representation and the elastic metric. Since shapes are inherently high-dimensional in a nonlinear space, we adopted a tangent space at the mean shape and a few principal components (PCs) on the linearized space. We proposed classification methods based on logistic regression using these PCs and tangent vectors with the elastic net penalty. We then compared its performance with other model-based methods for shape classification in application to shape of algae in watersheds as well as simulated data generated by the mixture of von Mises-Fisher distributions.