One of the important problems in the statistical shape analysis context is to predict the shape change. Rather than taking the change in terms of time, we confine ourselves to the deformation of the objects represented by a regression-type model. We properly combine the shape definition in terms of the Kendall and Bookstein shape coordinate systems to break down the problem on the sphere. This is achieved through the triangulation of objects; a very popular technique in geometrical mathematics. A novel idea on tracing the residuals of the spherical regression is then proposed, enabling us to invoke the well-known spherical distributions, including von Mises–Fisher density, to make the statistical inference. New directional residuals not only lie on the sphere but also help to easily simulate the spherical responses. The performance of our proposed method is highlighted via running a simulation study as well as analysing a real data set.

统计形状分析上下文中的重要问题之一是预测形状变化。而不是考虑时间的变化，我们将自己局限于回归型模型表示的对象的变形。我们根据Kendall和Bookstein形状坐标系适当地组合了形状定义，以解决球体上的问题。这是通过对象的三角剖分来实现的。几何数学中非常流行的技术。然后提出了一种关于追踪球面回归残差的新颖思想，使我们能够调用众所周知的球面分布，包括冯·米塞斯-费舍尔密度，以进行统计推断。新的方向性残差不仅位于球体上，而且还有助于轻松模拟球体响应。