Template shape estimation: correcting an asymptotic bias
This work addresses bias correction in shape estimation, which is incremental for researchers in geometric statistics and shape analysis.
The paper tackles the asymptotic bias in template shape estimation across various data types, demonstrating the bias using stratified geometry and proposing two bootstrap procedures to quantify and correct it, with validation on simulated and real data.
We use tools from geometric statistics to analyze the usual estimation procedure of a template shape. This applies to shapes from landmarks, curves, surfaces, images etc. We demonstrate the asymptotic bias of the template shape estimation using the stratified geometry of the shape space. We give a Taylor expansion of the bias with respect to a parameter $σ$ describing the measurement error on the data. We propose two bootstrap procedures that quantify the bias and correct it, if needed. They are applicable for any type of shape data. We give a rule of thumb to provide intuition on whether the bias has to be corrected. This exhibits the parameters that control the bias' magnitude. We illustrate our results on simulated and real shape data.