Template Shape Estimation:Correcting an Asymptotic Bias

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 template shape estimation using the stratified geometry of the shape space. We give a Taylor expansion of the bias with respect to a parameter sigma 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, which reveals the parameters that control the bias' magnitude. We illustrate our results on simulated and real shape data.