Learning how to be robust: Deep polynomial regression
This addresses the problem of biased regression in computer vision applications like motion analysis and video stabilization, offering a generic approach without supervised annotation, though it is incremental as it builds on existing deep learning techniques.
The paper tackles robust polynomial regression in the presence of structured outliers by using deep convolutional neural networks with a differentiable hard-wired decoder, achieving results that surpass traditional robust estimation methods in quantitative experiments.
Polynomial regression is a recurrent problem with a large number of applications. In computer vision it often appears in motion analysis. Whatever the application, standard methods for regression of polynomial models tend to deliver biased results when the input data is heavily contaminated by outliers. Moreover, the problem is even harder when outliers have strong structure. Departing from problem-tailored heuristics for robust estimation of parametric models, we explore deep convolutional neural networks. Our work aims to find a generic approach for training deep regression models without the explicit need of supervised annotation. We bypass the need for a tailored loss function on the regression parameters by attaching to our model a differentiable hard-wired decoder corresponding to the polynomial operation at hand. We demonstrate the value of our findings by comparing with standard robust regression methods. Furthermore, we demonstrate how to use such models for a real computer vision problem, i.e., video stabilization. The qualitative and quantitative experiments show that neural networks are able to learn robustness for general polynomial regression, with results that well overpass scores of traditional robust estimation methods.