The One Triangle Three Parallelograms Sampling Strategy and Its Application in Shape Regression

The purpose of this paper is threefold. Firstly, the paper introduces the One Triangle Three Parallelograms (OTTP) sampling strategy, which can be viewed as a way to index pixels from a given shape and image. Secondly, a framework for cascaded shape regression, including the OTTP sampling, is presented. In short, this framework involves binary pixel tests for appearance features combined with shape features followed by a large linear system for each regression stage in the cascade. The proposed solution is found to produce state-of-the-art results on the task of facial landmark estimation. Thirdly, the dependence of accuracy of the landmark predictions and the placement of the mean shape within the detection box is discussed and a method to visualize it is presented.