A Unified Framework for Compositional Fitting of Active Appearance Models

Joan Alabort-I-Medina,Stefanos Zafeiriou

doi:10.1007/s11263-016-0916-3

Joan Alabort-I-Medina, Stefanos Zafeiriou

Open Access

https://doi.org/10.1007/s11263-016-0916-3

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Abstract

Active appearance models (AAMs) are one of the most popular and well-established techniques for modeling deformable objects in computer vision. In this paper, we study the problem of fitting AAMs using compositional gradient descent (CGD) algorithms. We present a unified and complete view of these algorithms and classify them with respect to three main characteristics: (i) cost function; (ii) type of composition; and (iii) optimization method. Furthermore, we extend the previous view by: (a) proposing a novelBayesian cost function that can be interpreted as a general probabilistic formulation of the well-known project-out loss; (b) introducing two new types of composition, asymmetric and bidirectional, that combine the gradients of both image and appearance model to derive better convergent and more robust CGD algorithms; and (c) providing new valuable insights into existent CGD algorithms by reinterpreting them as direct applications of the Schur complement and the Wiberg method. Finally, in order to encourage open research and facilitate future comparisons with our work, we make the implementation of the algorithms studied in this paper publicly available as part of the Menpo Project (http://www.menpo.org).

Highlights

Active appearance models (AAMs) (Cootes et al 2001; Matthews and Baker 2004) are one of the most popular and well-established techniques for modeling and segmenting deformable objects in computer vision
We can observe that Inverse, Asymmetric and Bidirectional algorithms obtain a similar performance and significantly outperform Forward algorithms in terms of fitting accuracy, Fig. 5a, e
Gauss-Newton algorithms initialized with 5 % uniform noise. d Mean normalized cost versus number of second scale iterations on the Labelled Faces Parts in-the-Wild (LFPW) test dataset for all Project-Out Gauss-Newton algorithms initialized with 5 % uniform noise. e Table showing the proportion of images fitted with a normalized point-to-point error below 0.02, 0.03 and 0.04 together with the normalized point-to-point error mean, std and median for all Project-Out Gauss-Newton algorithms initialized with 5 % uniform noise

Summary

Introduction

Active appearance models (AAMs) (Cootes et al 2001; Matthews and Baker 2004) are one of the most popular and well-established techniques for modeling and segmenting deformable objects in computer vision. Several approaches (Cootes et al 2001; Hou et al 2001; Matthews and Baker 2004; Batur and Hayes 2005; Gross et al 2005; Donner et al 2006; Papandreou and Maragos 2008; Liu 2009; Saragih and Göcke 2009; Amberg et al 2009; Tresadern et al 2010; Martins et al 2010; Sauer et al 2011; Tzimiropoulos and Pantic 2013; Kossaifi et al 2014; Antonakos et al 2014) have been proposed to define and solve the previous optimization problem. Cootes and Taylor (2001) and Tresadern et al (2010) showed that the use of non-linear gradient-based and Haar-like appearance representations, respectively, lead to better fitting accuracy in regression based AAMs

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