A Unified Framework for Compositional Fitting of Active Appearance Models

TL;DR

This paper presents a comprehensive framework for fitting Active Appearance Models using compositional gradient descent, introducing novel cost functions, composition types, and insights to improve robustness and convergence.

Contribution

It introduces a unified view of CGD algorithms for AAMs, proposes a Bayesian cost function, new composition types, and reinterprets existing algorithms with theoretical insights.

Findings

Proposed a Bayesian cost function for AAM fitting.

Introduced asymmetric and bidirectional composition types.

Reinterpreted existing algorithms using Schur complement and Wiberg methods.

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 novel Bayesian 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 conver- gent 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 implementa- tion of the algorithms studied in this paper publicly available as part of the Menpo Project.