Extending procrustes analysis: building multi-view 2-D models from 3-D human shape samples

• Autores: Xavier Pérez Sala
• Directores de la Tesis: Sergio Escalera Guerrero (dir. tes.), Cecilio Angulo Bahón (dir. tes.)
• Lectura: En la Universitat Politècnica de Catalunya (UPC) ( España ) en 2015
• Idioma: inglés
• Tribunal Calificador de la Tesis: Jordi Vitrià Marca (presid.), Juan Aranda López (secret.), Kamal Nasrollahi (voc.)
• Materias:
  • Matemáticas
    • Álgebra
    • Ciencia de los ordenadores
      • Inteligencia artificial
      • Informática
• Enlaces
  • Tesis en acceso abierto en: TDX
• Resumen

  • This dissertation formalizes the construction of multi-view 2D shape models from 3D data. We propose several extensions of the well-known Procrustes Analysis (PA) algorithm that allow modeling rigid and non-rigid transformations in an efficient manner. The proposed strategies are successfully tested on faces and human bodies datasets. In human perception applications one can set physical restrictions, such as defining faces and human skeletons as sets of anatomical landmarks or articulated bodies. However, the high variation of facial expressions and human postures from different viewpoints makes problems like face tracking or human pose estimation extremely challenging. The common approach to handle large viewpoint variations is training the models with several labeled images from different viewpoints. However, this approach has several important drawbacks: (1) it is not clear how much it is necessary to enhance the dataset with images from different viewpoints in order to build unbiased 2D models; (2) extending the training set without this evaluation would unnecessarily increase memory and computation requirements to train the models; and (3) obtaining new labeled images from different viewpoints can be a difficult task because of the expensive labeling cost; finally, (4) a non-uniform coverage of the different viewpoints of a person leads to biased 2D models. In this dissertation we propose successive extensions of PA to address these issues. First of all, we introduce Projected Procrustes Analysis (PPA) as a formalization for building multi-view 2D rigid models from 3D datasets. PPA rotates and projects every 3D training shape and builds a multi-view 2D model from this enhanced training set. We also introduce common parameterizations of rotations, as well as mechanisms to uniformly sample the rotation space. We show that uniformly distributed rotations generate unbiased 2D models, while non-uniform rotations lead to models representing some viewpoints better than others. Although PPA has been successful in building multi-view 2D models, it requires an enhanced dataset that increases the computational requirements in space and time. In order to address these PA and PPA drawbacks, we propose Continuous Procrustes Analysis (CPA). CPA extends PPA within a functional analysis framework and constructs multi-view 2D rigid models in an efficient way through integrating all possible rotations in a given domain. We show that CPA models are inherently unbiased because of their integral formulation. However, CPA is not able to capture non-rigid deformations from the dataset. Next, in order to efficiently compute multi-view 2D deformable models from 3D data, we introduce Subspace Procrustes Analysis (SPA). By adding a subspace in the PA formulation, SPA is able to model non-rigid deformations, as well as rigid 3D transformations of the training set. We developed a discrete (DSPA) and continuous (CSPA) formulation to provide a better understanding of the problem, where DSPA samples and CSPA integrates the 3D rotation space. Finally, we illustrate the benefits of our multi-view 2D deformable models in the task of human pose estimation. We first reformulate the problem as feature selection by subspace matching, and propose an efficient approach for this task. Our method is much more efficient than the state-of-the-art feature selection by subspace matching approaches, and it is able to handle larger number of outliers. Next, we show that our multi-view 2D deformable models, combined with the subspace matching method, outperform state-of-the-art methods of human pose estimation. Our approach is more accurate in the joint positions and limb lengths because we use unbiased 2D models trained on 3D Motion Capture datasets. Our models are not biased to any particular point of view and they can successfully reconstruct different non-rigid deformations and viewpoints. Moreover, they are efficient in both learning and test times.