Screened poisson hyperfields for shape coding

We present a novel perspective on shape characterization using the screened Poisson equation. We discuss that the effect of the screening parameter is a change of measure of the underlying metric space. Screening also indicates a conditioned random walker biased by the choice of measure. A continuum of shape fields is created by varying the screening parameter or, equivalently, the bias of the random walker. In addition to creating a regional encoding of the diffusion with a different bias, we further break down the influence of boundary interactions by considering a number of independent random walks, each emanating from a certain boundary point, whose superposition yields the screened Poisson field. Probing the screened Poisson equation from these two complementary perspectives leads to a high-dimensional hyperfield: a rich characterization of the shape that encodes global, local, interior, and boundary interactions. To extract particular shape information as needed in a compact way from the hyperfield, we apply various decompositions either to unveil parts of a shape or parts of a boundary or to create consistent mappings. The latter technique involves lower-dimensional embeddings, which we call screened Poisson encoding maps (SPEM). The expressive power of the SPEM is demonstrated via illustrative experiments as well as a quantitative shape retrieval experiment over a public benchmark database on which the SPEM method shows a high-ranking performance among the existing state-of-the-art shape retrieval methods

Coding shape inside the shape

The shape of an object lies at the interface between vision and cognition, yet the field of statistical shape analysis is far from developing a general mathematical model to represent shapes that would allow computational descriptions to express some simple tasks that are carried out robustly and e↵ortlessly by humans. In this thesis, novel perspectives on shape characterization are presented where the shape information is encoded inside the shape. The representation is free from the dimensions of the shape, hence the model is readily extendable to any shape embedding dimensions (i.e 2D, 3D, 4D). A very desirable property is that the representation possesses the possibility to fuse shape information with other types of information available inside the shape domain, an example would be reflectance information from an optical camera. Three novel fields are proposed within the scope of the thesis, namely ‘Scalable Fluctuating Distance Fields’, ‘Screened Poisson Hyperfields’, ‘Local Convexity Encoding Fields’, which are smooth fields that are obtained by encoding desired shape information. ‘Scalable Fluctuating Distance Fields’, that encode parts explicitly, is presented as an interactive tool for tumor protrusion segmentation and as an underlying representation for tumor follow-up analysis. Secondly, ‘Screened Poisson Hyper-Fields’, provide a rich characterization of the shape that encodes global, local, interior and boundary interactions. Low-dimensional embeddings of the hyper-fields are employed to address problems of shape partitioning, 2D shape classification and 3D non-rigid shape retrieval. Moreover, the embeddings are used to translate the shape matching problem into an image matching problem, utilizing existing arsenal of image matching tools that could not be utilized in shape matching before. Finally, the ‘Local Convexity Encoding Fields’ is formed by encoding information related to local symmetry and local convexity-concavity properties. The representation performance of the shape fields is presented both qualitatively and quantitatively. The descriptors obtained using the regional encoding perspective outperform existing state-of-the-art shape retrieval methods over public benchmark databases, which is highly motivating for further study of regional-volumetric shape representations

From a Modified Ambrosio-Tortorelli to a Randomized Part Hierarchy Tree

We demonstrate the possibility of coding parts, features that are higher level than boundaries, using a modified AT field after augmenting the interaction term of the AT energy with a non-local term and weakening the separation into boundary/not-boundary phases. The iteratively extracted parts using the level curves with double point singularities are organized as a proper binary tree. Inconsistencies due to non-generic configurations for level curves as well as due to visual changes such as occlusion are successfully handled once the tree is endowed with a probabilistic structure. The work is a step in establishing the AT function as a bridge between low and high level visual processing

Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015

This volume contains the full papers accepted for presentation at the ECCOMAS Thematic Conference on Multibody Dynamics 2015 held in the Barcelona School of Industrial Engineering, Universitat Politècnica de Catalunya, on June 29 - July 2, 2015. The ECCOMAS Thematic Conference on Multibody Dynamics is an international meeting held once every two years in a European country. Continuing the very successful series of past conferences that have been organized in Lisbon (2003), Madrid (2005), Milan (2007), Warsaw (2009), Brussels (2011) and Zagreb (2013); this edition will once again serve as a meeting point for the international researchers, scientists and experts from academia, research laboratories and industry working in the area of multibody dynamics. Applications are related to many fields of contemporary engineering, such as vehicle and railway systems, aeronautical and space vehicles, robotic manipulators, mechatronic and autonomous systems, smart structures, biomechanical systems and nanotechnologies. The topics of the conference include, but are not restricted to: ● Formulations and Numerical Methods ● Efficient Methods and Real-Time Applications ● Flexible Multibody Dynamics ● Contact Dynamics and Constraints ● Multiphysics and Coupled Problems ● Control and Optimization ● Software Development and Computer Technology ● Aerospace and Maritime Applications ● Biomechanics ● Railroad Vehicle Dynamics ● Road Vehicle Dynamics ● Robotics ● Benchmark ProblemsPostprint (published version

Multibody dynamics 2015

This volume contains the full papers accepted for presentation at the ECCOMAS Thematic Conference on Multibody Dynamics 2015 held in the Barcelona School of Industrial Engineering, Universitat Politècnica de Catalunya, on June 29 - July 2, 2015. The ECCOMAS Thematic Conference on Multibody Dynamics is an international meeting held once every two years in a European country. Continuing the very successful series of past conferences that have been organized in Lisbon (2003), Madrid (2005), Milan (2007), Warsaw (2009), Brussels (2011) and Zagreb (2013); this edition will once again serve as a meeting point for the international researchers, scientists and experts from academia, research laboratories and industry working in the area of multibody dynamics. Applications are related to many fields of contemporary engineering, such as vehicle and railway systems, aeronautical and space vehicles, robotic manipulators, mechatronic and autonomous systems, smart structures, biomechanical systems and nanotechnologies. The topics of the conference include, but are not restricted to: Formulations and Numerical Methods, Efficient Methods and Real-Time Applications, Flexible Multibody Dynamics, Contact Dynamics and Constraints, Multiphysics and Coupled Problems, Control and Optimization, Software Development and Computer Technology, Aerospace and Maritime Applications, Biomechanics, Railroad Vehicle Dynamics, Road Vehicle Dynamics, Robotics, Benchmark Problems. The conference is organized by the Department of Mechanical Engineering of the Universitat Politècnica de Catalunya (UPC) in Barcelona. The organizers would like to thank the authors for submitting their contributions, the keynote lecturers for accepting the invitation and for the quality of their talks, the awards and scientific committees for their support to the organization of the conference, and finally the topic organizers for reviewing all extended abstracts and selecting the awards nominees.Postprint (published version