## Abstract

We present a novel framework for detection, tracking and recognition of deformable objects undergoing geometric and radiometric transformations. Assuming the geometric deformations an object undergoes, belong to some finite dimensional family, it has been shown that the universal manifold embedding (UME) provides a set of nonlinear operators that universally maps each of the different manifolds, where each manifold is generated by the set all of possible appearances of a single object, into a distinct linear subspace. In this paper we generalize this framework to the case where the observed object undergoes both an affine geometric transformation, and a monotonic radiometric transformation. Applying to each of the observations an operator that makes it invariant to monotonic amplitude transformations, but is geometry-covariant with the affine transformation, the set of all possible observations on that object is mapped by the UME into a distinct linear subspace - invariant with respect to both the geometric and radiometric transformations. This invariant representation of the object is the basis of a matched manifold detection and tracking framework of objects that undergo complex geometric and radiometric deformations: The observed surface is tessellated into a set of tiles such that the deformation of each one is well approximated by an affine geometric transformation and a monotonic transformation of the measured intensities. Since each tile is mapped by the radiometry invariant UME to a distinct linear subspace, the detection and tracking problems are solved by evaluating distances between linear subspaces.

Original language | English |
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Title of host publication | 2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings |

Publisher | Institute of Electrical and Electronics Engineers |

Pages | 3951-3955 |

Number of pages | 5 |

ISBN (Electronic) | 9781479999880 |

DOIs | |

State | Published - 18 May 2016 |

Event | 41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Shanghai, China Duration: 20 Mar 2016 → 25 Mar 2016 |

### Publication series

Name | ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings |
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Volume | 2016-May |

ISSN (Print) | 1520-6149 |

### Conference

Conference | 41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 |
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Country/Territory | China |

City | Shanghai |

Period | 20/03/16 → 25/03/16 |

## Keywords

- Dimensionality Reduction
- Manifold Learning
- Matched manifold detection
- Principal angles

## ASJC Scopus subject areas

- Software
- Signal Processing
- Electrical and Electronic Engineering