Ph.D. Thesis, 2008.

abstract bibtex

abstract bibtex

In this thesis, we consider the applicability and the significance of a mathematical discipline integral geometry for geometric computer vision. Especially its significance for dual distributions is considered. Dual distributions are computational tools derived by using the duality principle in projective geometry, and theoretically they are in the core of making geometric computer vision probabilistic in a fundamental way. This means using statistical inversion i.e., presenting the information of geometric entities by probability distributions instead of single estimates in order to avoid ill-conditioning of the problems caused by noise in the measurements.
Integral geometry appears as an ideal tool for this and seems to have a lot to provide for the field. In this thesis we make a journey to the concepts of integral geometry, present its mathematical construction and its fundamental formulas, some of which we find to be already in use in the field. We also consider dual distributions from several points of view to deepen the understanding of them and to strengthen their mathematical foundation.

@phdthesis{ title = {Integral geometry in geometric computer vision.}, type = {phdthesis}, year = {2008}, id = {8f510274-2d9a-3e77-aa2f-ca1085b36786}, created = {2019-11-19T13:01:06.592Z}, file_attached = {false}, profile_id = {bddcf02d-403b-3b06-9def-6d15cc293e20}, group_id = {17585b85-df99-3a34-98c2-c73e593397d7}, last_modified = {2019-11-19T13:47:39.199Z}, read = {false}, starred = {false}, authored = {false}, confirmed = {true}, hidden = {false}, citation_key = {mvg:1255}, source_type = {mastersthesis}, notes = {75 p}, private_publication = {false}, abstract = {In this thesis, we consider the applicability and the significance of a mathematical discipline integral geometry for geometric computer vision. Especially its significance for dual distributions is considered. Dual distributions are computational tools derived by using the duality principle in projective geometry, and theoretically they are in the core of making geometric computer vision probabilistic in a fundamental way. This means using statistical inversion i.e., presenting the information of geometric entities by probability distributions instead of single estimates in order to avoid ill-conditioning of the problems caused by noise in the measurements. Integral geometry appears as an ideal tool for this and seems to have a lot to provide for the field. In this thesis we make a journey to the concepts of integral geometry, present its mathematical construction and its fundamental formulas, some of which we find to be already in use in the field. We also consider dual distributions from several points of view to deepen the understanding of them and to strengthen their mathematical foundation.}, bibtype = {phdthesis}, author = {P, Koskenkorva} }

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