Molnár, József and Eichhardt, Iván (2018) A differential geometry approach to cameraindependent image correspondence. COMPUTER VISION AND IMAGE UNDERSTANDING, 169. pp. 90107. ISSN 10773142

Text
MolnarJCompVisionImageUnderstanding2018manu.pdf Download (10MB)  Preview 
Abstract
Projective geometry is a standard mathematical tool for imagebased 3D reconstruction. Most reconstruction methods establish pointwise image correspondences using projective geometry. We present an alternative approach based on differential geometry using oriented patches rather than points. Our approach assumes that the scene to be reconstructed is observed by any camera, existing or potential, that satisfies very general conditions, namely, the differentiability of the surface and the bijective projection functions. We show how the notions of the differential geometry such as diffeomorphism, pushforward and pullback are related to the reconstruction problem. A unified theory applicable to various 3D reconstruction problems is presented. Considering two views of the surface, we derive reconstruction equations for oriented patches and pose equations to determine the relative pose of the two cameras. Then we discuss the generalized epipolar geometry and derive the generalized epipolar constraint (compatibility equation) along the epipolar curves. Applying the proposed theory to the projective camera and assuming that affine mapping between small corresponding regions has been estimated, we obtain the minimal pose equation for the case when a fully calibrated camera is moved with its internal parameters unchanged. Equations for the projective epipolar constraints and the fundamental matrix are also derived. Finally, two important nonlinear camera types, the axial and the spherical, are examined. © 2018 Elsevier Inc.
Item Type:  Article 

Uncontrolled Keywords:  image processing; differential geometry; GEOMETRY; surface reconstruction; image reconstruction; Cameras; Fundamental matrix; UNIFIED THEORY; Epipolar geometry; Generalized epipolar geometry; Epipolar constraints; Cameraindependent approach; 
Subjects:  Q Science / természettudomány > QA Mathematics / matematika > QA72 Algebra / algebra Q Science / természettudomány > QA Mathematics / matematika > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány 
SWORD Depositor:  MTMT SWORD 
Depositing User:  MTMT SWORD 
Date Deposited:  31 Jan 2019 19:15 
Last Modified:  31 Jan 2019 19:15 
URI:  http://real.mtak.hu/id/eprint/90890 
Actions (login required)
Edit Item 