Photogrammetric analysis of image invariance for image transfer and object reconstruction

Hazem Fathi Barakat, Purdue University

Abstract

The original invariance theory for frame photography used in classical photogrammetry has been recently extended by researchers in Image Understanding (IU) and Computer Vision (CV). This thesis explores the potential of image invariance as an alternative or complementary approach to photogrammetric mensuration tasks. Invariance techniques, for planar objects, are linear in the unknowns. An inconsistency problem due to using different point and line sequences in forming the equations was discovered and a solution developed based on a refined least squares approach. For 3D objects, the use of the fundamental matrix in image transfer is shown to produce widely varying results. Introducing the constraint of zero determinant of the fundamental matrix stabilizes the solution. The photogrammetric equivalent technique to image transfer is developed through the introduction of the concept of Extended Relative Orientation (ERO). The trilinearity equations are developed to overcome the problems encountered when working with the fundamental matrix. A new technique is developed to recover the camera parameters from essential and fundamental matrices. The number of recoverable independent camera parameters for various cases of 2 or more cameras is derived and evaluated. Point-based invariance methods for 3D object reconstruction from two overlapping photographs are discussed and compared to the photogrammetric equivalent method which is based on the bundle adjustment technique. A multi-photo invariance technique is developed as an extension to the invariance method of F matrix factorization. Relationships between the imaging parameters and the variables involved in invariance are investigated. A new technique is proposed for invariance-supported photogrammetric triangulation where the invariance techniques are applied to provide initial approximations for the more robust photogrammetric solution. Line-based invariance techniques for 3D objects, both for image transfer and object reconstruction, are investigated. The trilinearity equations for lines are presented for image line transfer. Invariance techniques for 3D object reconstruction are analyzed and compared to recent photogrammetric formulations. A new linear technique is then developed, based on the combined advantages of invariance and photogrammetry, which provides input to the more accurate photogrammetric model.

Degree

Ph.D.

Advisors

Mikhail, Purdue University.

Subject Area

Civil engineering

COinS