We describe a hierarchical structure-from-motion pipeline.No information is needed beside images themselves.The pipeline proved successful in real-world tasks. This paper addresses the structure-and-motion problem, that requires to find camera motion and 3D structure from point matches. A new pipeline, dubbed Samantha, is presented, that departs from the prevailing sequential paradigm and embraces instead a hierarchical approach. This method has several advantages, like a provably lower computational complexity, which is necessary to achieve true scalability, and better error containment, leading to more stability and less drift. Moreover, a practical autocalibration procedure allows to process images without ancillary information. Experiments with real data assess the accuracy and the computational efficiency of the method.
Autocalibration (a.k.a. self-calibration) has generated a lot of theoretical interest since its introduction in the seminal paper by Maybank and Faugeras @cite_75 . The attention created by the problem however is inherently practical, since it eliminates the need for off-line calibration and enables the use of content acquired in an uncontrolled setting. Modern computer vision has partly sidestepped the issue by using ancillary information, such as EXIF tags embedded in some image formats. Unfortunately it is not always guaranteed that such data will be present or consistent with its medium, and do not eliminate the need for reliable autocalibration procedures.
@cite_75
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There is a close connection between the calibration of a single camera and the epipolar transformation obtained when the camera undergoes a displacement. The epipolar transformation imposes two algebraic constraints on the camera calibration. If two epipolar transformations, arising from different camera displacements, are available then the compatible camera calibrations are parameterized by an algebraic curve of genus four. The curve can be represented either by a space curve of degree seven contained in the intersection of two cubic surfaces, or by a curve of degree six in the dual of the image plane. The curve in the dual plane has one singular point of order three and three singular points of order two.