Is Epipolar Geometry Necessary?
نویسندگان
چکیده
We examine and contrast the projective properties of two simple 3D configurations. The first consists of six points, four of which are coplanar. We prove that epipolar geometry and the essential matrix can be recovered uniquely for this structure and give a constructive algorithm for this. The second configuration has four coplanar points and a single non-coplanar line. In this case it is not possible to determine the epipolar geometry. However, both structures have two projective invariants, and these are recoverable from two (uncalibrated) perspective images. We include examples of the invariants for real objects.
منابع مشابه
Cheirality in Epipolar Geometry
The image points in two images satisfy epipolar constraint. However, not all sets of points satisfying epipolar constraint correspond to any real geometry because there can exist no cameras and scene points projecting to given image points such that all image points have positive depth. Using the cheirality theory due to Hartley and previous work on oriented projective geometry, we give necessa...
متن کاملView Interpolation along a Chain of Weakly Calibrated Cameras
This paper presents an algorithm for interpolating intermediate views along a chain of cameras. There is no restriction on the camera placement as long as the distance between successive cameras is not too large. The interpolated views lie on a virtual poly-line defined by the (ordered) set of cameras. Our algorithm requires no strong camera calibration as the necessary epipolar geometry is est...
متن کاملEpipolar geometry in practice: 3D runtime odometry with a web-camera
This paper intends to present and analyze all the necessary steps one needs to take in order to build a simple application for structure from motion in practice using only the epipolar constraint. In other words, toillustratein practice (i.e,, cook-book style) about how the most fundamental of concepts in epipolar geometry can be combined into a complete and disambiguated series of steps for ca...
متن کاملIntegrating multiple levels of zoom to enable activity analysis
In this paper we present a multi-zoom framework for activity analysis in situations requiring combinations of both detailed and coarse views of the scene. The epipolar geometry is employed in several novel ways in the context of activity analysis. Detecting and tracking objects in time and consistently labeling these objects across zoom levels are two necessary tasks for such activity analysis....
متن کاملFringe Code Reduction for 3d Measurement Systems Using Epipolar Geometry
In this work a new approach for code reduction for fringe projection 3D measurement systems is introduced. These devices are used for contactless 3D surface measurement with high accuracy. In order to prevent ambiguities in the point correspondences usually Gray-Code sequences are used leading to long recording times. In our approach we use the restriction of the valid measuring volume and epip...
متن کامل