Structure and motion from points, lines and conics with affine cameras

AbstractÐThe minimal data necessary for projective reconstruction from image points is well-known when each object point is visible in all images. In this paper, we formulate and propose solutions to a new family of reconstruction problems for multiple images from minimal data, where there are missing points in some of the images. The ability to handle the minimal cases with missing data is of great theoretical and practical importance. It is unavoidable to use them to bootstrap robust estimation such as RANSAC and LMS algorithms and optimal estimation such as bundle adjustment. First, we develop a framework to parameterize the multiple view geometry needed to handle the missing data cases. Then, we present a solution to the minimal case of eight points in three images, where one different point is missing in each of the three images. We prove that there are, in general, as many as 11 solutions for this minimal case. Furthermore, all minimal cases with missing data for three and four images are catalogued. Finally, we demonstrate the method on both simulated and real images and show that the algorithms presented in this paper can be used for practical problems.

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“…n 4 4, n 3 3, n 2 0. This is the dual of Theorem 1 whose solution is given in Corollary 1 with incidence relation (11).…”

Section: Four Imagesmentioning

confidence: 98%

“…For example, the ªhallucinationº of Tomasi and Kanade [18], the closure constraints in the projective case of Triggs [21], and in the affine case of Kahl and Heyden [11]. The ability to deal with both a minimal case and missing data is, to our knowledge, new to the computer vision community.…”

Section: Introductionmentioning

confidence: 99%

Minimal projective reconstruction including missing data

Kahl

Heyden

Quan

2001

IEEE Trans. Pattern Anal. Machine Intell.

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“…While point features reveal little about surface topology, 3D curves provide such geometrical cues. The inference of 3D shape and scene geometry is perhaps the main application area [10,18,1]; others include object recognition [21], motion estimation [5] and determining whether a given image curve is the projection of a space curve or a surface contour [6,20]. Curves with known correspondences in multiple views have been studied in e.g.…”

Section: Introductionmentioning

confidence: 99%

Multiview reconstruction of space curves

Kahl

August

2003

Proceedings Ninth IEEE International Conference on Computer Vision

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“…The affine camera model, first introduced in [13], is a generalization of the orthographic, the weak perspective and the para-perspective camera models. Several algorithms exist for recovering structure and motion, mostly for points [17,9], but also for other image features [10,11,15].…”

Section: Introductionmentioning

confidence: 99%