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Section: Scientific Foundations

The geometry of multiple images

Computer vision requires models that describe the image creation process. An important part (besides e.g. radiometric effects), concerns the geometrical relations between the scene, cameras and the captured images, commonly subsumed under the term “multi-view geometry”. This describes how a scene is projected onto an image, and how different images of the same scene are related to one another. Many concepts are developed and expressed using the tool of projective geometry. As for numerical estimation, e.g. structure and motion calculations, geometric concepts are expressed algebraically. Geometric relations between different views can for example be represented by so-called matching tensors (fundamental matrix, trifocal tensors, ...). These tools and others allow to devise the theory and algorithms for the general task of computing scene structure and camera motion, and especially how to perform this task using various kinds of geometrical information: matches of geometrical primitives in different images, constraints on the structure of the scene or on the intrinsic characteristics or the motion of cameras, etc.


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