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• W2477461444 abstract "Vision is one of the most powerful sensing modalities. In robotics, machine vision techniques have beenextensively used in applications such as manufacturing, visual servoing [7, 30], navigation [9, 26, 50, 51],and robotic mapping [58]. Here the main problem is how to reconstruct both the pose of the cameraand the three-dimensional (3-D) structure of the scene. This reconstruction inevitably requires a goodunderstanding of the geometry of image formation and 3-D reconstruction. In this chapter, we providea survey of the basic theory and some recent advances in the geometric aspects of the reconstructionproblem. Specifically, we introduce the theory and algorithms for reconstruction from two views (e.g.,see [29, 31, 33, 40, 67]), multiple views (e.g., see [10, 12, 23, 37, 38, 40]), and a single view (e.g., see[1, 3, 19, 25, 28, 70, 73, 74]). Since this chapter can only provide a brief introduction to these topics,the reader is referred to the book [40] for a more comprehensive treatment. Without any knowledge ofthe environment, reconstruction of a scene requires multiple images. This is because a single imageis merely a 2-D projection of the 3-D world, for which the depth information is lost. When multipleimages are available from different known viewpoints, the 3-D location of every point in the scene can bedetermined uniquely by triangulation (or stereopsis). However, in many applications (especially those forrobot vision), the viewpoints are also unknown. Therefore, we need to recover both the scene structureand the camera poses. In computer vision literature, this is referred to as the “structure from motion”(SFM) problem. To solve this problem, the theory of multiple-view geometry has been developed (e.g., see[10, 12, 23, 33, 37, 38, 40, 67]). In this chapter, we introduce the basic theory of multiple-view geometryand show how it can be used to develop algorithms for reconstruction purposes. Specifically, for the twoview case, we introduce in Section 22.2 the epipolar constraint and the eight-point structure from motionalgorithm [29, 33, 40]. For the multiple-view case, we introduce in Section 22.3 the rank conditions onmultiple-view matrix [27, 37, 38, 40] and a multiple-view factorization algorithm [37, 40]." @default.
• W2477461444 created "2016-08-23" @default.
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• W2477461444 date "2018-10-03" @default.
• W2477461444 modified "2023-09-23" @default.
• W2477461444 title "A Survey of Geometric Vision" @default.
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• W2477461444 doi "https://doi.org/10.1201/9781315220352-25" @default.
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