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Invariants of six points and projective reconstruction from three uncalibrated images

机译:六个点的不变性和来自三个未校准图像的投影重建

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There are three projective invariants of a set of six points in general position in space. It is well known that these invariants cannot be recovered from one image, however an invariant relationship does exist between space invariants and image invariants. This invariant relationship is first derived for a single image. Then this invariant relationship is used to derive the space invariants, when multiple images are available. This paper establishes that the minimum number of images for computing these invariants is three, and the computation of invariants of six points from three images can have as many as three solutions. Algorithms are presented for computing these invariants in closed form. The accuracy and stability with respect to image noise, selection of the triplets of images and distance between viewing positions are studied both through real and simulated images. Applications of these invariants are also presented. Both the results of Faugeras (1992) and Hartley et al. (1992) for projective reconstruction and Sturm's method (1869) for epipolar geometry determination from two uncalibrated images with at least seven points are extended to the case of three uncalibrated images with only six points.
机译:在空间中通常有六个点的集合,其中三个射影不变量。众所周知,这些不变量不能从一张图像中恢复,但是空间不变量和图像不变量之间确实存在不变量关系。首先为单个图像导出该不变关系。然后,当有多个图像可用时,可以使用此不变关系得出空间不变性。本文确定了用于计算这些不变量的最小图像数为三个,并且从三个图像计算六个点的不变量可以具有多达三个解。提出了用于以封闭形式计算这些不变量的算法。通过真实和模拟图像研究了图像噪声,图像三联体的选择以及观看位置之间的距离的准确性和稳定性。还介绍了这些不变量的应用。 Faugeras(1992)和Hartley等人的结果。 (1992年)进行射影重建,Sturm方法(1869年)从两个至少有七个点的未校准图像中确定对极几何形状,扩展到只有六个点的三个未校准图像的情况。

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