Photogrammetric Theory in Stereo Vision
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摘要: 从引入空间投影变换的概念入手,证明了体积之交比为一般的投影不变量,从而将其作为描述物体的度量。通过对基础矩阵进行合适的分解,导出了确定投影变换模型之齐次坐标和投影坐标的方法。提出了三维直接线性变换用于由物体的投影变换模型进行物体重建。实验分析证实了所述理论和方法的正确性。Abstract: This article addresses the photogrammetric theory in stereo vision, particular with non-metric camera. The discussion is embedded in projective geometry, which can be regarded as an extension to conventional photogrammetry with metric camera in Euclidean geometry. The cross-ratio of volume elements is shown as projective invariant after the spatial projective transformation is properly introduced. The volume cross-ratio is thus defined as projective independent measure for object description. The fundamental matrix in stereo vision is decomposed into a production of two matrices, projective base matrix and projective-rotation matrix, as defined in the article. This concept inherits the one of the essential matrix for metric camera, and leads a concise soultion to projective coordinates and homogeneous corrdinates of the projective model. In order to reconstruct the object from its projective model, a three dimensional direct linear transformation (3-D DLT) is proposed, with which the object reconstruction can be performed linearly with minimum five conjugate known object points. Tests results and analyses verify the theory and methodology.
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