利用视觉和距离传感器数据的几何约束的代数框架

K. Deguchi
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引用次数: 3

摘要

提出了一种融合多个几何传感器输出以重建三维目标形状的新框架。提出的框架是吴氏力学定理证明方法在代数几何中的一个应用。首先,作者列出了约束条件下的三组方程。接下来,作者将所有的方程组分为两组,一组假设和一组猜想。然后,作者应用Wu的方法证明假设遵循猜想,得到猜想的伪分割余数,表示三维空间与它们在传感器上的投影数据之间的角度或长度等几何度量的新关系。以图像传感器和距离传感器共同用于三维物体形状的重建和识别为例。通过这种方法,作者得到了7种几何模型的新的几何关系。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An algebraic framework for using geometric constraints of vision and range sensor data
Proposes a new framework for fusing multiple geometric sensor outputs to reconstruct 3-dimensional target shapes. The proposed framework is of an application of Wu's mechanical theorem proving method in algebraic geometry. First the author lists three groups of equations on the constraints. Next, the author classifies all the groups of equations into two sets, a set of hypotheses and a conjecture. Then, the author applies Wu's method to prove that the hypotheses follow the conjecture and obtain pseudo-divided remainders of the conjectures, which represent new relations of geometric measures such as angles or lengths between 3-D space and their projected data on the sensors. As an example, a typical case is considered where an image sensor and a range sensor are used together to reconstruct and recognize 3-D object shapes. By this method the author obtained new geometrical relations for seven cases of geometrical models.<>
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