25行代码实现物体姿态估计：模型与迭代方法

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在本文中，我们将深入探讨一种仅用25行代码实现的基于模型的物体位姿（Model-Based Object Pose）估计方法，由Daniel FDeMenthon和Larry SDAvis在计算机视觉实验室——马里兰大学自动化研究中心开发。该方法的核心目标是通过单一图像确定物体的位置和姿态，即使只检测到四个或更多非共面特征点，并且对这些特征点在物体上的相对几何结构有所了解。首先，文章介绍的"POS (Pose from Orthography and Scaling)"算法是关键步骤。这个算法通过将实际的透视投影近似为缩放的正射投影，解决了旋转矩阵和位移向量的求解问题。这种方法简化了计算过程，通过一个线性系统来估计物体的旋转和位移参数。它假设我们已经成功地检测并匹配了图像中的特征点，并且这些点在三维空间中的位置已知。接着，"POSIT (Position with Iterations)"算法被引入，作为对POS算法的改进。POSIT利用迭代的方式，每次迭代都会利用前一次找到的近似位姿来计算更精确的特征点缩放正射投影。在每次迭代中，POSIT会用这些更新后的投影进行运算，而不是一开始就依赖于初始的近似结果。这种迭代过程有助于提高估计精度，尤其是在处理复杂场景和噪声数据时。整个过程结合了这两种算法的优势，既保持了计算效率，又确保了结果的准确性。通过这25行代码，作者展示了如何巧妙地运用数学建模和优化技术，使得物体位姿估计变得高效且实用。这对于计算机视觉领域，特别是那些需要实时定位和识别的应用来说，是一项重要的贡献。同时，这也为我们提供了一种简洁而有效的编程范例，展示了如何在实际项目中快速实现复杂的计算机视觉任务。

intersection of the line of sightof

with the image plane

. In SOP,we draw a plane

through

parallel to the image plane

. This plane is at a distance

from the center of

pro jection

. The p oint

is pro jected on

by an orthographic pro jection. Then

is pro jected on the image plane

by a perspective pro jection. The vector

parallel to

and is scaled down from

by the scaling factor

equal to

f=Z

. Eq. 1

simply expresses the proportionalitybetween these twovectors.

5 Fundamental Equations for Persp ective

Wenow consider equations that characterize \true" p erspective pro jection and relate the

unknown rowvectors

and

of the rotation matrix and the unknown

coordinate of the

translation vector to the known coordinates of the vectors

in the ob ject coordinate

system, and to the known co ordinates

and

of the image p oints

and

. Solving

these equations for these unknowns would provide all the information required to dene the

ob ject pose, as wehave seen in Section 3. These equations are



(1 +

)

;



(2)



(1 +

)

;

(3)

in which the terms

are dened as



(4)

and

is dened as



Proof

: In Fig. 1, consider points

of the ob ject, and the plane

parallel to the

image plane through

. The line of sight for

intersects plane

,and

pro jects

onto plane

. The vector

is the sum of three vectors

(5)

The vector

and its image

are proportional in the ratio

. The twovectors

and

are also prop ortional in the two similar triangles

and

,ina

ratio equal to the ratio of the

coordinates of the other two corresponding vectors of these

triangles,

and

. This ratio is



. The sum of the three vectors can then

be expressed as



(6)

We take the dot product of this expression with the unit vector

of the camera co ordinate

system. The dot product



is zero the dot pro duct



is the

{coordinate,

;

, of the vector

 the dot pro duct



is the coordinate

. With the

denition



, one obtains Eq. 2. Similarly, one obtains Eq. 3 by taking the

dot product of expression 6 with unit vector

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