Halcon 3D机器视觉应用指南

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"Halcon 使用说明，这是一份关于MVTec公司Halcon机器视觉软件的详细解决方案指南，涵盖了从版本7.0到10.0的不同更新版次。该指南涉及3D机器视觉在世界坐标系中的应用，是学习和理解Halcon算法的重要参考资料。" Halcon是MVTec公司开发的一款强大的机器视觉软件，广泛应用于工业自动化、质量检测等领域。此使用说明主要包含了以下几个关键知识点： 1. **3D机器视觉**：Halcon提供了全面的3D成像和分析功能，允许用户在三维空间中进行物体检测、测量和定位。通过不同类型的3D传感器（如立体相机、结构光扫描或激光三角测量），Halcon可以获取物体的三维信息，从而实现更复杂、精确的检测任务。 2. **算法描述**：文档详细阐述了Halcon的各种算法，包括形状匹配、模板匹配、特征提取、条码识别、OCR（光学字符识别）等。这些算法是Halcon的核心，帮助用户解决图像处理中的各种问题，例如识别、分类和定位目标对象。 3. **版本历史**：从7.0到10.0的多个版次更新，反映了Halcon的功能不断优化和完善。每个新版本通常会引入新的特性、性能提升和错误修复，比如更高效率的图像处理速度、更多预定义的模型库，以及对新技术的支持。 4. **机器视觉在世界坐标系中的应用**：在实际应用中，Halcon允许用户将图像数据转换到真实世界的坐标系统中，这对于机器人引导、装配验证和精密制造等应用场景尤其重要。用户可以通过Halcon的工具实现从图像坐标到实际世界坐标的转换，进行精确的定位和操作。 5. **专利保护**：MVTec的Halcon软件受到多项专利保护，这表明了其技术的创新性和独特性。这些专利可能涉及到图像处理的特定方法或流程，确保了Halcon在机器视觉领域的领先地位。 6. **兼容性**：Halcon支持多种操作系统和开发环境，如Windows系列和Visual Studio，这使得它能轻松集成到各种工业和研发环境中。通过这份使用说明，用户可以深入理解Halcon的工作原理，学习如何利用其丰富的功能来解决实际的机器视觉问题。无论是新手还是经验丰富的开发者，都能从中受益，提升项目实施的效率和精度。

C-16 Basics

2.1.2 Translation

2.1.2.1 Translation of Points

In ﬁgure 2.2, our example point has been translated along the x-axis of the camera coordinate system.

The coordinates of the resulting point P _2 can be calculated by adding two vectors, the coordinate vector

p_1 of the point and the translation vector t:

p_2 = p_1 + t =





p_1

+ x

p_1

+ y

p_1

+ z





(2.1)

Multiple translations are described by adding the translation vectors. This operation is commutative, i.e.,

the sequence of the translations has no inﬂuence on the result.

2.1.2.2 Translation of Coordinate Systems

Coordinate systems can be translated just like points. In the example in ﬁgure 2.3, the coordinate system

c_1 is translated to form a second coordinate system, c_2. Then, the position of c_2 in c_1, i.e., the

coordinate vector of its origin relative to c_1 (o

c_1

c_2

), is identical to the translation vector:

c_1

= o

c_1

c_2

(2.2)

2.1.2.3 Coordinate Transformations

Let’s turn to the question how to transform point coordinates between (translated) coordinate systems.

In fact, the translation of a point can also be thought of as translating it together with its local coordinate

system. This is depicted in ﬁgure 2.3: The coordinate system c_1, together with the point Q_1, is

3.3

), ,(

p =

), ,(

World coordinate system

p =

Camera coordinate system

Measurement plane

Figure 2.1: Coordinates of a point in two different coordinate systems.

2.1 3D Transformations and Poses C-19

Rotating a point is expressed by multiplying its coordinate vector with a 3 × 3 rotation matrix R. A

rotation around the z-axis looks as follows:

p_3 = R

(γ)·p_1 =





cos γ −sin γ 0

sin γ cos γ 0

0 0 1









p_1









cos γ · x

p_1

− sin γ · y

p_1

sin γ · x

p_1

+ cos γ · y

p_1





(2.5)

Rotations around the x- and y-axis correspond to the following rotation matrices:

(β) =





cos β 0 sin β

0 1 0

−sin β 0 cos β





(α) =





1 0 0

0 cos α −sin α

0 sin α cos α





(2.6)

2.1.3.2 Chain of Rotations

In ﬁgure 2.4b, the rotated point is further rotated around the y-axis. Such a chain of rotations can be

expressed very elegantly by a chain of rotation matrices:

p_4 = R

(β) · p_3 = R

(β) · R

(γ) · p_1 (2.7)

Note that in contrast to a multiplication of scalars, the multiplication of matrices is not commutative, i.e.,

if you change the sequence of the rotation matrices, you get a different result.

2.1.3.3 Rotation of Coordinate Systems

In contrast to points, coordinate systems have an orientation relative to other coordinates systems. This

orientation changes when the coordinate system is rotated. For example, in

ﬁgure 2.5a the coordinate

system c_3 has been rotated around the y-axis of the coordinate system c_1, resulting in a different

orientation of the camera. Note that in order to rotate a coordinate system in your mind’s eye, it may

help to image the points of the axis vectors being rotated.

Just like the position of a coordinate system can be expressed directly by the translation vector (see

equation 2.2 on page 16), the orientation is contained in the rotation matrix: The columns of the rotation

matrix correspond to the axis vectors of the rotated coordinate system in coordinates of the original one:

R =



c_1

c_3

c_1

c_3

c_1

c_3



(2.8)

For example, the axis vectors of the coordinate system c_3 in ﬁgure 2.5a can be determined from the

corresponding rotation matrix R

(90

◦

) as shown in the following equation; you can easily check the

result in the ﬁgure.

(90

◦

) =





cos(90

◦

) 0 sin(90

◦

)

0 1 0

−sin(90

◦

) 0 cos(90

◦

)









0 0 1

0 1 0

−1 0 0





⇒ x

c_1

c_3





−1





c_1

c_3









c_1

c_3









Basics

C-20 Basics

y z

)

Coordinate system 1

, ),(

Coordinate system 3

, ),(

Coordinate system 4

q =

R (90°) R (−90°)

q =

QQ =

a) first rotation b) second rotation

Figure 2.5: Rotate coordinate system with point: (a) ﬁrst around z-axis; (b) then around y-axis.

2.1.3.4 Coordinate Transformations

Like in the case of translation, to transform point coordinates from a rotated coordinate system c_3 into

the original coordinate system c_1, you apply the same transformation to the points that was applied to

the coordinate system c_3, i.e., you multiply the point coordinates with the rotation vector used to rotate

the coordinate system c_1 into c_3:

c_1

_3 =

c_1

c_3

·q

c_3

(2.9)

This is depicted in ﬁgure 2.5 also for a chain of rotations, which corresponds to the following equation:

c_1

_4 =

c_1

c_3

c_4

·q

c_4

_4 = R

(β) · R

(γ) · q

c_4

_4 =

c_1

c_4

·q

c_4

_4 (2.10)

2.1.3.5 In Which Sequence and Around Which Axes are Rotations Performed?

If you compare the chains of rotations in ﬁgure 2.4 and ﬁgure 2.5 and the corresponding equations 2.7

and 2.10, you will note that two different sequences of rotations are described by the same chain of

rotation matrices: In ﬁgure 2.4, the point was rotated ﬁrst around the z-axis and then around the y-axis,

whereas in

ﬁgure 2.5 the coordinate system is rotated ﬁrst around the y-axis and then around the z-axis.

Yet, both are described by the chain R

(β) · R

(γ)!

The solution to this seemingly paradox situation is that in the two examples the chain of rotation matrices

can be “read” in different directions: In ﬁgure 2.4 it is read from the right to left, and in ﬁgure 2.5 from

left to the right.

However, there still must be a difference between the two sequences because, as we already mentioned,

the multiplication of rotation matrices is not commutative. This difference lies in the second question in

the title, i.e., around which axes the rotations are performed.

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