RGB-D相机鲁棒内参与外参精确校准方法

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本文档探讨了"Robust Intrinsic and Extrinsic Calibration of RGB-D Cameras"（RGB-D相机的鲁棒内在和外在校准），发表在2018年国际知名期刊《机器人学交易》(IEEE TRANSACTION ON ROBOTICS, VOL.34, NO.5, OCTOBER 2018)上。随着机器人技术的发展，尤其是服务机器人和工业应用中，低成本的RGB-D相机因其直观性和广泛的应用成为主要传感器。然而，这些相机通常提供的粗略内在（内参）和外在（外参）校准往往无法满足高精度三维环境重建、物体识别和定位等复杂任务的需求。作者Filippo Basso、Emanuele Menegatti和Alberto Pretto提出了一种针对通用RGB-D传感器组合的人性化、可靠且准确的校准框架。他们关注的核心是设计一个新颖的两组件误差模型，该模型将不同技术（如结构光3D相机和时间飞行法相机）的RGB-D对中的错误源统一起来。这使得校准过程更加全面，能够有效地估计和补偿由于硬件差异导致的校准误差。他们的方法提供了几个关键优势： 1. **鲁棒性**：针对各种技术的RGB-D相机，确保在不同条件下的校准稳定性，降低环境变化或设备间差异带来的影响。 2. **易用性**：设计了一个用户友好的流程，使得即使是非专业人员也能轻松地执行高精度的校准。 3. **准确性**：通过精细的误差模型，显著提高校准结果的精度，满足机器人应用对精确度的高要求。文章详细介绍了校准算法的具体步骤，包括数据采集、特征提取、模型构建以及参数优化，可能还包含了一些实验验证和性能对比，以展示其相对于传统方法的优越性。此外，文中可能还会涉及一些实用技巧和注意事项，以帮助读者更好地理解和应用这一改进的校准框架。这篇论文为RGB-D相机的校准提供了一个重要的突破，对于提升机器人系统的性能，特别是对于那些对精度要求较高的应用，具有很高的参考价值。阅读者可以从中学习到如何提升深度相机在机器人领域的准确性和稳定性，这对于提升自动化水平和工作效率具有实际意义。

1318 IEEE TRANSACTIONS ON ROBOTICS, VOL. 34, NO. 5, OCTOBER 2018

Fig. 1. Top and side views of the point clouds generated by some different SL

depth sensors: two Kinects (

KINECT1A, KINECT1B) and an Asus Xtion Pro Live

(

ASUS). The gray lines represent the ground truth measured with the laser dis-

tance meters, points with different y-coordinates are drawn with different colors.

(a)

KINECT1A—top. (b) KINECT1B—top. (c) ASUS—top. (d) KINECT1B—side.

method is inspired by the work in [24] and [30], while our error

model has been designed taking inspiration from both the error

models presented in [14] and [29].

III. D

EPTH ERROR ANALYSIS

In this section, we introduce our depth error correction model,

derived from an experimental analysis performed using two

popular SL-based depth sensors (the Microsoft Kinect and the

Asus Xtion Pro Live RGB-D cameras) and a ToF sensor (the

Microsoft Kinect 2 RGB-D camera).

To analyze the systematic and random errors in the depth

measurements, we positioned each sensor parallel to a ﬂat wall at

increasing distances. For each position, we collected the sensors

readings (i.e., the depth images and the generated point clouds)

while measuring the real distances (i.e., the ground truth) using

two high precision laser distance meters [e.g., Fig. 12(a)]. Some

qualitative results of such analysis are r eported in Figs. 1 and 2.

From our analysis, we noticed the following statements.

1) In the case of the SL sensors, the surfaces deﬁned by

the point clouds are not properly planar as they should

be, and this “local distortion” effect becomes more

accentuated for increasing distances (this is the myopic

property deﬁned in [30]). Moreover, each sensor has

a different “distortion pattern.” The ToF sensor is also

affected by similar local distortion effect, but to a lesser

extent (typically less than 1 cm).

Fig. 2. Top and side views of the point clouds generated by a Kinect 2 ToF

camera (

KINECT2). The gray lines represent the ground truth measured with

the laser distance meters, points with different y-coordinates are drawn with

different colors. Note that the cloud on the right frames a part of the ﬂoor too.

(a)

KINECT2—top. (b) KINECT2—side.

2) The average depth of each point cloud is not generally

correct and, in the case of SL sensors, sometimes even the

average orientation is wrong.

3) The quantization error for the SL sensors becomes not

negligible for increasing distances. ToF sensors are

affected by a negligible quantization error.

The effect of 1) is to produce a local alteration of an object

shape, while 2) is a systematic bias in the measurements.

In this paper, we aim to remove both 1) and 2), while it is

usually not possible to remove the quantization error 3) of SL

sensors.

In the following, we refer to these error components as distor-

tion error and global error, respectively. These errors in the case

of SL sensors arise from a combination of two main sources:

The radial and tangential lens distortion of the camera used

for stereo triangulation [21], and the misalignment between the

pattern projector and the camera. In the case of ToF cameras,

there are different sources of errors that contribute to the distor-

tion error, among others the built-in pixel-related errors and the

amplitude-related errors, while the global error arise from the

so called wiggling error that appears due to irregularities in the

internal modulation process [8]. Our method does not directly

address other ToF related sources of errors, such as multipath

interference and reﬂectivity related deviations.

In order to analyze the distortion error trend, we compared

the measured point clouds with the planes that best ﬁt to them

(some results are reported in Fig. 3(a), where we used three SL

sensors and one ToF sensor). In particular, for each incoming

point cloud, we computed the root-mean-square (RMS) error on

the (signed) distance between the plane and the points. It can be

Continuous-wave-based ToF sensors like the Kinect 2 measure the depth by

means of a phase differences between an emitted sinusoidal light wave signal

and the backscattered signals received. This phase is evaluated in closed-form

using four equally spaced samples [10]: The quantization error, that is mainly

due to the precision used in storing the samples, is usually neglected.

In SL-based depth sensors, the quantization error originates from the discrete

nature of the disparity map used to extract the depth: This error is commonly

mitigated by means of subpixel stereo matching algorithms, unfortunately these

algorithms require to access low-level data that is usually not accessible from

the user side.

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