Quaternion-type moments combining both color and
depth information for RGB-D object recognition
Beijing Chen
1,2
, Jianhao Yang
2
, Mengru Ding
2
, Tianliang Liu
3
, Xinpeng Zhang
4*
1
Jiangsu Engineering Center of Network Monitoring, Nanjing University of Information Science & Technology, Nanjing, China
2
School of Computer & Software, Nanjing University of Information Science & Technology, Nanjing, China
3
College of Telecommunications & Information Engineering, Nanjing University of Posts & Telecommunications, Nanjing, China
4
School of Communication & Information Engineering, Shanghai University, Shanghai, China
nbutimage@126.com, {651419675, 906287196}@qq.com, liutl@njupt.edu.cn, xzhang@shu.edu.cn
Abstract—The existing quaternion-type moments (QTMs) are
based on the quaternion representation (QR) of color images.
However, this representation creates redundancy when using
four-dimensional quaternions to represent color images with
three components. In this paper, for RGB-D images, the QR is
improved by combining both color and depth information, which
is invariant to lighting and color variations. The improved QR
fully utilizes the four-dimensional quaternion domain. The new
QTMs (NQTMs) are defined using the improved QR. They are
combined with the quaternion back-propagation neural network
(QBPNN) for RGB-D object recognition. The experimental
results demonstrate that the NQTMs outperform our previous
QTMs considering only color information.
Keywords—RGB-D object recognition; quaternion moment;
color image; depth information
I. INTRODUCTION
Quaternion numbers are generalizations of complex
numbers. In the past two decades, they have been successfully
introduced to deal with color images by encoding three
components into the imaginary parts of quaternion numbers [1-
7]. The main advantage of quaternion-based color image
processing is that a color image can be treated holistically as a
vector field [1, 4-7].
However, because most color images have three
components, the extra fourth dimension in quaternions when
representing such images creates redundancy and the
corresponding computational cost involved is high. Aiming to
circumvent these disadvantages, Assefa et al. [8] introduced a
new representation scheme in three space using trinions, each
of which has one real and two imaginary components. After
that, they defined the trinion Fourier transform based on this
new representation. However, there are few color image
processing works using this representation, while more and
more published works still use the quaternion representation
(QR). The main reasons are that: (a) the theory of trinions
remains to be perfected while it is not the case for the theory of
quaternions, which is the theoretical basis of the quaternion-
based color image processing; (b) the QR has been successfully
used in many fields of color image processing [1-7]. So, this
paper also considers the QR. Certainly, the redundancy
problem will also be resolved.
Recently, due to the popularity of Kinect device, it becomes
easy to provide RGB-D images carrying both color and depth
information. It is well-known that the depth information has
many extra advantages: being invariant to lighting and color
variations, allowing better separation from the background and
providing pure geometry and shape cues [9]. So, combining
both color and depth information can dramatically improve the
performance of many vision problems, e.g., object recognition,
detection, tracking, and human activity analysis.
Moments are scalar quantities used to characterize a
function and to capture its significant features [5,6]. They have
been extensively considered for pattern recognition, scene
matching, and image registration, watermarking, and so on,
owing to their image description and invariance properties. Our
previous work [5] proposed the quaternion-type moments
(QTMs) using the QR and achieved good performance.
However, this work also suffers from the redundancy problem.
So, in this paper, we define the new QTMs (NQTMs) for
RGB-D images using an improved QR considering the
important depth information as well as the color information.
II. P
RELIMINARIES
A. Quaternion Number and Quaternion Representation of
Color Images
Quaternions are generalizations of complex numbers. A
quaternion has one real part and three imaginary parts given by
q = a + bi + cj + dk, (1)
where a, b, c, d R, and i, j, k are three imaginary units
obeying the following rules
i
2
= j
2
= k
2
= -1, ij = -ji = k, jk = -kj = i, ki = -ik = j. (2)
If the real part a = 0, q is called a pure quaternion.
The conjugate a quaternion is defined as
*qabcd
ijk
. (3)
This work was supported by the Natural Science Foundation of China unde
Grants 61572258, 61232016, and 61572257, the Natural Science Foundation
of Jiangsu Province of China under Grants BK20151530, and BK20150925,
the PAPD fund, and the CICAEET fund.
2016 23rd International Conference on Pattern Recognition (ICPR)
Cancún Center, Cancún, México, December 4-8, 2016
978-1-5090-4847-2/16/$31.00 ©2016 IEEE 704