基于周期函数相关性的可控空间滤波三维图像重建
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"3D图像重建与基于计算积分成像中多个周期函数相关性的可控空间滤波"
在本文中，作者 Jae-Young Jang、Myungjin Cho 和 Eun-Soo Kim 提出了一种新颖的方法，用于通过计算积分成像进行具有可控空间滤波的3D图像重建。这种方法的核心是利用周期性δ函数阵列（PDFAs）与元素图像的关联。计算积分成像是一个新兴的三维成像技术，它通过捕获多个二维投影来重建三维场景。
传统的计算积分成像方法通常针对单个物体深度进行重建。然而，这个新提议的方法引入了多个PDFAs，它们的空间周期对应于与元素图像阵列（EIA）相关的物体的不同深度。这意味着可以为多个不同深度的物体生成一套经过空间滤波的元素图像，从而增加了重建3D图像时的深度信息处理能力。
PDFAs的作用是通过对元素图像进行空间滤波，实现对3D图像的可控重建。通过调整PDFAs的参数，研究者能够控制滤波效果，进而优化重建图像的质量和深度分辨率。这种可控的空间滤波能够显著改善传统方法在处理复杂深度场景时的局限性。
为了证明所提出方法的可行性，作者进行了分析并可能进行了实验验证。通过这种方法，他们能够展示如何有效地从多个角度获取并处理图像数据，以生成具有高精度和细节的3D图像。这在虚拟现实、医学成像、工业检测和安全监控等领域具有广阔的应用前景。
这篇论文提出了一个创新的3D图像重建技术，利用PDFAs与元素图像的关联进行可控空间滤波。这种方法不仅扩展了计算积分成像的深度处理能力，还为多深度场景的3D重构提供了新的解决方案，有望推动三维成像技术的进步。
3D image reconstruction with controllable spatial
filtering based on correlation of multiple periodic
functions in computational integral imaging
Jae-Young Jang
1
, Myungjin Cho
2,
*, and Eun-Soo Kim
1
1
Department of Optometry, Eulji University, 553, Sanseong-daero, Sujeong-gu, Seongnam-si, Gyonggi-do, South Korea
2
Department of Electrical, Electronic, and Control Engineering, Hankyong National University,
Kyonggi-do 456-749, South Korea
*Corresponding author: mjcho@hknu.ac.kr
Received November 2, 2014; accepted December 22, 2014; posted online March 2, 2015
We propose a novel method of slice image reconstruction with controllable spatial filtering by using the corre-
lation of periodic delta-function arrays (PDFAs) with elemental images in computational integral imaging. The
multiple PDFAs, whose spatial periods correspond to object’ s depths with the elemental image array (EIA), can
generate a set of spatially filtered EIAs for multiple object depths compared with the conventional method
for the depth of a single object. We analyze a controllable spatial filtering effect by the proposed method.
To show the feasibility of the proposed method, we carry out preliminary experiments for multiple objects
and present the results.
OCIS codes: 110.6880, 110.4190.
doi: 10.3788/COL201513.031101.
Computational integral imaging (CII) is capable of
extracting 3D information for occluded 3D objects
[1–15]
.
In general, it is divided into two parts: pickup and com-
putational recon struction. In the pickup part, a set of 2D
images with different perspectives of the 3D objects can be
captured as elemental images through a lens array. From
this captured elemental image array (EIA), the digital
reconstruction part generates a set of slice images using
a computational reconstruction technique based on simu-
lated ray-optics. According to the reconstruction algo-
rithm, the slice images were generated with different
resolutions and viewing angles
[4–7,16–20]
. Among them, one
method is to use the reconstruction of the volume pixels
of the scene by computationally simulating optical
reconstruction in accordance with ray optics
[4]
. Another
method is based on rearrangement of pixels in the elemen-
tal image to reconstruct slice image with improved reso-
lution
[17]
. Recently, a depth extraction method by using
the periodic delta-function array (PDFA) in CII was
proposed
[18–20]
. In this method, this PDFA can also
generate the perspective slice image array with depth-
dependent spatial filtering. This method can be applied
to several applications including depth extraction, parti-
ally occluded 3D object reconstruction, optical refocusing
display, and so on
[19,20]
.
In this Letter, to improve the performance of the con-
ventional PDFA-based CII, we propose a novel method of
slice image reconstruction with controllable spatial filter-
ing by using the correlation of PDFAs with elemental
images in CII. The multiple PDFAs are generated with
spatial periods corresponding to object’s depths in accor-
dance with the EIA. They are used to generate a set of
spatially filtered EIAs for multiple object depths com-
pared with the conventional method for a single object
depth. We analyze a spatial filtering effect by the pro-
posed method and carry out preliminary experiments.
Before we explain the proposed method, we first present
the spatial period in the pickup process. The process of
capturing elemental images by the direct pickup method
in the integral imaging system is based on ray optics. In
the direct pickup method, the location of the pickup device
may be considered for the imaging points of elemental
images on the pickup sensor as shown in Fig.
1.
Let us consid er that the rays emitted from the point ob-
ject pass through the optical center of a pickup device’s
lens. The geometrical relation between a point object,
its corresponding points on the lens array, and location
of pickup device can be given by
x
0
En
¼
x
O
þ
z
O
z
O
þ f
n −
1
2
P − x
O
þ
z
O
f
z
O
f þ dðz
O
þ f Þ
×
x
d
−
x
O
þ
z
O
z
O
þ f
n −
1
2
P − x
O
: (1)
In Fig.
1 and Eq. (1), the origin of the coordinate system
is the edge of the elemental lens located at the bottom of
the lens array. z
O
and x
O
represent the positions of the
point object along the z- and x-axes, respec tively. P
represents the distance between the centers of the
neighboring elemental lenses as well as the diameter of
a single elemental lens. f denotes the focal length of an
elemental lens. In addition, x
0
En
represents a point on
the nth elemental lens, in which the valid x
0
En
is restricted
by ðn − 1ÞP ≤ x
0
En
≤ nP in the direct pickup condition
and n means the natural number. d and x
d
represent
COL 13(3), 031101(2015) CHINESE OPTICS LETTERS March 10, 2015
1671-7694/2015/031101(5) 031101-1 © 2015 Chinese Optics Letters
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