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2 PMD CAMERA
We are using Photonic Mixer Device (PMD) camera,
a TOF camera in this work, in figure 1. A time of
flight camera is a system that works with the TOF
principles (Weingarten et al., 2004), and resembles a
LIDAR scanner. In the TOF unit (Lange, 2000), a
modulated light pulse is transmitted by the illumina-
tion source and the target distance is measured from
the time taken by the pulse to reflect from the target
and back to the receiving unit. PMD cameras can gen-
erate the range information, which is almost indepen-
dent of lighting conditions and visual appearance, and
a gray scale intensity image, similar to conventional
cameras. The coordinates of the obstacle with respect
to the PMD camera are obtained as a 200 by 200 ma-
trix, each element corresponding to a pixel. It pro-
vides fast acquisition of high resolution range data.
As the PMD range camera provides sufficient infor-
mation about the obstacles, it is proposed to estimate
the trajectory of the moving obstacles.
These TOF camera provide a 3D point cloud,
which is set of surface points in a three-dimensional
coordinate system (X,Y,Z), for all objects in the field
of view of the camera.
Figure 1: PMD Camera.
3 SCENE FLOW
Optical Flow (Barron et al., 1992)is an approximation
of the local image motion based upon local derivatives
in a given sequence of images. That is, in 2D it speci-
fies how much each image pixel moves between adja-
cent images while in 3D, it specifies how much each
volume voxel moves between adjacent volumes. The
moving patterns cause temporal varieties of the image
brightness. In general, the process of determining op-
tical flow is using a brightness constancy constraint
equation(BCCE). The spatiotemporal derivatives of
image intensity are used in differential techniques to
get the optical flow.
Differential techniques can be classified as local
and global. Local techniques involve the optimiza-
tion of a local energy, as in the Lucas and Kanade
method. The global techniques determine the flow
vector through minimization of a global energy, as in
Horn and Schunck. Local methods offer robustness
to noise, but lack the ability to produce dense optical
flow fields. Global techniques produce 100 percent
dense flow fields, but have a much larger sensitivity
to noise. The paper (Bauer et al., 2006) involves com-
bining local and global methods of Lucas-Kanade and
Horn-Schunck, to obtain a method which generates
dense optical flow under noisy image conditions.
Scene Flow (Vedula et al., 2005) is the three-
dimensional motion fields of points in the world; just
as optical flow is the 2D motion field of points in an
image. Any optical flow is simply the projection of
the scene flow onto the image plane of a camera. If
the world is completely non-rigid, the motions of the
points in the scene may all be independent of each
other. One representation of the scene motion is there-
fore a dense three-dimensional vector field defined for
every point on every surface in the scene.
These 2D images are only the projection of the
actual 3D data on the camera image plane, which
is illustrated in figure 2. Figure 2 shows a point
M=(X,Y,Z) from world coordinates which is pro-
jected and imaged on a point m = x,y in the camera’s
image plane. These coordinates are with respect to a
coordinate system whose origin is at the intersection
of the optical axis and the image plane, and whose x
and y axes are parallel to the X and Y axes (Iwadate,
2010). The three dimensional coordinates are based
on the optical projection centre C. Here, (u,v) are the
C
u
v
X
Y
Z
M = (X,Y,Z)
Object
m = (x,y)
x
y
Camera Coordinates
Image Coordinates
c
Figure 2: Camera Coordinates and Image coordinates.
camera pixel coordinates or image coordinates. The
point M on an object with coordinates (X,Y, Z) will be
imaged at some point m = (x,y) in the image plane.
In order to compute the 3D motion constraint equa-
tion (Barron and Thacker,2005), the derivativesof the
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