PREDICTED POLAR MAPPING FOR MOVING OBSTACLE

DETECTION

Young–Joong Kim

Beom–Soo Kim

Myo–Taeg Lim

School of Electrical Engineering, Korea University

1 Ga Anam-dong, Sungbuk-ku, Seoul, Korea 136-701

Keywords:

Computer vision, obstacle detection, polar mapping, optical ﬂow, vision-based robot

Abstract:

This paper presents the predicted polar mapping that is to improve the efﬁciency of an unexpected moving

obstacle detecting system in a single vision-based robot. The polar mapping is used to simplify the segmenta-

tion of moving objects from the background and is performed with the focus of expansion (FOE) as the center.

When the movement of the robot per a step becomes a bit large, then static objects or background are detected

as moving objects. Thus, the velocity of the robot becomes so slow. Therefore, to enlarge the movement of

the robot and to improve this system, we propose the predicted polar mapping that predicts the polar mapped

image after robot moves to be admissible. In order to verify experimentally our proposed procedure, we make

several comparative tests in the corridor.

1 INTRODUCTION

Vision systems are used more and more for the nav-

igation of mobile robot because visual sensing can

provide the robot with an incredible amount of in-

formation about its environment. One of the central

problems of vision-based navigation is moving ob-

stacle avoidance. Many approaches have been taken

to solve the problems of moving obstacle avoidance

and a wide variety of approaches and algorithms were

researched in this ﬁeld (Bhaunu, 1988), (Thompson,

1988). One of the key issues is differentiating non-

stationary objects from the stationary background in

a moving platform, since both the background and

the object appear to be moving (Frazier, 1992), (Nair,

1994), (Nair, 1998).

The algorithms for detecting moving objects from

a moving platform compute the global optical ﬂow

(Enkelmann, 1996). Other algorithms use image

transformations and qualitative analysis of the motion

of points to detect and segment the moving objects

(Bhaunu, 1988), (Nair, 1994), (Nair, 1998). These

methods are typically more effective in the purpose to

get information about the detected motion of a robot.

In these methods, the camera provides the global in-

formation on the working environment, so that it can

separate the moving and static objects without chang-

ing its pose by ﬁnding the difference of two consec-

utive images. A more sophisticated method is to ﬁnd

the optical ﬂow using two consecutive polar map-

ping images (Nair, 1994), (Nair, 1998), (Enkelmann,

1996).

In this paper, we present a procedure using the pre-

dicted polar mapping and the segmentation to detect

unexpected moving objects that appear in the path of

a navigating robot and to estimate the relative motion

of the object with respect to the robot. After qualita-

tive detection of the moving obstacles, relative mo-

tion information of the object is obtained by com-

puting the time-to-impact between the robot and the

obstacles (Tistarelli, 1991), (Tistarelli, 1993). Since

this method requires the determination of correspon-

dences between all pixels in the image, the computa-

tional cost and error rate are very high. Therefore, by

the help of the method in (Nair, 1994), (Nair, 1998),

moving objects are segmented from image for effec-

tive use of this method or less computation. But, it has

the terrible limitation as follows. If the movement of

robot increase, then the static objects or background

is detected as moving objects. Thus, we use the im-

age that is acquired after very small movement. As

a consequence, the velocity of robot becomes slow.

Therefore, to improve the efﬁciency of this method,

we proposed the predicted polar mapping that pre-

dicts the polar mapped image after robot moves to be

admissible.

421

Kim Y., Kim B. and Lim M. (2004).

PREDICTED POLAR MAPPING FOR MOVING OBSTACLE DETECTION.

In Proceedings of the First International Conference on Informatics in Control, Automation and Robotics, pages 421-424

DOI: 10.5220/0001127904210424

 SciTePress

2 PREDICTED POLAR MAPPING

To segment moving object from the background, each

image acquired by the robot is transformed from

Cartesian coordinates to polar coordinates, using a

polar mapping that transforms the image to a polar

coordinate system with the focus of expansion (FOE)

as the center. The image is transformed to polar coor-

dinates using the following equations.

ρ =

(x − x

F OE

)

+ (y − y

F OE

)

(1)

η = tan

−1

(x − x

F OE

)

(y − y

F OE

)

(2)

In the above equations, ρ is the radial distance from

the FOE to the Cartesian image coordinate (x, y),

and η represents the angle 0 ∼ π subtended by the

Cartesian image coordinates (x, y), the FOE, and the

Cartesian image coordinates (1, 0). The advantages

of using the polar and the log-polar or complex loga-

rithmic mapping (CLM) have been shown in (Bishay,

1994), (Tistarelli, 1993). Two successive images

(a) (b)

Figure 1: (a) The ﬁrst image with moving forward of a robot

= 0. (b) The second image with moving forward of a robot

= 3cm.

from a typical sequence in a corridor are shown in

Fig.1. When this transformed image is represented

with radial, ρ, and angular, η, axis as the Cartesian

coordinates, the motion of the stationary objects

will be in the horizontal direction. Objects that are

moving with respect to the observer will have motion

in an angular direction in this transformed space. To

perform the polar mapping, the FOE must be located

accurately. For the experiments presented in this

paper the FOE is determined using the vision-based

algorithm described in (Frazier, 1992).

For the system that detects unexpected moving

objects that appear in the path of a navigating robot,

the difference image between the ﬁrst image and

the second image after robot moves is used. In this

detecting system, if the movement of robot per step

become a bit large, then the static objects or back-

ground is detected as moving object. Thus, we use

the difference image after robot moves very small.

As a consequence, the velocity of robot becomes

so slow. Therefore, for more large movement of

robot, we predict the polar mapping image after

robot moves to be admissible. The followings are the

procedure of the predicted polar mapping.

Procedure 1: The predicted polar mapping

A. Acquire an image from camera.

B. Execute polar mapping of the image.

C. Compute the optical ﬂow with respect to movement

of robot.

D. Compute the zooming rate.

E. Enlarge the polar mapping image with zooming

rate horizontally. (i.e., Enlarge the radial axis of the

polar mapping image with zooming rate.)

F. Cut off the end part of radial axis of the polar

mapping image with zooming rate. (i.e., Cut off the

right end part of the polar mapping image.)

The zooming rate used in procedure 1 is deﬁned as

follows:

α =

(3)

where α is a zooming rate, W

is a radial component

of the optical ﬂow, which is described in (Tistarelli,

1991), (Tistarelli, 1993) and H is the size of horizon-

tal axis (i.e., radial, ρ, axis). The (a) in Fig.2 is the

resultant image from procedure 1 that is the predicted

polar mapping of the ﬁrst image, and the (b) in Fig.2

is general polar mapping of the second image that is

acquired after robot moves forward at 3cm.

(a) (b)

Figure 2: (a) The predicted polar mapping of (a) in Fig.1.

(b) The polar mapping of (b) in Fig.1.

3 DETECTING VERTICAL

MOTION

After transforming the image into the predicted polar

mapping, the problem of detecting a moving obsta-

cle is to ﬁnd vertical motion along an angular axis

in sequence of transformed images. If a horizontal

edge in an image moves horizontally, then the over-

lap between the edge from one image to the next im-

age is very large. On the other hand, if a horizontal

ICINCO 2004 - ROBOTICS AND AUTOMATION

422

edge moves vertically, then there is very little over-

lap. Hence, the qualitative measure of the motion

is obtained by detecting the vertical motion of edges

present in the transformed image. In this paper, we

use the Sobel operator presented in (Gonzalez, 1992),

(Forsyth, 2003) to detect edges from each image. The

(a) in Fig.3 shows the edge detected images of the pre-

dicted polar mapping (i.e., (a) in Fig.2), and the (b) in

Fig.3 shows the edge detected images of the general

polar mapping (i.e., (b) in Fig.2). A qualitative es-

(a) (b)

Figure 3: (a) The edges detected image of (a) in Fig.2. (b)

The edges detected image of (b) in Fig.2.

timate (reported in (Nair, 1994), (Nair, 1998)) of the

motion of the object in these images is obtained as fol-

lows. First, horizontal and angular edges in the trans-

formed images are enhanced. Let I

(p)

sobel

and I

(n)

sobel

represent the edge images of predicted polar mapping

and second polar mapping obtained by Sobel opera-

tor, respectively. Then, the resultant image I

det

that

detects moving objects is obtained as following equa-

tion.

det

= I

(p)

sobel

· I

(p)

sobel

− I

(p)

sobel

· I

(n)

sobel

(4)

In above equation, we can enlarge the positive val-

ues along horizontal edge components of each image

using multiplication. Edges that move vertically pro-

duce little overlap, so they are eliminated. Hence, (4)

is a map of all horizontal and angular edges that have

moved vertically. Some edges that have moved hor-

izontally may be present in this resultant image, but

they are usually small pieces. Actually, this map con-

tains small pieces of horizontally moving edges that

did not completely cancel out. In practice, however,

these small pieces are very weak, and are ﬁltered out

by a thresholding process (Gonzalez, 1992), (Forsyth,

2003). As a consequence, this map, I

det

, contains the

detected motion. Next, this map is transformed back

into the rectangular frame. In order to compute the

optical ﬂow, rather than use the qualitative motion de-

tected entire image, the segmentation can be used to

ﬁnd the region where the moving object may be lo-

cated (i.e., the region of interest) in consecutive im-

ages.

In this paper, we use a region using a rectangular area

as the base template. A rectangular was chosen as the

shape that best represents the area occupied by the

moving object because in most cases, the moving ob-

jects in a man-made environment are in the forms of

people or opening doors (Nair, 1994), (Nair, 1998).

To obtain the regions that enclose the detected motion

pixels, general rectangular clustering method (Gon-

zalez, 1992), (Forsyth, 2003) is used. In using this

method, to reduce errors or disturbance, we discard

the detected pixels that are the most outer of each side

as Fig.5. The (a) in Fig.4 shows the resultant image

that is transformation of the motion detected image

using the predicted polar mapping back into rectan-

gular coordinates, and the (b) in Fig.4 is the restored

motion detected image using the general polar map-

ping. Fig.5 is segmentation of Fig.4, respectively.

(a) (b)

Figure 4: (a) The restored motion detected image of the

predicted polar mapping. (b) The restored motion detected

image of the general polar mapping.

(a) (b)

Figure 5: (a) The segmented image of (a) in Fig.4. (b) The

segmented image of (b) in Fig.4.

To verify our proposed method that is predicted po-

lar mapping, we make the simple comparative test. In

this test, we make a robot move at 9cm for compar-

ison of the predicted polar mapping with the general

polar mapping. The results of this test are shown in

Fig.6, and we see that the result of the polar mapping

has great noise as compared with the predicted polar

mapping. It is obvious that the general polar mapping

is not suitable to the system that needs a little more

movement of robot. As a consequence, our proposed

method can be of help to detect a moving object. In

addition, The optical ﬂow can be obtained by the help

of (Tistarelli, 1991), (Tistarelli, 1993).

PREDICTED POLAR MAPPING FOR MOVING OBSTACLE DETECTION

423

(a) (b)

Figure 6: (a) The segmented image using the predicted po-

lar mapping with moving forward of a robot = 9cm. (b) The

the segmented image using the polar mapping with moving

forward of a robot = 9cm.

4 EXPERIMENTAL RESULTS

The moving object detecting system using the pro-

posed method was implemented on the Pioneer 2–

AT mobile robot of ActivMedia. The main control

processor of this robot is a Simens 88C166(20MHz)

microprocessor. For image processing and control of

the robot, a industrial computer with Intel Pentium

III(850MHz) and Windows 98, a Panasonic CCD

camera, and frame grabber (DataTranslation DT3132)

are mounted on the robot. The images have been ac-

quired at a resolution of 480×360 pixels. The optical

axis of the camera is almost parallel to the ground. In

order to verify experimentally the proposed method

outlined in procedures 1, we make several compara-

tive tests in the corridor. We make a robot move at

3cm to 15cm for comparison of the predicted polar

mapping with the general polar mapping. The results

are shown in Fig.7, and we see that the polar map-

ping has great noise as compared with the predicted

polar mapping. Hence, the predicted polar mapping

is robustly admissible to the system that needs a little

more movement of robot.

Figure 7: Errors of the optical ﬂow in comparative test

5 CONCLUSION

In this paper, the procedure using the predicted polar

mapping and the segmentation to detect unexpected

moving objects has been presented, and has been im-

plemented with a Pioneer 2–AT mobile robot. In or-

der to enlarge movement of robot per a step and im-

prove the effective use of polar mapping, we have pro-

posed the procedure that predicts the polar mapping

image after robot moves to be admissible. To ver-

ify experimentally our proposed procedure, we make

several comparative tests in the corridor. It is obvi-

ous the predicted polar mapping has a little noise as

compared with the polar mapping.

REFERENCES

Bhaunu, B. (1988). Qualitative motion detection and track-

ing of targets from a mobile platform. In DARPA Im-

age Understanding Workshop, Cambridge, MA. pp.

289–313.

Bishay, M. (1994). Object detection in indoor scenes using

log-polar mapping. In IEEE International Conference

on Robotics and Automation. 1, pp. 775–780.

Enkelmann, R. (1996). An experimental inverstigation of

estimation approaches for optical ﬂow ﬁeld. In Motion

Understanding: Robot and Human Vision. 6, pp 189–

226.

Forsyth, A. (2003). Digital Image Processing. Prince Hall,

Pearson Education.

Frazier, J. (1992). Detecting moving objects from a mov-

ing platform. In Proceedings of IEEE International

Conference on Robotics and Automation. 2, pp. 1627–

1633.

Gonzalez, C. (1992). Digital Image Processing. Addiison–

Wesley.

Nair, D. (1994). Detecting unexpected moving obstacles

that appear in the path of a navigating robot. In IEEE

International Conference on Image Processing. 2, pp.

311–315.

Nair, D. (1998). Moving obstacle detection from a navi-

gating robot. In IEEE Transactions on Robotics and

Automation. 8, pp. 39–57.

Thompson, W. (1988). Detecting moving objects. In Int. J.

Computer Vision. 8, pp. 39–57.

Tistarelli, M. (1991). Direct estimation of time-to-impact

from optical ﬂow. In IEEE Workshop on Visual Mo-

tion. Princeton, NJ, Oct. 7–9, pp. 226–233.

Tistarelli, M. (1993). On the advantages of polar and log-

polar mapping for direct estimation of time-to-impact

from optical ﬂow. In IEEE Transactions on Pattern

Analysis and Machine Intelligence. 15, pp. 401–410.

ICINCO 2004 - ROBOTICS AND AUTOMATION

424