Application of linear scan camera sytem to motion analysis
Naoki Yokoyama*
Research Institute of Science and Technology, Tokai University
1117 Kitakaname, Hiratsuka, Kanagawa, 259-1292 JAPANABSTRACT
With limited spatial and temporal resolution of video recording camera, it is very difficult task to analyze object
motion with higher accuracy. In addition, target object or target points of object in one-frame can be hardly
recognized automatically in ordinary two-dimensional video recordings. If correlation or template matching
methods is used to detect object position, initial object area or template should be decided manually. So fully
automatic detection process is difficult.
But with linear scan camera (LSC) utilizing line-image sensor, object position detection can be done
easily with much higher accuracy. This article describes this feature of LSC in motion analysis. First d-value isintroduced to evaluate correlation of two line images. This d-value is calculated in quarter pixel width for higheraccuracy. Object displacement between given two-line image can be decided by monitoring this d-value. Steep
drop of d-value means match of lines and higher correlation. Because d-value increases as line separation
becomes bigger, this variation should be checked simultaneously for consistency. Typically over about 100-line
separation this value increases, so pivoting line (template line) should be changed.
Selecting suitable combination of two lines based on d-value will be important for overall accuracy oftime-displacement analysis Two lines should be selected to decide pixel shift where spatial quantum error isminimum. Suitable two line images can be selected by searching less d-value. Prior to that, two-dimensional dvalue table should be made. Then one-pass trace of suitable two-line selection is carried out for time-velocity
analysis.
Fully automatic analysis method of position detection with LSC was proposed. To estimate object
displacement, d-value was introduced and its validity was proved experimentally. In addition, by selecting
suitably separated two points, resultant velocity at middle point can be much accurate than direct differentiation oftime-displacement data.
Keywords: Linear image sensor, Template Matching, Network distribution
1. INTRODUCTION
With limited spatial and temporal resolution of video recording camera, it is very difficult task to analyze object
motion with higher accuracy. In addition, in ordinary two dimensional video recordings, target object or target
points of object in one-frame can be hardly recognized automatically. If some type of correlation or templatematching method is used to detect object position, initial object area or template should be decided manually. So
fully automatic detection process is difficult.
But with linear scan camera (LSC) utilizing line-image sensor, object position detection can be done
easily with much higher accuracy. This article describes this feature of LSC in motion analysis. Whole line image
data is used as template for correlation to another whole line image data. d-value was introduced for evaluation ofcorrelation. Suitable two line images can be selected by searching less d-value. Prior to that, two-dimensional d*E-mail: nao@rist.u-tokai.ac.jp

value table should be made. Then one-pass trace of suitable two-line selection is carried out for time-velocityanalysis.
2. BASIC CONCEPT OF LINEAR SCAN CAMERA
Fig. 1 shows basic concept of this proposed linear scan camera. This camera compiles line-images sampled atgiven time interval into two-dimensional image. Thus resultant image or trajectory of object in motion can beobserved and analyzed. So this image is much similar to those obtained by traditional streak cameras. Typicalsample image is shown in Fig. 2. The horizontal axis is space and the vertical axis is time. Because object steelball (diameter: 25.5mm) drops freely, resultant trajectory displayed in Fig. 2 is parabolic curve. Spatial resolutionof one line image is 4096, which is decided by linear image sensor in camera head. Maximum read-out clock ofthis sensor is 60 MHz. Minimum time interval between lines is 210 µsec.

sensorResultant image
Displacement

Free FallTimeFigure 1. Basic concept of linear scan camera

Figure 2. Typical resultant image by LSC

3. POSITION DETECTION BY CROSS-CORRELATION
Resultant image can be analyzed line by line basis. To make this process fully automatic, the following evaluation
d-value is calculated in given shift value. Here pixel shift varies in quarter pixel width. Linear interpolation
method is used to decide between-the-pixel intensity. Estimated shift value of line image is evaluated by R.M.S.
of two line image intensity arrays. Intensity will be used by cyclic, so positive and negative shift value can bedetected. And whole line data is used, i.e. 4096 data points.

4095

D (n, m , s ) =∑ (i n , p − i m , p + s )2p =0(1)4096 × 4 . 0

where i n , p denotes image intensity at p-th position of n-th line data. Here pixel pitch is shifted by quarter-pixel
width, so p varies from 0 to 4095*4.0 actually.
Fig. 3 shows variation of this d-value in typical situation. In this case, 50th line data is compare to 100thline data. The steep drop of d-value can be recognized in around 400-pixel position. This drop gives shift value inquarter pixel width. And this value also gives object displacement between 50th line and 100th line, where time ofsampling of these lines can be decided separately. So highly accurate time-position data of moving object can beanalyzed using relatively simple method. This is simple but time-consuming one, because whole line must becompared with another whole line data with quarter pixel width shift value. But typical calculation time of this dvalue is 1.0 second for one-line pair comparison. This is done by Intel Pentium II (400MHz) machine.
Fig. 4 shows analyzed displacement variation from Fig. 2, pivoting 50th line data with respect to from50th to 300th line data. So displacement variation from 50th line to 300th line is acquired. Because d-value
increases as line separation becomes bigger, this d-value variation should be checked simultaneously forconsistency.
Fig. 5 shows this d-value variation with respect to line separation 0 to 250 lines. Over about 100-line
separation this value increases, so pivoting line (template line) should be changed. Selecting suitable combinationof two lines based upon d-value will be important for accuracy. Two lines should be selected to decide pixel shift
where spatial quantum error is minimum.

D-value201612801000

2000

3000

Pixel position

Figure 3. d-value variation with shift

4000Dispacement [pixel]

4003002001000050100150200250

Time [line]

Figure 4. Analyzed displacement with time

D-value

6420050100150200250

Line separation

Figure 5. d-value variation with line separation

Selecting suitable combination of two lines based upon d-value is required for quantum error reduction.
First all combination of d-value table as to two line selection should be made. Then successive suitable two-lineselection should be done for velocity calculation. Table 1 shows this two-dimensional d-value table.
Table 1. Two dimensional table of d-values

0012

1
D0-1

2D0-2
D1-2

D1-0 =
D0-1
D2-0 =
D0-2

D2-1 =
D1-2

D1023-0= D0-D1023-1= D1-D1023-2= D2-1023

1023

1023

1023
D0-1023
D1-1023
D2-1023.
1023.

And Fig. 6 shows flow chart of successive two-line selection suitable for velocity calculation. Typicalstart position is the first line. Average velocity, which equals instant velocity at the middle point of two sampled
data points can be calculated by suitably separated two measurement points. Fig. 7 shows this principle. Object
motion in this case is free fall of steel ball, so average velocity of spatially separated two points equals instantvelocity at the middle point. Then picking up points separated in rather big span and calculating velocity based onthese points, quantum error reduction can be done. Fig. 8 shows velocity variation as to time that is calculated
from direct differentiation from displacement vs. time data. Due to large fluctuation of velocity, acceleration cannot be acquired from this results. Contrary to that, Fig. 9 shows velocity variation as to time, which is calculated
by suitably separated two-point method. In this case fluctuation of velocity is much smaller.

Starti = startscan for d-value table
for minimum value Di,jIgnore
Di,jIf Di,j isregistered?
Yes

i=jNo
register i,j combinationNo
finished?
Yes
end

Figure 6. Flow of suitable two-line selection

D2
parabolic curve
average velocity

D1
instant velocity
span/2
spanFigure 7. Average velocity gives instant velocity at the middle point

Velocity [pixel/line]

864200200400600800Time [line]

Figure 8. Variation of velocity as time

Velocity [pixel/line]

65432100200400600800

Time [line]

Figure 9. Variation of velocity calculated from suitable two-line selection

But making d-value table is very time consuming task, any kind of parallel processing or distributed processing
should help system’s performances. In this paper network distributed system is proposed. Basic concept or scheme is showedin Fig. 10. This system consists of various performance computers and one supervising host. Systems can talk each other by
RPC through Ethernet (TCP/IP). So various ranges of OS can attend this system. Rough flow of processing procedure is on
the figure.

Broad band network (ex. 100Base‑TX)

Supervisor System

1. Boardcasting and collecting
engines information withperformance factor.
2. Weighted distribution of d‑value calculation task.
3. Synchoronization and image
service if needed.
4. Making final d‑value table.
Various perfomance hosts

Figure 11. Rough schematic of networked distributed d-value processing system

4. CONCLUSION

Fully automatic analysis method of position detection with LSC was proposed. To estimate object displacement,
d-value was introduced and its validity was proved experimentally. In addition, by selecting suitably separated
two points, resultant velocity at middle point can be much accurate than direct differentiation of timedisplacement data. Thus time-velocity analysis based on minimum d-value searching method is proved to beeffective by experiment this time. But prior to that, complete d-value table should be calculated. And it is very
time-consuming task. So a network distributed d-value calculation system was proposed.

REFERENCE
1. 1. N. Yokoyama: Position detection by cross-correlation with linear scan camera (one-dimensional high-speed videocamera), Int. J. Japan Soc. Prec. Eng., Vol. 33, No.1 (Mar. 1999) 57-58