6.4 Experiments
6.4.3 Detection and labeling
We run detection and labeling (section 6.3) experiments using the models obtained.
Instead of a xed threshold, we represent the detection performance by receiver op-
erating characteristics (ROC) curves. Figure 6.4 shows some ROC curves using the
single-subjectmodelasinFigure6.3(a)-(b). Figure6.4(a)isthe ROC curvesofposi-
tivewalkingsequences(typep1top3)vs. personbikingR-Lsequences(b+),and (b)
isthe ROC curves ofpositivewalkingsequences vs. car movingR-Lsequences (c+).
The positive examples for the solid curves are the positive R-L walking sequences
(type p1 to p3) of subject LG excluding the sequences used for training, and the
positive examples for the dashed curves are the R-L walking sequences (type p1 to
p3) of other subjects not in the training set. From Figure 6.4 (a) and (b), we see
that the single-subject model performs similarly well on the in-training-set subject
and the out-of-training-set subjects. To further test if the single-subject model can
distinguish the in-training-setsubject fromother subjects, we obtainan ROC curve
(Figure 6.4 (c)) by taking the R-L walking sequences of subject LG as positive ex-
amplesand the R-L walkingsequences of other subjects asnegativeexamples. From
Figure6.4, wesee that itishardtodistinguish the in-training-setsubjectfromother
subjectsusingthesingle-subjectmodelasinFigure6.3(a). Inotherwords,the model
is invariantwith respect to the subject being observed.
FromanROCcurve,wecantakethedetectionratewhenP
detection
=1 P
fal seal arm
asanindicatorof detectionperformance. Figure6.5summarizessuchdetection rates
of positive R-L walking sequences vs. dierent types of negative sequences. The
x-axisof Figure6.5displaysthe dierenttypesof negative examples(asdescribed in
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π 1 =0.417
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π 2 =0.26537
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π 3 =0.31763
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π 1 =0.19758
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π 2 =0.58151
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(d)
Figure6.3: Examples of 12-part3-cluster models. (a)-(b)are a single-subject model
(correspondingtothe thickcurveinFigure6.2(a)), and(c)-(d)areamultiple-people
model(correspondingtothethickcurveinFigure6.2(b)). (a)(or(c))givesthemean
positions and mean velocities (shown in arrows) of the parts for each component
model. The number
i
, i = 1;2;3, on top of each plot is the prior probability
for each component model. (b) (or (d)) is the learned decomposable triangulated
probabilistic structure for models in (a) (or (c)). The letter labels show the body
0 0.2 0.4 0.6 0.8 1 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
false alarm rate
detection rate
(a)
0 0.2 0.4 0.6 0.8 1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
false alarm rate
detection rate
(b)
0 0.2 0.4 0.6 0.8 1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
false alarm rate
detection rate
(c)
Figure 6.4: ROC curves using the single-subject model as in Figure 6.3 (a). (a)
positivewalkingsequencesvs. personbikingR-Lsequences(b+);(b)positivewalking
sequences vs. car moving R-L sequences (c+). Solid curves use positive walking
sequences of subject LG as positive examples, and dashed curves use sequences of
other subjects. (c) is obtained by taking the R-L walking sequences of subject LG
as positive examples and the R-L walking sequences of other subjects as negative
a certain type of negative sequences, and the average detection rate is shown either
instar (*) orincircle (o). The error bars showthe maximum orminimum detection
rate. The stars (*) with error bars use the positive walkingsequences of subject LG
aspositiveexamples,and the circles(o)with errorbars use the positive sequences of
other subjects not in the trainingset. Figure 6.5(a)is from the single-subject model
asin Figure6.3(a),and Figure6.5(b) isfromthe multiple-peoplemodelasinFigure
6.3(c).
All the negativesequences endingwith (+) haveR-L motion,and (-)means that
L-Rmotionisthe majormotion. DetectionisalmostperfectwhenimagesfromaL-R
(-) type of sequences are used as negative examples. Among the R-L (+) types of
sequences,thewatermovingR-Lsequence(withalotoffeatures)andthesequencesof
aperson standingstillwithcamerapanningarethe hardest. From Figure6.5,we see
that the two models perform similarly, with overall detection rates (out-of-training-
set subjects) of 97:0% and 96:1% for the single-subject model and multiple-people
model, respectively.
Figure 6.6 shows results on some images using the 12-part 3-cluster multiple-
people model (Figure 6.3 (c)). The text string at the bottom right corner of each
imageindicateswhichtypeofsequencestheimageisfrom. Thesmallblackcirclesare
candidatefeaturesobtained fromthe Lucas-Tomasi-Kanadefeaturedetector/tracker.
The arrows associated with circles indicate the velocities. The horizontal lines at
the bottom left of each image give the log-likelihoods. The top three lines are the
log-likelihoods(P
G
j(X)) of the three component models, respectively. The bottom
line is the overall log-likelihood ( P
C
j=1
j
P
G j(X
)) (section 6.3). The short vertical
bar (at the bottom) indicates the threshold for detection, under which we get equal
missed detection rate and false alarm rate for all the available positive and negative
examples. If a R-L walking motion is detected according to the threshold, then the
best labeling from the component with the highest log-likelihood is drawn in solid
blackdots, andthe letterbeside each dotshows the correspondence withtheparts of
the componentmodel inFigure6.3 (c). The numberatthe upperrightcornershows
b+ b− c+ c− r+ r− w+ cp+ cp− cps+ cps− cpt+ cpt−
0.5 0.6 0.7 0.8 0.9 1
average detection rate: subject L 0.978; out−training−subjects 0.970
types of negative examples
detection rate
(a)
b+ b− c+ c− r+ r− w+ cp+ cp− cps+ cps− cpt+ cpt−
0.5 0.6 0.7 0.8 0.9 1
average detection rate: subject L 0.955; out−training−subjects 0.961
types of negative examples
detection rate
(b)
Figure 6.5: Detection rates vs. types of negative examples. (a) is from the single-
subject model (Figure 6.3 (a)), and (b) is from the multiple-people model (Figure
6.3 (b)). Stars (*) with error bars use R-L walking sequences of subject LG as
positive examples,and circles(o)with error barsuse R-Lwalkingsequences of other
subjects. The stars (or circles)show the average detection rates, and error bars give
the maximum and minimum detection rates. The performance is measured on pairs
in Figure 6.3 (c) from left to right. For the samples in Figure 6.6, all the positive
R-L walking examples are correctly detected, and only one negative example (from
the waterrunningR-Lsequence) is wronglyclaimedasapersonR-L walking(afalse
alarm).