Expanding gait identification methods from straight to curved trajectories
Yumi Iwashita, Ryo Kurazume
Kyushu University
744 Motooka Nishi-ku Fukuoka, Japan

Koichi Ogawara
Wakayama University
930 Sakaedani Wakayama, Japanyumi@ieee.org

Abstract

ing direction in respect to the camera is different from thatin the database (e.g. in Fig. 1(a) walking direction (1) of thesubject is different from the direction (2) in the database).
To deal with this problem, several methods have been
proposed so far. Makihara et al. introduced a view transformation model to synthesize virtual viewpoint images from
captured images [14]. In this method, the view transformation model is obtained from training datasets of multiple people which were taken from multiple view points.
Iwashita et al. introduced a 4D gait database consistingof multiple 3D shape models of walking subjects and amethod which identified a subject and estimated his walking
direction with synthesized virtual viewpoint images from
3D models in the database [7]. Kusakunniran proposeda method to create a View Transformation Model (VTM)from the different point of view using Support Vector Regression (SVR) [10]. These methods have an implicit assumption that people walk straight and their walking direction does not change during one gait cycle (i.e. he does notwalk on curved trajectory). However, in reality people walkon curved trajectories for turning a corner or avoiding an
obstacle as shown in Fig. 1 (b).
The large diversity of curved trajectories makes the collection of complete real world data in a database infeasible.
This change of the direction of the velocity vector of walking people causes a decrease in performance for conventional methods, which assume the walk direction is straight.
In this paper we propose a method to identify people walking on curved trajectories. To the best of our knowledge,
this is the first time such a method is introduced to deal
with the problem of the decrease of the identification performance due to walking on curved trajectories.
The cause of the performance decrease is that, when asubject walks on a curved trajectory, the observation angle
φ between the walking direction of the subject and direction of the camera to the subject is gradually changed at allframes in one gait cycle as shown in Fig. 1 (b) (hereafter
we call this as ”local angle change”). This problem occurs
in fact even on a straight walk [3] as shown in Fig. 1 (c).
Akae et al. showed that the local angle changes in one gait
cycle affects the performance of gait identification theoretically, especially in case that the distance between a camera

Conventional methods of gait analysis for person identification use features extracted from a sequence of camera images taken during one or more gait cycles. An implicit assumption is made that the walking direction does
not change. However, cameras deployed in real-world environments (and often placed at corners) capture imagesof humans who walk on paths that, for a variety of reasons, such as turning corners or avoiding obstacles, are notstraight but curved. This change of the direction of the velocity vector causes a decrease in performance for conventional methods. In this paper we address this aspect, andpropose a method that offers improved identification resultsfor people walking on curved trajectories. The large diversity of curved trajectories makes the collection of complete
real world data infeasible. The proposed method utilizes a
4D gait database consisting of multiple 3D shape models
of walking subjects and adaptive virtual image synthesis.
Each frame, for the duration of a gait cycle, is used to estimate a walking direction for the subject, and consequently
a virtual image corresponding to this estimated direction is
synthesized from the 4D gait database. The identification
uses affine moment invariants as gait features. Experiments
using the 4D gait database of 21 subjects show that the proposed method has a higher recognition performance thanconventional methods.

1. Introduction
Person identification methods have been used for a wide
variety of applications, such as surveillance or use of service
robots co-located with humans to provide various services
in daily life. Gait is one of biometrics that do not requireinteraction with a subject and can be performed from a distance [11] [15] [12]. Person identification methods which
extract features from gait images taken by a camera havebeen used with good results for human identification [6] [2][14] [9]. However, since image-based gait recognition issensitive to appearance changes, the correct classification
rate gets low in case that the subject’s appearance is different from that in the database. One of possible situations inwhich this problem occurs is the case that the subject’s wak1

and a subject is small and side view images are captured[3]. Figures 1 (c) and 2 (b) show examples of images from
top and actual images, and it is clear that observation angles
between the first frame and the last frame in one gait cycle
are different. To deal with this problem, Iwashita et al. [8]introduced a method for estimating local angles of a subject
walking straight, and an experiment with gait images was
carried out to illustrate the method.
In this paper, we expand this method [8] to estimate local angles of the subject walking on a curved trajectory.
The proposed method utilizes a 4D gait database consisting of sequential 3D models of multiple people walking
straight and adaptive virtual image synthesis. In the proposed method, one first estimates a walking direction of
a subject at each image for the duration of one gait cycle.
Next, an observation angle at each frame is estimated fromestimated walking direction, and a virtual image is synthesized from each 3D model for the duration of one gait cyclein the 4D gait database so that an observation angle of a synthesized image is the same with that of a frame of the subject. Here, a virtual images is synthesized from a 3D model
whose phase is the same with that of a frame of the subject,and virtual images are synthesized from all people in the
database. Finally, the subject is identified using affine moment invariants extracted from images as gait features. Our
experiments show the effectiveness of the proposed method
using two types of gait images: (i) images of people walking on curved trajectories. (ii) images of people walking
straight (to evaluate the theory introduced by Akae [3]).
This paper is organized as follows. Section 2 describes
the details of the proposed person identification method.
Section 3 describes experiments performed using the 4D
gait database. Section 4 presents our conclusions.

Walking direction

(a1)
(a2)
(a) Walking on a curved trajectory

Walking direction

(b1)

(b2)
(b) Walking straight

Figure 2. Walking on a curved trajectory and straight. (a1) and(b1) are the first frames in one gait cycle, and (a2) and (b2) are thelast frames.

position Pn in one gait cycle as shown in Fig. 3(a). Whenthe subject walks on a curved trajectory as shown in Fig.
3(a), the local angle varies gradually from frame to frame;
this deteriorates the performance of gait identification by
conventional methods, which have an implicit assumptionthat the subject walks straight.
When the subject walks straight and the azimuth angle is around ±90 degree and the elevation angle is small(front/back view images are captured), the local angle
change between frames in one gait cycle is small. However,if the azimuth angle is small and camera’s position is close
to the subject, then the local angle change between frames
in one gait cycle cannot be ignored.
Captured images(1) Subject

φ1(2) DB

φ2

φ1

Σw

φ2

CameraCameraCamera(a) Different walking
directions(b) Walking on curved
trajectory(c) Walking straight

Figure 1. (a) Walking direction change, (b) local angle changes(walking on a curved trajectory), and (c) local angle changes(walking straight).

2. Person identification robust to local angle
changes in one gait cycle
In this section, we explain the local angle changes in one
gait cycle when a subject walks either on a curved trajectoryor straight, and then introduce the proposed method.

Σ Pn
P1

Σc

PN

Camera

a φPn
φPn

PN

Pn

One gait cycle

e

a
φPN

Pn
a
φPn

P1
a
φP1

Camera(a) Oblique view(b) Top view

Figure 3. Local angle changes in one gait cycle.

2.2. The proposed person identification method

2.1. Local angle changes in one gait cycle

In this section we describe the details of the proposed
method. To summarize, the main steps of processing are as
follows.

The local angle at each frame in one gait cycle is definedwith the azimuth angle φaPn and elevation angle φePn at each

Step 1 One first estimates a walking direction of a subject at each image for the duration of one gait cycle asshown in Fig. 3.
Step 2 An observation angle at each frame is estimatedfrom estimated walking direction, and a virtual image
is synthesized from each 3D model for the duration of
one gait cycle in the 4D database (Fig 4) so that an
observation angle of a synthesized image is the samewith that of a frame of the subject as shown in Fig. 5.
Here, positions (P1 , Pn , PN ) and angles (φaP1 , φaPn ,φaPN ) correspond to those in Fig. 3. Virtual images aresynthesized from all people in the database
Step 3 Affine moment invariants are extracted as gait features from captures images of a subject and synthesized images, respectively, and the subject is identified.
The 4D gait database includes time-series 3D models of all
subjects which were built in advance. The following offers
more details.

(a) 3D model(b) A sequence of 3D models

Figure 4. Examples of 3D models in the database.
Side view

Top view
P1

Walking direction

Virtual camera PN

Pn

PN

a
φPn

a
φP1

Pn

a
φPN

P1

Synthesized images
from virtual cameras

Figure 5. Examples of synthesized virtual images.

2.2.1 Estimation of local angles
In this section we explain a method for estimation of thelocal angle. Estimating the local angle at each frame in one
gait cycle is equivalent to estimating rotation and translation
matrices (c RPn and c TPn ) from a coordinate system of eachfoot position ΣPn to a coordinate system of the camera Σcas shown in Fig. 6 (a) (c APn = [c RPn | c TPn ]). To estimate

rotation and translation matrices at each frame in one gait
cycle, we estimate foot position and walking direction in
3D space from each captured image. We assume here thatthe external and internal camera parameters and the positionof the floor are known.

Σw
wA
Pn

wA
Pm
wA

Pn

P1

c

Σw
Pm

PM

Σ Pn
c

A Pn

Σc
Camera(a) Estimation of transformation matrix
of a subject

c

A Pn

wA

vc

Virtualvc
camera Σ(b) Estimation of a pose ofa virtual camera

Figure 6. Estimation of transformation matrix of (a) a subject and(b) a virtual camera.

A background subtraction method is applied to captured
images to extract silhouette areas. The foot position in theimages are estimated as follows: (1) principal component
analysis is applied to a silhouette area of each image, and(2) two intersection points of the first principal component
and the convex hull of the silhouette area are calculated,
and the lower point along the first principal component isestimated as the foot position as shown in Fig. 7.
Next, foot positions w TPn (0 ≤ n < N , N is the numberof frames in one gait cycle) in 3D space are determined byprojecting the estimated foot positions on 2D images onto
the floor. Here, w TPn is a transformation matrix from acoordinate system of each foot position ΣPn to that of 3D
space Σw . There are several methods to estimate the walking direction, and one of them is to estimate walking direction at each foot position from difference of the current
foot position and its previous one. However, for example
when people walk straight, in general they swing from side
to side. This swinging can be considered as outliers, and thewalking direction calculated by the above method may bedifferent from the real walking direction. Thus, to decrease
the influence of outliers, we apply the least square method
to foot positions of one gait cycle. In case the subject walks
on a curved trajectory, the walking trajectory is estimatedby fitting a 2D polynomial to the foot positions of one gait
cycle. In case the subject walks straight, the walking trajectory is estimated by fitting a line to the foot positions.
Here, to distinguish the walking direction straight and on
curved trajectories, at first we fit a line to the foot positions.
Then if the sum of distances between the fitted line and footpositions is large, we consider the subject walks on curved
trajectory. Finally, the walking direction at each foot position in 3D space is estimated from a differential of the fitted
function.

From the estimated walking direction in 3D space andthe normal direction of the floor, a rotation matrix w RPn isdetermined. Finally the rotation matrix c RPn from a coordinate system of each foot position ΣPn to that of thecamera Σc and the translation matrix c TPn are calculated
as c RPn =c Rw w RPn and c TPn =c Rw (w TPn −w Tc ) as
shown c APn in Fig. 6 (a). Here, c Rw and w Tc are obtained
from external camera parameter.
The 1st principal
component

The 2nd principal
component

Foot position

Figure 7. Foot position detection.

2.2.3 Extraction of gait features and person identification
For feature extraction, at first a silhouette area is scaled toa uniform height, set to 128 pixels, and the average image I average from images
L of one gait cycle is defined by
I average (x, y) = L1 l=1 I(x, y, l) (L is either N for an
average image of a subject or M for an average image ofsynthesized images of each person in the database). Figure 8 shows an example of average images. Then, affine
moment invariants are extracted from the average image as
gait features [9]. In [9], Iwashita showed that affine moment invariants had the same discrimination capability with
GEI [6] and DFT [14] even thought the number of featuresof affine moment invariants is much smaller than those [6][14].
Affine moment invariants are moment-based descriptors,
which are invariant under a general affine transform. The
moments describe shape properties of an object as it appears. For an image the centralized moment of order (p + q)of an object O is given by(x − xg )p (y − yg )q I(x, y). (1)μpq =(x,y)∈O

2.2.2 Synthesis of virtual images from 3D models
The proposed method relies on a 4D gait database consisting of time-series 3D models of walking subjects which aremeasured using multiple cameras [8]. The details of thedatabase are explained in Section 3. Figure 4 shows examples of 3D models of a walking person in the database.
Note that the database consists of 3D models of multiple
people who walked straight. To synthesize virtual viewpoint images, at first the foot position w TPm (0 ≤ m < M ,M is the number of models in one gait cycle) of each 3Dmodel of the walking person in the database is estimatedas the intersection point of the floor and the first principal
component, which is calculated by applying the principal
component analysis to each 3D model. Then the walking
direction of the person is estimated from a line fitted to thefoot positions by the least square method, and a rotation
matrix w RPm at each foot position is calculated. Finally, as
shown in Fig. 6 (b) the external parameter (w Avc ) of a camera at a virtual viewpoint is calculated from c RPn , c TPn ,w
RPm , and w TPm , and a virtual viewpoint image is synthesized from a 3D model M odelm . Here, we assume that thephase of the first frame of one gait cycle of the subject isthe same with that of each person in the database. But the
number of frames of the subject in one gait cycle may bedifferent from that of a person in the database, so in generala phase of each frame of the subject should be aligned tothat of a synthesized image. In this paper, we align them byn× M as a linear solution. Virtual images are synm= N
thesized from 3D models at all people in the database withrespect to each subject.

Here, xg and yg are the center of the object. In our
method we used thirty affine moment invariants I ={I1 , I2 , . . . . , I30 }, and we show two of them [4] [5].
I1

=

I2

=

1
(μ20 μ02 − μ211 )μ400
1(μ230 μ203 − 6μ30 μ21 μ12 μ03 + 4μ30 μ312 + 4μ03 μ321
μ1000

−3μ221 μ212 )(2)
In this paper, we divide each average image into K multiple areas as shown in Fig. 8 to obtain features from local
areas, and extracted gait features from each area. Here, K
is the number of divided areas.

Figure 8. An example of average images (K=4).

2.2.4 Person identification
In the proposed method, we use the nearest neighbor as theclassifier. In the training phase, we extract gait features by

the affine moment invariants from synthesized virtual images, and then build a database. Then in the identification
phase, gait features are extracted from silhouette images ofa subject and the subject is identified by the classifier.
Shakhnarovich et al. also utilized 3D models reconstructed with multiple cameras and synthesized images ata virtual camera from 3D models [13]. However, they used
multiple cameras for capturing images of subjects and synthesize images from side view only. On the other hand, ourproposed method uses only one camera for capturing images of subjects and is able to synthesize images from arbitrary view points.

Camera B
1.2 m
Camera A

(2)

3.5 m

1.5 m
(1)

Figure 9. Experimental setting.

3. Experiments

3.1. Identification of people walking on curved trajectories

This section shows results of person identification experiments using a database which includes the 4D gait databaseand 2D images of people walking on curved trajectories andstraight as test datasets. This database comprises of 21 subjects, with 4 sequences for each subject. All people walked
straight as shown in the dashed line (2) in Fig. 9. Multiple 3D models were reconstructed by the visual hull technique with 16 cameras placed in a studio as shown in Fig.
9. We utilized sequential 3D models of all subjects as training datasets and 2D images captured from a camera as test
datasets.
Test datasets consist of images of two ways of walking;(walki) walking on a curved trajectory and (walkii) walking straight. For capturing images of people walking on
curved trajectories as shown the dashed line (1) in Fig.9(walki), we selected camera A. The trajectory is part ofa circle with radius 1.5 m. The test datasets consist of 21
subjects with 1 sequence. Each gait sequence consists of 15∼ 20 images. The height of the camera is approximately
1.2 [m], and the distance from each camera to the center ofthe studio is 3.5 [m].
For test datasets of people walking straight (walkii), we
utilized captured images taken from a camera (either camera A or camera B). People walked straight as shown thedashed line (2) in Fig.9, and camera A and camera B captured frontal view gait images and side view gait images,
respectively. The test datasets for each camera consist of 21
subjects with 4 sequences. Note that for synthesizing virtual
images of a subject we eliminated 3D models created fromgait images of the same sequence with that of the subject.
There are gait databases publicly available [1], which arefor changes of walking direction, and these databases include 2D gait images captured by multiple cameras. However, since these databases does not include information ofcamera parameters, 3D models of walking people cannot be
obtained. Besides, these databases contain images of people
walking only straight. Thus we do not use these databasesin our experiments.

In the first experiments, we applied the proposed method
to gait images of people walking on curved trajectories. In
the experiments, we applied two methods: (i) the proposed
method and (ii) the conventional method [8]. Figure 10(a)shows examples of captured images of a subject, and Figs.
10(b) and (c) show those corresponding synthesized imagesby the propose method and the conventional method [8],respectively. From these results, it is clear that the proposed
method could synthesize similar silhouette of actual images.
To extract gait features, we separate each average image into 1, 2, and 4 areas (K=1, 2, and 4), and we combined gait features from all areas for identification. The
correct classification rate by the conventional method [8]and the proposed method were 14.3 % and 71.4 % with sixteen affine moment invariants, which showed high performance in the experiments in the next section. The proposed
method showed much higher performance than the conventional method. Moreover, to show the effectiveness of theaffine moment invariants, we extracted gait features fromsynthesized images with GEI [6]. Here, to compare the discrimination capabilities of the affine moment invariants and
GEI, we didn’t apply any dimensionality reduction methods
to GEI. The correct classification rate was 28.6 %, which
was much lower than the affine moment invariants. The
reason is as follows. In both methods using affine moment
invariants and GEI, features are extracted from an average
image, and each pixel value of this image can be affected
due to slight error of the estimation of the walking direction. Moreover, as we explain in the next paragraph, since
the subject walked on a small circle, the number of frames
in one gait cycle is less than that in the database. So this canalso change pixel values of the average image. In GEI gaitfeature is extracted at each pixel, so this may be sensitive tothe change of pixel values. On the other hand, in the affine
moment invariants, gait features, which represents the shapeand pixel values of the area, are extracted at each area, so
this is robust to the change of pixel values compared withGEI.

When we checked captured images of people walking
on curved trajectories, we noticed that some of subjects
changed their way of walking due to the small circle. There
are some changes which affected their way of walking, suchthat (i) the length of stride of a subject got short comparedwith that of the subject walking straight, when the subject
walked on a small circle, (ii) the distance between the subject’s left and right legs in the frontal plane got bigger orsmaller than that of the subject walking straight. Figure 11
shows an example of captured images in the test datasets, animage of the same person from the database with Fig.11(a),and synthesized image of Fig.11(a) from the 3D model ofFig.11(b) by the proposed method. In Figures 11(a) and (b)the person was in the same phase, but it is clear the lengthof stride in Fig.11(a) is shorter than that in Fig.11(b). In
test datasets of 21 people, 3 of them changed their lengthsof stride bigger than those of the rest of people. When weremoved these 3 people from the test datasets, the correctclassification rates by the conventional method and the proposed method were improved to 16.7 % and 83.3 %, respectively.
From above results, the change of their way of walking
affected the discrimination capability of gait features fromaverage images. Near term is as follows. When a subject walks, his appearance may be similar to the one in the
database even if his way of walking is different from that in
the database, so we utilize features from these images forclassification.

(a1) frame#53

(b1)

(c1)

(a2) frame# 68(a) Examples of captured
images(b2)(b) Synthesized images by
the proposed method(c2)(c) Synthesized images by
the conventional method

Figure 10. Examples of actual images of a subject walking on a
curved trajectory and synthesized virtual images of the subject by
the proposed method and the conventional method [8].

(a) An example of captured
images(b) An example of images
from camera A(c) Synthesized image by
the proposed method

Figure 11. (a) An example of actual images of a subject walking
on a curved trajectory, (b) an example of captured images of thesame person walking straight with (a), and (c) synthesized imageof (a).

3.2. Identification of people walking straight
In the last experiments, we applied the proposed method
to images of people walking straight. Figure 12(a1) and(a2), which were captured from camera A show the first
frame and the last frame of one gait cycle, respectively,
and Fig.12(b) show those corresponding synthesized virtual viewpoint images. Here, for the purpose of visualization of the effectiveness of the proposed method, we utilized 3D models from images of the same sequence withthat of the test dataset. From the results of Fig. 12, theproposed method synthesized similar images to the actual
images compared with the conventional method.
To evaluate the effectiveness of the proposed method, weapplied one of conventional methods [7] to the same test
datasets. This conventional method [7] utilizes a fixed local angle (e.g. a local angle at the center position in one
gait cycle) to synthesize virtual images of one gait cycle,
so a synthesized image at a frame with different local angle
from the fixed local angle is different from actual image.
This method extracted gait features from average images byaffine moment invariants in the same way with the proposed
method. Figure 12(c) shows synthesized images which correspond to Fig.12(a).
Figures 13(a) and (b) show examples of captured images
from camera B and synthesized images by the proposed
method, respectively. These results show that the synthesized images are similar to actual images, and especially in
Fig.13(b1) the subject’s arm was separated from one’s body
like the one in Fig.13(a1). The subject’s arm in the synthesized image by the conventional method (Fig. 13(c1))
was connected to one’s body. From these results, the images synthesized by the proposed method are more similar
to captured images.
Figure 14 show the results of correct classification rates
from camera A by the proposed method and the conventional method. The highest correct classification rates by the
proposed method and the conventional method were 90.5
% and 86.9 %, respectively. Figure 15 shows the results ofcorrect classification rates from camera B by the proposed
method and the conventional method with respect to thechange of number of affine moment invariants. The highest
correct classification rates by the proposed method and theconventional method were 85.7 % and 79.8 %, respectively.
Akae et al. showed that the local angle changes in
one gait cycle affects the performance of gait identification especially in case that side view images are captured[3]. From above results, when local angle changes are
small (camera A), the results obtained using the proposed
method are only slightly better than those by the conventional method, due to little local angle changes. However,when local angle changes are big (camera B), the proposed
method showed better results than those by the conventional
method. These results support the correctness of [3].

(a1) frame# 14

(b1)

(c1)

(a2) frame# 31(a) Examples of captured
images(b2)(b) Synthesized images by
the proposed method(c2)(c) Synthesized images by
the conventional method

Figure 12. Comparison of virtual images by the proposed method
and the conventional method [7] (camera A).

(a1) frame# 14

(b1)

(c1)

(a2) frame# 31(a) Examples of captured
images(b2)(b) Synthesized images by
the proposed method(c2)(c) Synthesized images by
the conventional method

Figure 13. Comparison of virtual images by the proposed method
and the conventional method [7] (camera B).
100
90
80
70
60
50
40
30
20
10
0

CCR [%]The proposed method

The conventional method
The numberof features
0

5

10

15

20

25

30

Figure 14. Correct classification rates (camera A).
100
90
80
70
60
50
40
30
20
10
0

CCR [%]The proposed method

The conventional method
0

5

10

15

20

The numberof features
25

30

Figure 15. Correct classification rates (camera B).

4. Conclusions
We proposed in this paper the method to identify people walking on curved trajectories by utilizing a 4D gait
database and adaptive virtual images synthesis. In thismethod, we estimated a walking direction of a subject in 3D
space from foot positions of the subject, and we estimatedin one gait cycle an observation angle between the walking
direction of the subject and direction of the camera to thesubject at each frame. Next, a virtual image based on local
angle at each position was synthesized from 3D models of
all people in the database. Then the subject was identified
by gait features extracted by affine moment invariants. We
carried out experiments with the 4D database, and showed
the effectiveness of the proposed method.

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