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Hand Gesture Recognition based on Radar

Micro-Doppler Signature Envelopes

Moeness G. Amin

Center for Advanced Communications

Villanova University

Villanova, PA 19085, USA

moeness.amin@villanova.edu

Zhengxin Zeng, Tao Shan

School of Information and Electronics

Beijing Institute of Technology

Beijing, China

{3120140293,shantao}@bit.edu.cn

Abstract—We introduce a simple but effective technique in

automatic hand gesture recognition using radar. The proposed

technique classiﬁes hand gestures based on the envelopes of

their micro-Doppler signatures. These envelopes capture the

distinctions among different hand movements and their corre-

sponding positive and negative Doppler frequencies which are

generated during each gesture act. We detect the positive and

negative envelopes separately, and form a feature vector of their

augmentation. We use the k-nearest neighbor (kNN) classiﬁer and

Manhattan distance (L1) measure, in lieu of Euclidean distance

(L2), so as not to diminish small but critical envelope values.

It is shown that this method outperforms both low-dimension

representation techniques based on principal component anal-

ysis (PCA) and sparse reconstruction using Gaussian-windowed

Fourier dictionary, and can achieve very high classiﬁcation rates.

Keywords—Hand gesture recognition; time-frequency repre-

sentations; micro-Doppler signature envelope.

I. INTRODUCTION

Radar systems assume an important role in several areas of

our daily life, such as air trafﬁc control, speed enforcement

systems, and advanced driver assistance systems [1–3]. Re-

cently, radar has also become of increased interest for indoor

applications. In particular, human activity monitoring radar

systems are rapidly evolving with application that include gait

recognition, fall motion detection for elderly care and aging-

in-place technologies [4, 5].

Over the past decade, much work has been done in hu-

man motion classiﬁcations which include daily activities of

walking, kneeling, sitting, standing, bending, falling, etc. [6–

16]. Distinguishing among the different motions is viewed

as an inter-class classiﬁcation [6–13], whereas the intra-class

classiﬁcation amounts to identifying the different members of

the same class, e.g., classifying normal and abnormal gaits

[14–16]. There are two main approaches of human motion

classiﬁcations, namely those relying on handcrafted features

that relate to human motion kinematics [7–9, 14], and others

which are data driven and include low-dimension represen-

tations [6, 15], frequency-warped cepstral analysis [13], and

neural networks [10–12, 16].

The work of Mr. Zhengxin is funded by the International Graduate

Exchange Program of Beijing Institute of Technology, and was performed

while he was a Visiting Scholar at the Center for Advanced Communications,

Villanova University

In addition to classifying human motions, radars have been

recently used for gesture recognition which is an important

problem in a variety of applications that involve smart homes

and human-machine interface for intelligent devices [17–21].

The latter is considered vital in aiding the physically impaired

who might be wheelchair conﬁned or bed-ridden patients.

The goal is to enable these individuals to be self-supported

and independently functioning. In essence, automatic hand

gesture recognition is poised to make our homes more user

friendly and most efﬁcient through the use of contactless

radio frequency (RF) sensors that can identify different hand

gestures for instrument and household appliance control.

The same approaches employed for classifying human daily

activities can be applied for recognition of hand gestures using

the electromagnetic (EM) sensing modality. However, there is

an apparent difference between micro-Doppler signatures of

hand gestures and those associated with motion activities that

involve human body. Depending on the experiment and data

collection radar specs and setting, Micro-Doppler representa-

tions of hand gestures can be simple, limited to short time

duration and small bandwidth, and are mainly characterized

by their conﬁned power concentrations in the time-frequency

domain. On the other hand, the micro-Doppler signatures of

body motions are intricate, of multi-component signals, span

relatively longer time periods and assume higher Doppler

frequencies.

In this paper, we present a method to discriminate ﬁve

classes of dynamic hand gestures using radar micro-Doppler

sensor. These classes are swiping hand, hand rotation, ﬂip-

ping ﬁngers, calling and snapping ﬁngers. We begin with

many types of hand motions, and use the canonical angle

metric to assess the subspace similarities constructed from

their respective time-frequency distributions [22, 23]. Based

on the results, we group these motions into the ﬁve most

dissimilar classes. Two micro-Doppler features are extracted

from the data spectrograms. They correspond to the upper and

lower envelopes of the hand gesture micro-Doppler signatures.

The two envelopes implicitly capture, for each motion, the

positive-negative frequency differences, the time alignments

and misalignments of the peak positive and negative Doppler

frequencies, and the signature extent and occupancy over the

joint time and frequency variables.

We compare the proposed approach with that based on

PCA [6, 15] and on sparse reconstruction employing Gaussian-

windowed Fourier dictionary [17]. In the latter, the classiﬁer

was applied to hand gesture data showing signatures com-

prising rather detached power concentrated time-frequency

regions The experimental results applied to our measured data

demonstrate that the proposed method outperform the above

two methods, and achieve a classiﬁcation accuracy higher than

96%.

The remainder of this paper is organized as follows. In Sec-

tion II, we present the extraction method of micro-Doppler sig-

nature envelopes and discusses the employed classiﬁer. Section

III describes the radar data collection and pre-processing of

hand gestures. Section IV gives the experimental results based

on the real data measurements. Section V is the conclusion of

the paper.

II. HA ND GE ST UR E RECOGNITION ALGORITHM

A. Time-frequency Representations

Hand gestures generate non-stationary radar back-scattering

signals. Time-frequency representations (TFRs) are typically

employed to analyze these signals in the joint-variable do-

mains, revealing what is referred to as micro-Doppler signa-

tures. A typical technique of TFRs is the spectrogram. For a

discrete-time signal s(n)of length N, the spectrogram can be

obtained by taking the short-time Fourier transform (STFT)

S(n, k) =

L−1

X

m=0

s(n+m)h(m)e−j2πmk

N

2

(1)

where n= 0,· · · , N −1is the time index, k= 0,· · · K−1

is the discrete frequency index, and Lis the length of the

window function h(·).

B. Extraction of the Micro-Doppler Signature Envelopes

We select features speciﬁc to the nominal hand gesture

local frequency behavior and power concentrations. These

features are the upper and lower envelope in the spectrograms.

The envelopes attempt to capture, among other things, the

maximum positive frequency and negative frequencies, length

of the event and its bandwidth, the relative emphases of the

motion towards and away from the radar, i.e., positive and

negative Doppler frequencies. In essence, the envelopes of

the signal power concentration in the time-frequency domain

may uniquely characterize the different hand motions. The

envelopes of the micro-Doppler signature can be determined

by an energy-based thresholding algorithm [24]. First, the

effective bandwidth of each gesture frequency spectrum is

computed. This deﬁnes the maximum positive and negative

Doppler frequencies. Second, the spectrogram S(n, k)is di-

vided into two parts, the positive frequency part and the

negative frequency part. The corresponding energies of the two

parts, EU(n)and EL(n), at slow-time are computed separately

as

EU(n) =

K

2−1

X

k=0

S(n, k)2(2)

EL(n) =

K−1

X

k=K

2

S(n, k)2(3)

These energies are then scaled to deﬁne the respective thresh-

olds, TUand TL,

TU(n) = EU(n)·σU(4)

TL(n) = EL(n)·σL(5)

where σUand σLrepresent the scale factors, both are less

than 1. These scalars can be chosen empirically. However, an

effective way for their selections is to maintain the ratio of

the energy value to the threshold value constant over all time

samples. For the upper envelope, this ratio can be computed

by ﬁnding both values at the maximum positive Doppler

frequency. Once the threshold is computed per equation (4),

the upper envelope is then found by locating the Doppler

frequency for which the spectrogram assumes equal or higher

value. Similar procedure can be followed for the lower enve-

lope. The upper envelope eU(n)and lower envelope eL(n),

are concatenated to form a long feature vector e= [eU, eL].

C. Classiﬁer

We apply proper classiﬁers based on the envelope features

extracted from the spectrograms. The kNN and Support vector

Machine (SVM) are among the most commonly used classi-

ﬁers in pattern recognition which are used in this paper. In

particular, the kNN is a simple machine learning classiﬁcation

algorithm. For each test sample, the algorithm calculates the

distance to all the training samples, and selects the kclosest

training samples. Classiﬁcation is performed by assigning the

label that is most frequent among these samples [25]. Clearly,

the best choice of kwould depend on the data. In this work,

kis set to 1. Four different distance metrics are considered,

namely, the Euclidean distance, the Manhattan distance [26],

the Earth Mover’s distance (EMD) [27] and the modiﬁed

Hausdorff distance (MHD) [28].

SVM is a supervised learning algorithm [29]. It exhibits

clear advantages in nonlinear and high dimension problems.

III. HAND GES TU RE SUBCLASSES

The data analyzed in this paper was collected in the Radar

Imaging Lab at the Center for Advanced Communications,

Villanova University. The radar system used in the experi-

ment generates continuous wave, with carrier frequency and

sampling rate equal to 25 GHz and 12.8 kHz, respectively.

The radar was placed at the edge of a table. The hand was

approximately 20 cm away from radar at zero angle, and the

arm remained ﬁxed as much as possible during each gesture

motion.

As depicted in Fig.1. The following 15 hand gestures were

conducted: (a) Swiping hand from left to right, (b) Swiping

hand from right to left, (c) Swiping hand from up to down,

(d) Swiping hand from down to up, (e) Horizontal rotating

hand clockwise, (f) Horizontal rotating hand counterclockwise,

(g) Vertical rotating hand clockwise, (h) Vertical rotating

hand counterclockwise, (i) Opening hand, (j) Flipping ﬁngers,

(k) Clenching hand, (l) Calling, (m) Swipe left with two

ﬁngers, (n) Snapping ﬁngers, (o) Pinching index. Four persons

participated in the experiment. Each hand gesture was recorded

over 8 seconds to generate one data segment. The recording

was repeated for 5 times. Each data segment contained 2 or

3 individual hand motions, and a 1 second time window is

applied to capture the individual motions. As such, repetitive

motions and associated duty cycles were not considered in

classiﬁcations. In total, 755 segments of data for 15 hand

gestures were generated.

(a) (b) (c) (d) (e)

(f) (g) (h) (i) (j)

(k) (l) (m) (n) (o)

Fig. 1. Illustrations of 15 different hand gestures.

Fig. 2 shows examples of spectrograms and corresponding

envelopes for different hand gestures. The employed sliding

window h(·)is rectangular with length L=2048 (0.16 s),

and Kis set to 4096. It is clear that the envelopes can well

capture the salient features of the respective spectrograms. It

is also evident that the micro-Doppler characteristics of the

spectrograms are in agreement and consistent with each hand

motion kinematics. For example, for the hand gesture ‘Swiping

hand’, the hand moves closer to the radar at the beginning

which causes the positive frequency, and then moving away

from the radar which induces the negative frequency.

Observing the spectrograms in Fig. 2, it is noticeable that

similar motions generate similar signatures. To mathematically

conﬁrm these resemblances, we consider sub-grouping the 15

hand gestures using the Canonical correlation measure [22]. In

this case, the spectrograms are converted to gray-scale images

with the size 100 ×100, and then vectorized with the size

1×10000.

Deﬁne matrix Xcontains Mvectorized images Si, i =

1,· · · , M of a speciﬁc hand gesture,

X= [x1|x2|···|xM](6)

The d-dimensional subspace of a speciﬁc hand gesture can

be obtained by taking PCA of X[30]. Suppose Φ1and Φ2are

two d-dimensional linear subspaces, the canonical correlations

of the two subspaces are the cosines of principal angles, and

are deﬁned as [31]:

cos θi= max

ui∈Φ1

max

vi∈Φ2

uT

ivi(7)

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j)

(k) (l) (m)

(n) (o)

Fig. 2. Spectrograms and corresponding envelopes of 15 different hand

gestures.

subject to ||u|| =||v|| = 1, uiTuj=viTvj= 0, i 6=j. Let U

and Vdenote unitary orthogonal bases for two subspaces, Φ1

and Φ2. The singular value decomposition (SVD) of UTVis

UTV=PΛQ(8)

The canonical correlations are the singular values Λ, i.e.,

cos(θi) = λi, i = 1,· · · , d. The minimum angle is used

to measure the closeness of two subspaces. Table I shows

the canonical correlations coefﬁcients, from which we can

clearly see the similarities between the different hand gestures;

larger coefﬁcient indicates the two hand gestures are more

similar. The red part of the table indicates the coefﬁcient

exceeds 0.9, and the yellow part means the coefﬁcient is over

0.85. According to the Table numbers, we group the 15 hand

gestures into 5 Class. Class I is the gesture ‘Swiping hand’

which contains motions (a), (b), (c) and (d). Class II represents

the gestures ‘Hand rotation’ which contains motions (e), (f),

(g) and (h). The gesture ‘Flipping ﬁngers,’ which involves

motions (i) and (j), makes Class III. Class IV is the gesture

‘Calling,’ which has motions (k), (l) and (m). The last Class

V is the gesture ‘Snapping ﬁngers’; it has motions (n) and

(o). It is important to note that other similarity measures [*]

can be applied, in lieu of the canonical correlation. However,

we found the canonical correlation most consistent with the

visual similarities.

IV. EXPERIMENTAL RESU LTS

In this section, all 755 data segments are used to validate the

proposed method where 70% of the data are used for training

and 30% for testing. The classiﬁcation results are obtained

TABLE I. CANONICAL CORRELATIONS COEFFI CIE NT S

b c d e f g h i j k l m n o

a0.79 0.83 0.91 0.70 0.75 0.79 0.84 0.69 0.66 0.78 0.77 0.76 0.77 0.81

b0 0.92 0.80 0.70 0.68 0.82 0.82 0.65 0.61 0.78 0.82 0.83 0.73 0.60

c0 0 0.76 0.64 0.59 0.85 0.88 0.72 0.65 0.80 0.80 0.82 0.76 0.69

d0 0 0 0.61 0.68 0.81 0.75 0.57 0.55 0.78 0.67 0.60 0.63 0.64

e0 0 0 0 0.86 0.70 0.75 0.59 0.66 0.56 0.72 0.66 0.72 0.71

f0 0 0 0 0 0.78 0.83 0.70 0.70 0.67 0.73 0.70 0.78 0.79

g0 0 0 0 0 0 0.85 0.67 0.67 0.78 0.66 0.71 0.74 0.73

h0 0 0 0 0 0 0 0.55 0.60 0.72 0.67 0.61 0.71 0.71

i0 0 0 0 0 0 0 0 0.87 0.75 0.61 0.67 0.76 0.74

j0 0 0 0 0 0 0 0 0 0.68 0.61 0.68 0.83 0.73

k0 0 0 0 0 0 0 0 0 0 0.94 0.94 0.83 0.76

l0 0 0 0 0 0 0 0 0 0 0 0.93 0.73 0.66

m0 0 0 0 0 0 0 0 0 0 0 0 0.77 0.63

n0 0 0 0 0 0 0 0 0 0 0 0 0 0.82

by 1000 Monte Carlo trials. Three different automatic hand

gesture approaches are compared with the proposed method.

These are: 1) the empirical feature extraction method; 2) the

PCA-based method [15]; 3) the sparse reconstruction-based

method [17].

A. Empirical Feature Extraction Method

Three empirical features are extracted from the spectro-

grams to describe the hand gestures motions, namely the

length of the event, the ratio of positive-negative frequency

and the signal bandwidth. Fig. 3 is an example showing these

handcrafted features.

Fig. 3. Empirical feature extraction.

1) Length of the event T:This describes the effective time

duration to perform each hand gesture,

T=te−ts(9)

where tsand terepresent the start time and the end time of a

single hand gesture, respectively.

2) Ratio of positive-to-negative peak frequencies R:This

feature is obtained by ﬁnding ratio of the maximum positive

frequency value,fp, and maximum negative frequency value,

fn,

R=

fp

fn

(10)

where |·| is the absolute function.

3) Bandwidth Bw:This is a measure of the the signal

effective width,

Bw=|fp|+|fn|(11)

The scatter plot of the above extracted features is shown in

Fig. 4. Table II depicts the nominal behavior of these values

over the different classes considered. When using kNN-L1 as

the classiﬁer, the recognition accuracy based on these features

is only 68% with the confusion matrix shown in Table II.

Fig. 4. Scatter plot of three extracted empirical features.

TABLE II. CONFUSION MATRIX YIE LDE D BY EMPIRICAL FE ATURE EX-

TR ACTI ON ME THO D

I II III IV V

I66.79% 13.80% 4.08% 9.18% 6.15%

II 20.04% 64.65% 3.53% 4.88% 6.90%

III 9.94% 5.59% 76.53% 0.03% 7.91%

IV 19.04% 6.74% 0.65% 71.79% 1.78%

V12.03% 10.96% 12.28% 11.59% 53.14%

B. Proposed Envelope-based Method

As discussed in Section II, the extracted envelopes are fed

into the kNN classiﬁer, with different distance measures, and

SVM classiﬁer. The recognition accuracy are presented in

Table III. It is cleat that the kNN classiﬁer based on L1

distance achieves the highest accuracy, over 96%, followed

by those employing the modiﬁed Hausdorff distance and

the Euclidean distance. Different from other distances, the

L1 distance attempts to properly account for small envelope

values. The confusion matrix of the kNN classiﬁer based on

the L1 distance is shown in Table IV, from which we can ﬁnd

that Class III and Class IV are most distinguishable with the

accuracy over 98%.

TABLE III. RECOGNITION AC CUR ACY W ITH DI FFE REN T TYP ES OF CL AS -

SI FIER

Accuracy

SVM 83.07%

kNN-L1 95.23%

kNN-L2 93.87%

kNN-EMD 81.51%

kNN-MHD 93.95%

TABLE IV. CONFUSION MATRIX YIE LD ED BY ENVELOPE ME THO D

BAS ED O N kNN-L1 CLAS SI FIER

I II III IV V

I95.23% 3.17% 0.14% 1.46% 0

II 3.03% 95.39% 0.01% 0.06% 1.51%

III 0.07% 0 99.01% 0.28% 0.64%

IV 0.61% 0 1.16% 98.21% 0.02%

V0 2.31% 2.61% 2.83% 92.25%

C. PCA-based Method

For the PCA-based method, each sample represents a spec-

trogram image of 100 ×100 pixels. The number of principal

TABLE V. C ONFUSION MATRI X YIEL DE D BY PCA-BA SED ME THO D WI TH

d= 30

I II III IV V

I89.50% 3.02% 0.67% 6.80% 0.01%

II 2.92% 94.83% 0 1.45% 0.80%

III 2.85% 1.23% 94.42% 0 1.50%

IV 5.24% 0.25% 1.37% 93.14% 0

V3.24% 8.14% 5.03% 1.83% 81.76%

components dis determined by the eigenvalues. Fig.5 shows

how the classiﬁcation accuracy changes with d, with the

recognition rate increases as dincreases. However, there is

no signiﬁcant improvement of the recognition accuracy past

d= 30. Table V is the confusion matrix using 30 eigenvalues.

Although the PCA method can achieve an overall accuracy of

92.71%, it is clearly outperformed by the proposed method.

Fig. 5. Performance of PCA with different number of principal components.

D. Sparsity-based Method

The features used for this method are the time-frequency

trajectories. Details of the sparsity-based method can be found

in [17]. The trajectory consists of three parameters, namely

the time-frequency position (ti, fi), i = 1,· · · , whereP and

the intensity Ai,Pis the sparsity level that is set to 10

in this paper. Hence, each sample contains 30 features. The

spectrograms of reconstructed signals and the Plocations

of time-frequency trajectory are plotted in Fig. 6 and Fig.

7. In the training process, the K-means algorithm is used

to cluster a central time-frequency trajectory [32]. In the

testing process, the kNN classiﬁer based on the modiﬁed

Hausdorff distance is applied to measure the distance between

the testing samples and central time-frequency trajectories.

The corresponding confusion matrix is presented in Table VI.

The overall recognition accuracy was found to be only about

70% when applied to our data.

TABLE VI. C ONFUSION MATRIX YIELD ED BY SPARSITY-BASED ME TH OD

I II III IV V

I71.72% 11.36% 1.45% 11.74% 3.73%

II 10.95% 81.29% 2.57% 0.28% 4.91%

III 7.40% 2.10% 83.63% 0.69% 6.18%

IV 16.04% 6.52% 1.22% 74.14% 2.08%

V6.65% 15.05% 9.96% 10.02% 58.32%

V. CONCLUSION

We introduced a simple but effective technique for auto-

matic hand gesture recognition based on radar micro-Doppler

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j)

(k) (l) (m)

(n) (o)

Fig. 6. Spectrograms of reconstructed signals with P= 10.

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j)

(k) (l) (m)

(n) (o)

Fig. 7. Locations of time−frequency trajectories with P= 10.

signature envelopes. An energy-based thresholding algorithm

was applied to separately extract the upper (positive) envelope

and the lower (negative) envelope of the signal spectrogram.

We used the canonical correlation coefﬁcient to group 15

hand gestures into ﬁve different classes. The members of

each class have close signature behavior. The extracted en-

velopes were concatenated and inputted to different types

of classiﬁers. It was shown that the kNN classiﬁer based

on L1 distance achieves the highest accuracy and provided

over 96 percent classiﬁcation rate. The experimental results

also demonstrated that the proposed method outperformed

the lower dimensional PCA-based method, the sparsity-based

approach using Gaussian-windowed Fourier dictionary, and

existing techniques based on handcrafted features.

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