texture feature extraction method for ground nephogram

Texture Feature Extraction Method for Ground Nephogram Based on HilbertSpectrum of Bidimensional Empirical Mode Decomposition

XIAOYING CHEN

School of Instrument Science and Engineering, Southeast University, and College of Meteorology and Oceanography,

People’s Liberation Army University of Science and Technology, Nanjing, China

AIGUO SONG AND JIANQING LI

School of Instrument Science and Engineering, Southeast University, Nanjing, China

YIMIN ZHU AND XUEJIN SUN

College of Meteorology and Oceanography, People’s Liberation Army University of Science and Technology, Nanjing, China

HONG ZENG

School of Instrument Science and Engineering, Southeast University, Nanjing, China

(Manuscript received 31 October 2013, in final form 19 May 2014)

ABSTRACT

It is important to recognize the type of cloud for automatic observation by ground nephoscope. Although

cloud shapes are protean, cloud textures are relatively stable and contain rich information. In this paper,

a novel method is presented to extract the nephogram feature from the Hilbert spectrum of cloud images

using bidimensional empiricalmode decomposition (BEMD). Cloud images are first decomposed into several

intrinsic mode functions (IMFs) of textural features through BEMD. The IMFs are converted from two- to

one-dimensional format, and then the Hilbert–Huang transform is performed to obtain the Hilbert spectrum

and theHilbertmarginal spectrum. It is shown that theHilbert spectrum and theHilbertmarginal spectrumof

different types of cloud textural images can be divided into three different frequency bands. A recognition

rate of 87.5%–96.97% is achieved through random cloud image testing using this algorithm, indicating the

efficiency of the proposed method for cloud nephogram.

1. Introduction

The global radiation budget and hydrological cycle

are highly influenced by the variability and potential

trends of cloud properties. Clouds can provide abundant

information on climate change in the past, present, and

future (Heintzenberg and Charlson 2009). Therefore,

clouds are part of the essential elements of meteoro-

logical observations.

Nowadays, land-based weather stations and satellites

are all part of integrated monitoring systems. However,

land-based images have not been carefully analyzed so

far. Automated ground-based cloud recognition is dif-

ficult because instruments cannot detect cloud structural

characteristics as easily as human eyes can (Liu et al.

2011).

Automated cloud observation systems have been de-

veloped based on a number of visible light– or infrared-

basedmeasuring equipment, such as thewhole-sky imager

(WSI), total sky imager (TSI), all-sky digital camera,

infrared cloud analyzer, infrared cloud imager, micro-

pulse lidar (MPL; e.g., Zhao et al. 2014a), and Milli-

meter cloud radar (MMCR; e.g., Garrett and Zhao

2012). This equipment has provided quantitative mea-

surements of cloud cover. However, there are limited

studies on automated identification of cloud type at

present, and only a simple classification exists, which

identifies from three to four kinds of typical clouds.

Buch et al. (1995) classified altocumulus, cirrus, stratus,

Corresponding author address: Aiguo Song, School of In-

strument Science and Engineering, Campus Sipailou, Southeast

University, Nanjing 210096, China.

E-mail: [email protected]

1982 JOURNAL OF ATMOSPHER IC AND OCEAN IC TECHNOLOGY VOLUME 31

DOI: 10.1175/JTECH-D-13-00238.1

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mailto:[email protected]

and cumulus based on the WSI, using a binary-tree

strategy with success rates of 43%, 35%, 54%, and 46%,

respectively. They suggested some texture-related fea-

tures and obtained a misclassification rate of 39% of

their test pixels when compared with visual classifica-

tion. Peura et al. (1996) outlined a classification method

for land-based images that extracted several features

like clarity, size, fiber, physical level, and edge infor-

mation from the WSI for identification of cloud type.

The overall accuracy of this method is about 65%, but it

does not effectively identify stratocumulus, cumulo-

nimbus, and altocumulus because the recognition rates

are only 38%, 0%, and 44%, respectively. Wang and

Sassen (2001) classified clouds observed from MMCR

and MPL into nine types based on radar reflectivity,

cloud temperature, and so on. This classification has

been widely used by cloud-related studies such as Zhao

et al. (2014b). Singh and Glennen (2005) used five-

feature extraction methods in the K-nearest neighbor

and neural network classifier to recognize cumulus and

cumulonimbus clouds with the recognition rates of

86.3% and 83.3%, respectively, from digital camera

cloud images. Calbó and Sabburg (2008) extracted sev-

eral characteristics that are useful in cloud type classi-

fication and identification of eight categories of sky

conditions according to their definitions from the TSI

and theWSI. Sun et al. (2009a) analyzed the local binary

pattern (LBP) spectra and variance (VAR) character-

istics for five cloud classes—cirrus, undulatus, cumulus,

stratus, and clear sky—based on a whole-sky infrared

cloud image. The classification success rates for the

above-mentioned five classes in the class recognition of

274 cloud image samples are 100.0%, 84.2%, 70.3%,

64.7%, and 99.0%, respectively, with an overall average

of 87.2%. Sun et al. (2009b) proposed a method using

a fuzzy uncertainty texture spectrum and essential in-

formation of cloud images to identify cumulus, altocu-

mulus, and cirrus, and the recognition rates are 100%,

90%, and 100%, respectively, from the whole-sky in-

frared cloud image. Heinle et al. (2010) presented a set

of statistical features about the color of the cloud image

and distinguished seven sky conditions: high patched

cumuliform clouds, high thin clouds, stratiform clouds,

stratocumulus clouds, low cumuliform clouds, thick

clouds, and clear sky. The success rates of identification

for random images reached 75%–88%. Zhang et al.

(2010) recognized cloud types by neural network and co-

occurrence matrices. Liu et al. (2011) discovered that

several structural features are effective for identifying

cumuliform, cirriform, and waveform clouds, with

a recognition accuracy of 90.97%.

These methods have provided some interesting cloud

detection results, but they can only identify several kinds

of typical clouds and the recognition rates are not suf-

ficiently high.

A thermal imaging camera is very expensive, and its

sensitivity is greatly reduced for high (cold) clouds such

as cirrus. Smith et al. (2004) showed the advantages of

visible cloud detection, which is inexpensive and has

higher resolution. Therefore, a study on the identifica-

tion of visible clouds is necessary and urgent. Our

analysis in this study involves the visible cloud images

taken by digital camera on the ground. It is more difficult

to recognize a visible channel cloud image without ad-

equate multichannel data analysis. Automatic identi-

fication of clouds using computers faces enormous

challenges for the ever-changing shape of clouds. Al-

though the texture of a cloud is exceedingly rich and

relatively stable, the frequency information of different

clouds varies greatly. It is just an effective method based

on the spatial frequency domain analysis of texture. This

method is similar to the human visual perception system,

which automatically decomposes an image into different

frequency and direction components when watching

texture images (Shan et al. 2007).

The bidimensional empirical mode decomposition

(BEMD) and the Tamura texture featuremethod (Chen

et al. 2010) refer to the features of cloud image. Then,

the average sample method is used for classification.

However, the recognition rate is still not satisfactory

because these features extracted from images are in-

effective for identifying some clouds. Considering the

fact that a cloud is first divided into categories and

further judged by the observer in human observation,

cloud images are then divided into three main types of

cloud. The features of cloud images are extracted by

the Hilbert spectrum method of BEMD to facilitate

cloud classification and to improve the recognition rate.

Compared to the algorithms in the literature, our

method provides a novel means to classify a sky image

by extracting the frequency information of cloud. This

method has obvious advantages in terms of objectivity

and resolution. In addition, a test run of random images is

presented, which outperforms existing algorithms by

yielding a higher success rate. The paper is organized as

follows. The cloud image data are introduced in section 2.

Section 3 describes the proposed algorithm. In section 4,

the experimental results are presented. The conclusions

are summarized and the method is discussed in section 5.

2. Data

The 115 cloud images used in the study are obtained

from the National Weather Service website, and their

types are clearly labeled. The format of each image is

Joint Photographic Experts Group (jpeg), and the

SEPTEMBER 2014 CHEN ET AL . 1983

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resolution is more than 600 pixels3 450 pixels with an 8-

bit color depth. The images were captured with 250 3250 pixels as learning samples and resized to 50 pixels350 pixels because of the costly time consumption of the

BEMD algorithm. The 50 pixel3 50 pixel image cannot

be intercepted directly from the original cloud during

cloud identification; otherwise, it does not reflect the

overall cloud type. The images are converted to a 256-

shade grayscale format before BEMD. The images of 10

types of ground nephogram samples used in the analysis

are given in Fig. 1. They are cumulus humili, cumulo-

nimbus, cirrus, stratus, nimbostratus, altostratus, cirro-

stratus, stratocumulus, altocumulus, and cirrocumulus.

3. Methodology

a. BEMD texture analysis

Empirical mode decomposition (EMD), proposed by

Huang et al. (1998), is a time–frequency analysis tool.

For signal processing, it decomposes data into several

intrinsic mode functions (IMF) by a sifting process. It is

completely driven by data, with good localization and

adaptability.

BEMD can be applied for analysis in the spatial fre-

quency domain, because of its advantage in texture

image analysis and in multiscale decomposition of

a texture image. Nunes et al. (2003) derived a useful

algorithm of BEMD. The extreme value is detected by

the morphological operator method in the bidimen-

sional sifting process. Radial basis functions are used to

obtain surface interpolation for regional maxima and

minima. It is a new and promising method for decom-

posing an image into multiple scales and extracting

unique features while avoiding choosing a wavelet base,

as required by wavelet transform for BEMD. We use

this method to preprocess cloud images.

First, the cloud image is transformed to grayscale

format. Thenceforward, it is decomposed into three

IMFs and residue using BEMD. The sifting process is

defined as follows (Long et al. 2009):

The original image is M3N in pixels, with a gray

value of f (x, y) for (x5 1, . . . , M, y5 1, . . . , N).

1) Initialization:

Iresij(x, y)5 Ir5 f (x, y) , (1)

where Iresij(x, y) is the sifting result in the jth

iteration, Ir is the residue, i is the number of layers

of decomposition of the IMF, and j is the iteration

times used to seek the IMF.2) Search for the local maxima and minima of

Iresij(x, y).

3) Fit the extreme points and form the envelopments.

Calculate the average of the top and bottom envelopes:

mij(x, y)5Topj(x, y)1Bottomij(x, y)

2. (2)

4) Extract the details:

Iresij(x, y)5 Iresij(x, y)2mij(x, y) . (3)

5) Repeat steps 2–4 untilmij satisfies the iteration criteria:

imfj(x, y)5 Iresij(x, y) . (4)

The standard deviation (SD) is computed from

the two continuous sifting results to stop the IMF

extraction as follows:

SD5

�X

x50�Y

y50

24jIresi(j21)(x, y)2 Iresij(x, y)j2

[Ires2i(j21)(x, y)]2

35,« ,

(5)

where « is typically less than 0.3. BEMD is stopped,

and then several IMFs are obtained. The selection of

« determines the number and quality of IMF for the

BEMD. A smaller « gives more detail of how IMFs

are decomposed (Song and Yu 2010). To better

reflect the detail of various clouds, « is set to 0.0003

in this study.6) Ir(x, y)5Ir(x, y)2imfi(x, y) and resij(x, y)5Ir(x, y).

7) Repeat steps 2–6; the image can be decomposed

into

f (x, y)5 �N

j51

imfj(x, y)1 IrN(x, y) . (6)

In Eq. (6), imfj(x, y) is the jth IMF for the de-

composition and IrN(x, y) is the monotonous residual

function.

It is a fundamental step for BEMD to solve the dis-

crete data interpolation problem. In this study, the two-

dimensional envelope construction method based on

radial basis function interpolation is used (Gao 2008).

BEMD is based on the following assumptions (Hu

2008). Any signal is made up of different IMFs. Each

IMF, linear or nonlinear, has the same number of

zero-crossing and extreme points. There is only one

extremum in the adjacent zero crossing. Modes are

independent of each other.

In this way, the signal would be decomposed into the

sum of several IMFs. The data must be able to represent

the overall texture characteristics of an image, which is



FIG. 1. The images of 10 types of ground nephogram samples: (a) cumulus humili, (b) cumulonimbus, (c) cirrus, (d) stratus, (e) nimbostratus,

(f) altostratus, (g) cirrostratus, (h) stratocumulus, (i) altocumulus, and (j) cirrocumulus.



computed for texture classification. The characteristic

scale is defined by the extreme distance of BEMD; that

is to say, extreme spacing reflects the scale features of

the IMFs. The original texture image is decomposed

into several periodical, stationary processes of the

IMFs that are self-adaptive. The IMFs represent the

characteristics of the texture image from high to low

frequency.

The IMFs manifest different frequency characteris-

tics in the texture image (Hu 2008). In this experiment,

it is found that the unique frequency information for

some textures decomposed by BEMD can be identified

effectively. The detailed texture of each IMF varies

within the diverse types of clouds. For instance, Fig. 2a

is the image of an altocumulus at 250 3 250 pixels.

Figures 2b–d show the amplitude and frequency char-

acter of altocumulus clouds from three IMFs of the

BEMD algorithm. The main texture information is

focused in the second (Fig. 2c) and third (Fig. 2d) IMFs,

different from a cumulonimbus that is concentrated in

the first IMF. It is shown that the details of their tex-

tures are concentrated in different frequencies. This

helps us to improve the recognition rate of cloud clas-

sification.

Some features of instantaneous amplitude can be used

as a texture classification method (Shan et al. 2007).

However, the identification results of cloud image

feature extraction based on these characteristics are

FIG. 2. (a) An original sample of an altocumulus, and (b)–(d) the three associated IMFs decomposed by the BEMD

algorithm. The main texture information is focused on the (c) second and (d) third IMFs.



unsatisfactory (Chen et al. 2010). The discrimination of

some clouds is not good using these features.

Clouds can be divided into cumuliform, waveform,

and stratiform clouds according to genetic-cloud for-

mation and evolution in the actual ground detection.

This classification is more suitable than the idea that

a cloud can be identified by image texture. A cumuli-

form cloud is a gigantic cloud formed by vertical air

convection condensation and includes cumulus, cumu-

lonimbus, and cirrus. A waveform cloud is an undulating

cloud formed by fluctuation of the air, including cirro-

cumulus, altocumulus, and stratocumulus. The genera-

tion of a stratiform cloud is horizontal and uniform,

curtainlike, by uplifting the air of a whole layer (Sun

et al. 2009c), including cirrostratus, altostratus, nimbo-

stratus, and stratus. Identification of the three clouds

and then more detailed classification can be further ac-

complished with additional features.

b. The Hilbert spectral analysis

Texture frequency distribution characteristics of var-

ious types of cloud images can be clearly seen, and

amplitude and frequency information can be extracted

from the Hilbert spectrum and the Hilbert marginal

spectrum.

The Hilbert–Huang transform (HHT) is a new

adaptability time–frequency analysis method with clear

physical meaning for nonlinear and nonstationary sig-

nals. The time–frequency–amplitude distribution of the

signal can provide rich information to HHT.

It is well known that the resolutions of time and fre-

quency in the preceding time–frequency analysis are

incompatible because of the restrictions of Heisenberg’s

uncertainty principle. However, the advantage of HHT

is that the Hilbert spectrum can be obtained from the

instantaneous frequency and amplitude of the IMFs.

Thus, the resolutions of time and frequency are in-

dependent of each other in HHT.

The Hilbert transform is a linear transformation with

a focus on local properties that thus avoids the excrescent

and inexistent high- and low-frequency components of

the Fourier transform for fitting the original sequence.

Although a two-dimensional Hilbert transform is feasi-

ble, some studies have shown that the Hilbert spectrum

can be derived from the IMF of EMD by the Hilbert

transform, whose input is a one-dimensional array.

However, the IMF of BEMD is a two-dimensional array

and should be first converted to a one-dimensional ar-

ray. Then, the Hilbert spectrum can be obtained by the

Hilbert transform.

The IMFs from BEMD must be converted to one di-

mension, so the two-dimensional array of 50 pixels3 50

pixels needs to be converted to a one-dimensional array

of 2500 pixels. The method of conversion is as follows.

The matrix size of the IMF component is 50 pixels 350 pixels—that is

X5

266664

x(1, 1) x(1, 2) ⋯ x(1, 50)

x(2, 1) x(2, 2) ⋯ x(2, 50)

..

. ... ..

. ...

x(50, 1) x(50, 2) ⋯ x(50, 50)

377775 , (7)

where X is converted to a one-dimensional array X0,where X05[x(1, 1), x(1, 2), ... , x(1, 50), x(2, 1), x(2, 2), ... ,

x(2, 50), ... , x(50, 1), x(50, 2), ... , x(50, 50)].

The Hilbert spectrum and the Hilbert marginal spec-

trum of various types of cloud images are obtained by

the Hilbert transform for X0.The texture frequency of the decomposed cloud im-

age is spatial rather than time frequency. The spatial

frequency domain is the spatial frequency (wave-

number) characteristic that is an independent variable

that describes the image. The change of pixel values in

space can be decomposed into a linear superposition of

harmonic vibration function with different amplitude,

spatial frequency, and phase. The composition and dis-

tribution of the spatial frequency components of the

image are called the spatial frequency spectrum. The

decomposition, processing, and analysis of the spatial

frequency characteristics of the image are referred to as

the spatial frequency or wavenumber domain process-

ing. Similar to the time–frequency transformation, the

spatial domain and the spatial frequency domain can

also be converted to each other. In this paper, the units

of spatial frequency, namely, the texture frequency, are

per meter.

The Hilbert transform cannot be used for IrN(x, y)

because its monotonicity does not reflect the oscillation

mode of the signal. First, each intrinsic mode component

imfj(x, y) is converted to a one-dimensional array imfj(t)

(with t5 tx 3 ty, tx, and ty for image pixel rows and col-

umns, respectively), then imfj(t) can be obtained for

imfj(t) by the Hilbert transform (Chen et al. 2009):

imfj(t)51

pp � y

ð1‘

2‘

imfj(t)

t2pdt (8)

where p � y denotes the integral principal value.

Then, the analytic signal is constructed using

zj(t)5 imfj(t)1 j � imfj(t)5 aj(t)ejf

j(t) , (9)

where aj(t) 5ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiimf2j (t) 1 imf2j (t)

q, and fj(t) 5

arctan[imfj(t)/imfj(t)].



Further, the instantaneous frequency can be obtained

using

fj(t)51

2pvj(t)5

1

2p3

dfj(t)

dt. (10)

So, H(v, t) becomes

H(v, t)5Re �N

j51

aj(t)ejf

j(t) 5Re �

N

j51

aj(t)ejÐvj(t)dt .

(11)

Equation (11) is called the Hilbert spectrum. The

signal amplitude variation with time and frequency in

the entire frequency band is described by H(v, t). The

instantaneous frequency has a definite physical meaning

after BEMD is introduced into the HHT. The frequency

of HHT is the best sine approximation for the local

waveform. Therefore, the frequency can be defined at

every point of the waveform rather than as a global sine

function.

The amplitude of the IMF is displayed by grayscale

on the frequency–time–amplitude diagram, that is,

the Hilbert spectrum. The gray level indicates ampli-

tude: the brighter the scale, the greater amplitude.

Frequency variation with time and the relative change

of energy can be revealed by the Hilbert spectrum.

The Hilbert spectrum amplitude is the normalized

value. The relative change of the amplitude is repre-

sented by the relative change of the color. The Hilbert

spectrum is the time–frequency distribution based on

a profile or a skeleton diagram to describe the signal

energy, and it changes instantly with the frequency

distribution.

The characteristics of cloud image texture frequency

and intensity with spatial variation can be clearly dis-

tinguished by the Hilbert spectrum, which reveals the

energy distribution on the surface of the three-

dimensional time (spatial) frequency (Xiong et al. 2002).

c. Hilbert marginal spectrum

The Hilbert marginal spectrum can be derived from

the time integration of the Hilbert spectrum (Nunes

et al. 2005) using

h(v)5

ðT0H(v, t) dt . (12)

The amplitude of instantaneous frequency is acquired

from theHilbert marginal spectrum, which describes the

cumulative amplitude distribution of each frequency

point for all data with statistical significance. The am-

plitude of a certain point in the Fourier spectrum

represents the trigonometric function component con-

taining this frequency in the entire signal. The greater

the amplitude, the greater the possibility of local exis-

tence in the entire data. A fast Fourier transformation

(FFT) represents the possibility of energy distribution in

a frequency, while the Hilbert marginal spectrum de-

scribes the accumulative amplitude of instantaneous

frequency of the entire data.

The meaning of the (instantaneous) frequency in the

Hilbert spectrum and the Hilbert marginal spectrum is

different from the frequency in the Fourier analysis

(Fourier frequency). The presence of energy in a fre-

quency for Fourier analysis denotes a sine or cosine

wave present in the entire timeline. A greater Hilbert

marginal spectrum indicates a greater probability of the

frequency.

The texture frequency distribution characteristics of

various cloud images can be more clearly revealed, and

the amplitude and frequency information by the Hilbert

spectrum and the Hilbert marginal spectrum can be

easily extracted.

4. Results

Texture classification is an important branch of tex-

ture analysis and an important research area in machine

vision. The characteristics of different textures in an

image are first determined. These characteristics are

used to classify in view of classification and discrimina-

tion, and the feature vectors are obtained to build the

classifier. The feature vectors in the training set are

trained with a classifier, and finally the test set is classi-

fied using the trained classifier.

a. Feature extraction

First, each cloud image is decomposed by BEMD;

that is, the image is converted into grayscale and

decomposed to three IMFs and the residual. Then, the

two-dimensional data are transformed into the one-

dimensional data to calculate the Hilbert spectrum and

Hilbert marginal spectrum. After that, the features are

extracted, and a gross error test is performed.At last, the

cloud image is classified.

The Hilbert spectrums of the 10 types of ground

nephogram samples derived by the HHT are shown in

Figs. 3a–j. The number of pixels of the space is used as

the abscissa in Fig. 3, and there are a total of 2500 pixels.

The ordinate is the spatial frequency (wavenumber; per

meter).

The characteristic of the IMFs by BEMD is shown in

Fig. 3 in a graph with high resolution. The depth of color

represents the energy level in the color bars. The red

pixels mean that the energy level is relatively higher, and



FIG. 3. (a)–(j) The Hilbert spectrums of the 10 types of ground nephogram samples derived from the HHT. The

abscissa denotes the number of pixels, and the ordinate represents the spatial frequency (wavenumber;m21).



the blue pixels mean that the energy level is lower; it is

not very obvious in the limited resolution of the image,

seen more clearly in the three-dimensional time (space)–

frequency Hilbert spectrums. We can see that the fre-

quency of the IMF is not a constant value but fluctuates

around the central frequency—the higher the frequency,

the greater the volatility (Zhao et al. 2005). The figure

shows a detailed IMF component frequency change that

accurately reflects the time–frequency characteristics.

The signal discontinuity of frequency in time can be

clearly identified, and the main frequency can be accu-

rately distinguished without cross terms. In addition, the

time–frequency concentration appears very well.

TheHilbert spectrum of various types of cloud images

indicates that the number of pixels of some clouds is

fewer, as in Figs. 3d–g. The high energy of the cloud

image signal in the Hilbert spectrum is mainly concen-

trated in the low frequency within 50m21 because the

cloud images are uniform, curtainlike. Thus, stratiform

clouds are easy to identify from the other clouds ac-

cording to the Hilbert spectrum. The energy in Fig. 3a is

primarily concentrated within 150m21, but its pixels are

relatively denser.

The Hilbert spectrum of other types of cloud images

can be divided into two categories based on their con-

centration, although the pixels are dense. The number of

pixels for the first category of clouds is very dense, and the

frequency distribution of the signal varies from 0 to

500m21, such as in altocumulus (Fig. 3i) and cirrocu-

mulus clouds (Fig. 3j), which all belong to the wave cloud.

Their texture frequency distribution becomes wider be-

cause of the volatility of the cloud image texture. The

number of pixels for the second category of clouds is

moderately dense, and the frequency of the signal mainly

changes from 0 to 300m21, as shown in cumulonimbus

(Fig. 3b), cirrus (Fig. 3c), and stratocumulus clouds

(Fig. 3h). The first two clouds belong to the cumuliform

cloud, and the third (stratocumulus) is a wave cloud.

The above-mentioned cloud classifications are in ac-

cordance with the genetic-cloud classification, but there

are still two other types of clouds that are different from

those already discussed. First, stratocumulus cloud,

which belongs to the wave cloud, is classified as the last

category. The reason for this is that its overall shape is

characterized by wave cloud, while its local form is

similar to cumuliform cloud and only partial cloud im-

ages are selected as the cloud image sample for the

calculation, thus resulting in the classification of cumu-

liform cloud. Second, cumulus humilis, which belongs to

the cumuliform cloud, is classified as stratiform cloud.

This is mainly because cumulus humilis only covers the

sky partially, and the texture information of the sky is

more uniform and similar to the stratiform cloud.

Therefore, according to the texture frequency of the

Hilbert spectrum, clouds can be basically divided into

three main types—that is, stratiform, cumuliform, and

wave cloud.

To further describe the accumulated amplitude dis-

tribution of cloud image in each frequency and to ef-

fectively extract the Hilbert spectrum information of

different clouds, the Hilbert marginal spectrums of the

10 types of ground nephogram samples are derived from

time integration of the Hilbert spectrum in Figs. 4a–j.

The abscissa denotes the spatial frequency (wave-

number; per meter), and the ordinate represents the

amplitude.

The texture frequency distribution characteristics of

the three types of cloud images are shown in Fig. 4.

Several typical cloud images can be further identified by

the Hilbert marginal spectrum. The frequency distribu-

tion range of the three main types of clouds can be more

clearly seen from the information of the amplitude and

frequency in the Hilbert marginal spectrum. The texture

frequency range of stratiform cloud, such as stratus

(Fig. 4d), nimbostratus (Fig. 4e), altostratus (Fig. 4f),

and cirrostratus (Fig. 4g), varies from 0 to 150m21. The

frequency of the most amplitude accumulation is within

10m21, and the frequency changes comparatively

monotonically. The texture frequency range of cumulus

humilis of cumuliform cloud (Fig. 4a) is from 0 to

150m21, but its frequency is much more varied. The

texture frequency range of cumulonimbus (Fig. 4b),

cirrus (Fig. 4c), and stratocumulus (Fig. 4h) is from 0 to

300m21. The texture frequency range of wave cloud,

such as altocumulus (Fig. 4i) and cirrocumulus (Fig. 4j),

is from 0 to 500m21.

To further extract information, the texture frequency is

filtered when its amplitude is less than 10% of the max-

imum. Therefore, themaximum frequency is extracted as

the eigenvalue for the amplitude information.

b. Classification process

In the classification process, a target cloud image is

first decomposed by BEMD, and its Hilbert spectrum

and Hilbert marginal spectrum are calculated. Then,

the texture frequency is filtered to extract the maxi-

mum frequency as eigenvalue. Finally, the target

cloud is classified into a category according to its main

feature.

After repeated experiments, clouds are divided into

three categories according to the eigenvalues: less than

150, between 150 and 300, and larger than 300m21.

c. Recognition results

According to the above-mentioned analysis, 115 cloud

images samples were identified and the experimental



FIG. 4. (a)–(j) TheHilbert marginal spectrums of the 10 types of ground nephogram samples derived from the

time integration of the Hilbert spectrum. The abscissa denotes the spatial frequency (wavenumber;m21), and

the ordinate represents the amplitude.



results are displayed in Table 1. It is the confusionmatrix

of classification. Three different clouds are distin-

guished: low-, mid-, and high-frequency clouds. Among

them, low-frequency clouds include stratus, nimbostra-

tus, altostratus, cirrostratus, and cumulus humilis. Mid-

frequency clouds include cirrus, cumulonimbus, and

stratocumulus. High-frequency clouds include altocu-

mulus and cirrocumulus.

The experimental results show that the typical

ground-based cloud images are preliminary classified

using this method. The cloud classification is exceed-

ingly complicated. First, the cloud is divided into cate-

gories, and then subdivided according to other

characteristics. This method coincides with the idea of

a weather observer.

Figure 5 shows an original sample of altostratus, the

associated Hilbert spectrum, and the Hilbert marginal

spectrum decomposed by the BEMD algorithm. In

Fig. 5b, the abscissa denotes the number of pixels and

the ordinate represents the spatial frequency (wave-

number; per meter). In Fig. 5c, the abscissa denotes

the spatial frequency (wavenumber; per meter) and

the ordinate represents the amplitude. Further study

finds that the distribution of the pixels in the Hilbert

spectrum can well describe the uniformity of the cloud

image grayscale texture, such as the altostratus in

Figs. 2f and 5a. Their Hilbert spectrum and Hilbert

marginal spectrum are compared. Few pixels are

found in the mid-frequency of Fig. 5b compared to

Fig. 3f, and two extra peaks appear in Fig. 5c com-

pared to Fig. 4f. The altostratus in Fig. 5a contains the

outline of the sun. Thus, the sun in the background of

altostratus can also be recognized by the frequency

distribution of the Hilbert spectrum and the Hilbert

marginal spectrum.

5. Conclusions

In this paper, we presented a cloud image feature

extraction method based on the Hilbert spectrum of

BEMD that can efficiently extract the minutiae of

a texture image. The experimental results showed that

FIG. 5. (a) An original sample of altostratus, (b) the associated Hilbert spectrum, and (c) the Hilbert marginal

spectrum decomposed by the BEMD algorithm. In (b), the abscissa denotes the number of pixels, and the ordinate

represents the spatial frequency (wavenumber;m21) In (c), the abscissa denotes the spatial frequency (wave-

number;m21), and the ordinate represents the amplitude.

TABLE 1. The confusionmatrix of classification for 115 cloud images samples. Refer to the text for a list of clouds in each frequency.A total

of 107 images are correctly classified and eight images are misclassified.

Low-frequency clouds Mid-frequency clouds High-frequency clouds Total Correct rate (%)

Low-frequency clouds 54 3 1 58 93.10

Mid-frequency clouds — 32 1 33 96.97

High-frequency clouds — 3 21 24 87.50



this method is a simple but effective one for cloud

image feature extraction. The time–frequency density

and the trend of the energy with time–frequency can be

easily identified from the Hilbert spectrum because of

its high time–frequency resolution and superior capa-

bility of describing local time–frequency characteris-

tics. The HHT is applied to the ground-based cloud

image analysis and processing. The precise time–

frequency structure of the cloud image texture can be

obtained by HHT to facilitate ground-based cloud

image recognition.

There are still some problems with the HHT, how-

ever, such as the end effect, the interpolation method,

parametric forms, and normalization processing, among

others. It takes a longer time for complex BEMD.

Therefore, considerable research is needed to refine the

algorithm in order to increase the rate of decomposition

in the future.

Acknowledgments. This project is supported by the

National Natural Science Foundation of China (Grants

41305137, 61272379, 61105048, and 41205125), and the

Specialized Research Fund for the Doctoral Program of

Higher Education of China (Grant 20110092120034).

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texture feature extraction method for ground nephogram

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