Elliptic Fourier Descriptors in the Study of Cyclone Cloud Intensity Patterns

Ishita Dutta & S. Banerjee
International Journal of Image Processing, Volume (7) : Issue (4) : 2013 402
Elliptic Fourier Descriptors in the Study of Cyclone Cloud
Intensity Patterns
Ishita Dutta idutta_kalyani@yahoo.co.in
Department of Computer Science and Engineering
West Bengal University of Technology
Kolkata 700064, India
S. Banerjee sreeparnab@hotmail.com
Department of Natural Science
West Bengal University of Technology
Kolkata 700064, India
Abstract
Cyclone cloud intensity analysis is conducted to study the evolution of a cyclone storm mainly
using two approaches, namely: wind field analysis and pattern recognition. Of the pattern
recognition based approaches , the Dvorak technique has been a pioneering effort which is
widely used today. However, the Dvorak technique is subjective, as it relies on human judgment
and is, therefore, error prone. Efforts have been described in the literature to automate the
classification process. In this paper, we describe our efforts to perform a semi-automatic
computer analysis of the cyclone cloud intensity evolution pattern which compares preprocessed
visible (VIS) and enhanced infra-red (EIR) satellite images with the corresponding prototype
Dvorak patterns using Elliptic Fourier Descriptors (EFD) and Principal Component Analysis (PCA)
techniques. This novel approach is simple and intuitive and is robust to noise, and at the same
time provides classification in cases where the cyclone exhibits fluctuations during its evolutionary
cycle.
Keywords: Cyclone Cloud Intensity, Dvorak Technique, Elliptic Fourier Descriptors, PCA, Spiral
Band.
1. INTRODUCTION
A Tropical Cyclone (also known as hurricane / typhoon) is an area of low atmospheric pressure
characterized by rotating and converging winds and ascending air, with the central core being
warmer than the surrounding atmosphere. The evolution of the cyclone is manifest as changing
cloud intensity patterns, with the development of a central eye at an early stage of its evolution
surrounded by spiraling cloud bands of varying intensity. The cyclone then intensifies, matures
and finally dissipates. At each stage of its evolutionary sequence, the cyclone is characterized by
a set of physical parameters related to wind intensity, as well as characteristic cloud intensity
patterns obtained from Visible (VIS) and Enhanced Infra-Red (EIR) images obtained using
satellite technology. Hence, there are two approaches to TC intensity determination: namely
pattern matching and wind field analysis [1,2]. In this note we will describe our attempts in the
study of cyclone cloud intensity patterns from VIS and EIR images. A pioneering effort in
comprehensive pattern recognition based analysis for estimating tropical cyclone intensity from
satellite imagery can be attributed to Dvorak [3] for visible and, later EIR [4] images. The latter
set of images wears the additional advantage that intensity estimates can be made at night.
Dvorak describes the evolution of the cyclone through the various stages of evolution, viz.,
formation from a disorganized cloud structure through intensification, maturity and finally
dissipation using different cloud intensity templates, as depicted in Figure 1. Satellite images are
matched by visual inspection with these templates to obtain a classification using a characteristic
number referred to as T-number. There are eight different T-numbers for the different stages.

However, Dvorak's technique [5] is based on human judgement, requires expert training and is
thus, subjective. Hence, there have been a number of attempts to automate this analysis
procedure over the past three decades. This paper presents a semi-automated approach to
classify cyclone images based on Dvorak's technique.
2. PREVIOUS WORK
The pattern recognition based approaches can be broadly classified into three categories. The
earlier approaches focussed on the location of the cyclone eye. These include Griffin et. al. [6]
who have defined the geometric centre of the TC eye wall. Wood [7] used an axi-symmetric
hurricane vertex flow model to locate the ideal TC. Using Doppler velocity data, a TC is identified
by locating areas with cyclonic shear, and its center is then located by the identification of
extreme Doppler velocity value duplex. However, this method only works well for an ideal TC.
Later approaches in this category include those of Tsang et. al. [8] and Pao and Yeh [9]. Tsang
et al. [8] suggested morphology operations like erosion and region growing to automatically locate
the TC center but their approach is limited to TCs whose main bodies are the most significant
characteristics of circle regions. Using infrared and visible time series satellite images, Pao and
Yeh [9] have attempted to locate the center of the typhoon and segment it from the background
using morphology operations and statistical image classification methods. Some other distinctive
features from slices of typhoon satellite cloud images, especially the rotation feature of wind
movement vector were also found.
Another set of approaches involved the extraction of the contours of the dominant cyclone and
compared with templates either generated from modeling based on the spiral helix equation or
from prototype images. The works of Lee et. al. [10], Lee et. al. [11], Lui et. al. [12], Zhang et. al.
[13] and Pineros et. al. [14], fall into the category of matching with prototype images. Lee
et.al.[10] proposed a neural oscillatory elastic graph matching (NOEGM) model, for automatic TC
pattern identification and track mining. The procedure is comprised of three steps, feature
extraction, segmentation of cyclone contours using neural oscillators and elastic graph matching.
This procedure could not develop a high level data mining and pattern prediction model by the
generation of the time dependent relationship of the TC templates based on the past TC cases.
Therefore they (Lee et. al.[11]) have proposed another elastic graph dynamic link model
(EGDLM) based on the elastic contour matching to automate Dvorak technique. Lui et al. [12]
proposed the use of angle features and time warping for TC forecast. The Gradient Vector Flow
(GVF) snake model is applied to extract the contour points a tropical cyclone from the satellite
image. Similarity among Dvorak templates and the candidate cyclone were retrieved using angle
features found among the successive contour points. Zhang et. al. [13] extended the model of
artificial ant colony (AAC) to continuous space by aid of multi-kernel Gaussian functions. The
whirling shapes of real unclear typhoon eyes are simulated by snake contour boundaries.
However, the stability of calculation, the selection of an effective initial Gaussian kernel and its
deviation need to be improved. In addition, the performance of Gaussian parameter calculations
may limit the number of selected kernels. Pineros et. al. [14] propose a technique using gradient
vectors for obtaining features associated with shape and dynamics of cloud structures in
cyclones. This method was not able to characterize intensity curves of some systems which
exhibit extremely strong oscillations on time frames of 18–20 hours that overwhelm the intensity
trend.
The third category, which is an extension of the second category, uses gradient vectors along
the contours of the cyclone pattern. Contour matching based on the mathematical modeling of the
spiral band of the cyclone is also performed. Wong et. al. [15] modelled the spiral rain-band of a
TC by a polar equation given below, in which all vectors are tangents to the logarithmic spiral
R=ae
θcot (α)
where (R, θ) are the polar co-ordinates at any point R is radial coordinate and θ the angular
coordinate, a determines the rate of growth of the spiral, and α (pitch angle ) is the angle between
the radial line and the tangent to the spiral at (R, θ ). Cot (α) is the rate of change of R w.r.t. θ per
(1)

unit R. Templates generated by the estimated parameters are then used to match against radar
images at plausible latitude– longitude positions. By using a genetic algorithm suggested by Yip
and Wong [16] this method is automated by Wong et. al. [17]. Such a model may be unsuitable if
images are sampled infrequently, or when TCs are rapidly moving. In another paper Wong et. al.
[18] introduced a method of finding the centers of circulating and spiraling vector field patterns
that can handle vector fields with multiple centers and is robust against noise. However, some
vector field parameters must be defined beforehand, which limits the method’s applicability. Wei
and Jing [19] have also performed optimization of the spiral band model. Also, a novel Spiral
Band Model (SBM) is designed to extract and describe the spiral pattern of a spiral
band which spirals out from a TC's center.
Although Fourier descriptors have been used extensively for boundary description, matching and
recognition, no work appears to have been done in using Fourier Descriptors or Elliptic Fourier
Descriptors (EFD) for decomposing cyclone cloud intensity shapes. Abidi and Gonzalez [20]
have decomposed time varying shapes associated with cells of tornadic thunderstorms using
EFD. These time varying shapes evolve rapidly, in a matter of a few seconds. In this work we
only use primary, EIR and VIS patterns. The next sections outline the Methodology, followed by
Results and Discussion and finally some Concluding Remarks and Future Work.
3. METHODOLOGY
Satellite images of several cyclones /hurricanes/typhoons spanning over two decades have been
used for the study. Of these 252 images, 227 are EIR images and 15 are visible images. As
depicted in the flowchart of Figure 2, the input images are first pre-processed followed by shape
analysis in the post-processing stage.
3.1 Pre-processing
In the pre-processing step, image enhancement and filtering is applied to obtain high quality
images.A median filter is used to remove additive noises. In order to separate the target image (
dominant cyclone ) from the background, segmentation is performed. The segmentation,
binarization, opening and hole filling operations are carried out subsequently, following Guo et.
al.'s [21] methodology for galaxy image segmentation. This is done using Otsu's [22]
thresholding which separates the predominant cyclone from the background. Otsu's algorithm
for automated thresholding is a popular choice in 2D scenes because it is simple to implement,
easy to use and gives satisfactory results in 2D when number of pixels in each class are close
to each other. A small offset ranging from -0.2 to 0.3 was given in some cases to improve the
visual quality of the results. After binarization, an opening operation was performed to remove
neighboring cloud disturbances from the dominant cyclone (to be referred to as the region of
interest or ROI ). A hole filling operation was then performed for boundary extraction. The
boundary can then be chain coded using the Freeman code [23] for segmentation purposes.
This chain coding procedure is implemented as part of the SHAPE package to be described
below.

FIGURE 1: Typical Dvorak templates for cyclone cloud intensity patterns (from [35]).
3.2 Post Processing
The second part of our procedure is the post-processing part which involves shape analysis. For
this purpose we use the SHAPE software package developed by Iwata ans Ukai [24]. SHAPE is
an open-source software that was originally used for the analysis of biological shapes. This
package extracts the contour shape from a full color bitmap image, delineates the contour shape
with Elliptic Fourier Descriptors and finally performs the Principal Component Analysis (PCA) of
the EFDs for summarizing the shape information. The package, SHAPE is open source and easy
to use as a researcher can analyze 2 D shapes on a personal computer without special
knowledge about procedures related to the method. However, in the following, details of the
processes involved will be described below, for completeness. It may also be noted in passing
that, SHAPE is characterized by the following features: (1) the packaged programs are easily
operated with the aid of a graphical user interface (GUI); (2) No special computer devices for
image processing are required; (3) A large number of samples (say 1,000) can be treated; (4)
The scores of principal components are stored in tabbed text format files and can be easily
exported for analysis by other software; and (5) The variations in shape accounted for by the
principal components can be visualized and printed out.
SHAPE essentially performs the following operations on our images: After noise reduction, the
closed contour is extracted by edge detection. The contours of the cyclone cloud shapes
(candidate images) are then encoded in the Freeman chain code form and then approximated
with the coefficients of Elliptic Fourier Descriptors. (EFD). The coefficients of the EFDs are
normalized to be invariant with respect to size, rotation and starting point.
Principal Component Analysis (PCA) is then performed to reduce dimensionality, based on the
variance-covariance matrix of scores. He scores of derived principal components are also
calculated and stored in text format files which were used for quantitative analysis. SHAPE also
visualizes shape variations accounted for by each principal component. Reconstructed contours
can be printed. The classification is performed with the help of PCA. There are 6 classes of
prototype images images used for the classification of both for EIR and VIS images,
corresponding to T-numbers T1.5, T2.5 etc., increasing in steps of unit T numbers. There are 252
candidate images of which 227 are EIR images which were classified. Since there are at most
three to five spiral turns due to the banding effect of the cyclones, we have used five harmonics,
although for our results, results converged for three harmonics.

FIGURE 2: Flowchart for the Proposed Algorithm.

Cyclone Name Number of
Images
Number of
Images Whose
Computed T-
numbers are in
Agreement with
Indian
Meteorological
Department (IMD)
Percentage (%)
Agreement
Comments
Aila 29 28 96.55 Excellent
Bijli 50 35 70 Fairly Good
Phyan 24 19 79.2 Fairly Good
Rashmi 14 10 71.42 Fairly Good
Ward 4 4 100 Excellent
TABLE 1: Comparison of calculated table numbers with IMD T-numbers.
Cyclone
Name
Number
of
Images
Number of Images Whose
Computed T-numbers are
in Agreement with Cyclone
Evolution Trend
Percentage
(%) Agreement
Comments
Emily 9 8 89 Very Good
Andrew 4 3 75 Fairly Good
Roxanne 10 7 70 Fairly Good
Nargis 7 6 86 Very Good
Irene 9 8 88 Very Good
Others
(Elida,
Jeanne,
Darby,
Flossie)
4 3 75 Fairly Good
TABLE 2: Comparison of Calculated T-numbers with Cyclone Evolution Trend.
A similar procedure is repeated for prototype images corresponding to the Dvorak [3,4] templates.
The Euclidean distances between the score value of candidate images we have used and the
prototype images are then computed. The best match corresponds to the minimum Euclidean
distance between the candidate and prototype image, and the T-number obtained from the
prototype image is taken to be the T-number of the candidate image.
After chain coding using the Freeman code [23] , SHAPE then approximates the cyclone contours
using Elliptic Fourier Descriptors (EFD) proposed by Kuhl and Giardina [25] , who claim that
there are several advantages of EFDs over standard Fourier descriptors. Firstly, integration and
Fast Fourier transforms are not required. Moreover, bounds on the accuracy of image contour
reconstruction are easy to specify. In addition, EFDs provide a convenient and intuitively pleasing
procedure of normalizing a Fourier contour representation. The steps that have been followed for
obtaining EFDs in SHAPE have been outlined below (Yoshioka et.al. [26]).
Each contour is represented as a sequence of x and y coordinates of ordered points that are
measured counter-clockwise from an arbitrary starting point. Assume that the contour between
the (i-1)-th and the i-th chain coded points is linearly interpolated, and that the length of the
contour from the starting point to the p-th point and the perimeter of the contour are denoted by tp
and L, respectively. The quantity tp is defined as:

and L = tK.
Here Δti and K are the distances between the (i - 1)-th and the i-th points and the total number of
the chain-coded points on the contour, respectively. One point to note is that the K-th point is
equivalent to the starting point. The x and y coordinates of the p-th point are
And
where Δxi and Δyi are the distances along the x and y axes between the (i - 1)-th and the i-th
point. Thus, the elliptic Fourier expansions of the coordinates on the contour are
and
with summation n=1, …, ∞, and an, bn, cn, and dn being the Elliptic Fourier coefficients of the n-th
harmonic and P being the period. As said earlier the coefficients of an elliptic Fourier descriptor
[20],[25], are not invariant in size, rotation, shift and starting point of chain-coding about a
contour, the Fourier coefficients are standardized (Yoshioka et al. 2008). Let the standardized
coefficients of the n-th harmonic be an**, bn**, cn** and dn**. Then,
Where
and
(2)
(3)
(4)
(6)
(7)

In the above equations, E* is the distance between the centre point (A0, C0) and a specific point
(xq, yq), and ψ is the spatial rotation angle. These two parameters are for the size invariance and
the rotation invariance. θ is a parameter for chain-code starting point invariance. This
standardization makes an**, bn**, cn** and dn** independent of the size, rotation, shift and chain-
code starting point of a contour. The coefficients of the EFDs are thus, subsequently normalized
to be invariant with respect to the size, rotation, and starting point, with the procedure based on
the ellipse of the first harmonic. The normalized coefficients of the EFDs can still not be used
directly as shape characteristics because the number of coefficients is generally very large and
the morphological meaning of each coefficient is difficult to interpret separately and so, Principal
Component Analysis (PCA) is to be performed.
Principal component analysis is effective for summarizing the information of the variations
contained in the coefficients. The scores of the derived principal components are also calculated
and stored in text format files, which can be provided as input files for the various subsequent
analysis. Then scores of the derived principal components are calculated. Then, score values for
the Principal component for candidate images and model images are calculated. Then the
Euclidean distance between a particular candidate image and all the model images are calculated
and the best match is chosen.. This process was performed both for candidate and prototype
images.
4. RESULTS
The images that we have used in our study include image sequences (i.e. images depicting
successive stages of evolution of the cyclone) of cyclone Ward , cyclone Aila, cyclone Phyan , as
well as images of hurricane Emily, hurricane Andrew, hurricane Roxanne, Nargis and individual
images of hurricanes Elida, Jeanne, Darby and Flossie. Some images of the recent hurricane,
Irene have also been been included in our study.
Input images are first digitized and subsequently Otsu's method is applied with a small offset
ranging from -0.2 to 0.3 to threshold the images. Then morphological opening operation is applied
with the structuring element of disk shaped with a radius of 60 pixels. This is followed by a hole
filling operation to enable boundary extraction. Figure 3 depicts images of cyclone Ward,
hurricanes Emily, Andrew and Roxanne (first column) and the images after Otsu thresholding
(column 2), morphological opening (column 3) and hole filling (column 4), respectively.
During the post-precessing stage, the software package SHAPE extracts contours and assigns
chain codes to the contours. Then EFDs are extracted followed by PCA. PCA results of
candidate images are compared with PCA results of prototype images corresponding to the
Dvorak templates. Best matches correspond to the minimum Euclidean distance between
candidate and prototype images. Figure 4 gives principal components for Andrew (EIR T1.5) and
Emily (VIS T1.5) with the template images with which they are matched.
Results obtained will be discussed under two categories. In the first category, our results will be
compared with the T-numbers estimated by meteorological experts. In the second category, we
correlate our results with reports of cyclone evolution trends. In the second set of experiments, T
numbers of the cyclones were determined with the algorithm described above and compared with
the description of the cyclone evolution given in the reports, since some cyclones have been
described with the help of the Saffir Simpson Hurricane Scale (SSHS) a gradation scheme for
hurricanes, based on wind field analysis. This set of experiments have been conducted on
hurricanes Emily, Andrew, Roxanne, Irene and Nargis image sequences, as well as as individual
images of Darbie, Elida, Flossie and Jeanne.
Cyclone Ward [27] formed and intensified to storm status and further intensified to cyclone
status before finally weakening due to wind shear and eventually dissipating. Cyclone Nargis [28]
formed and quickly intensified to severe storm status before weakening and dissipating. Table 1
gives the comparisons of the T-numbers obtained using our methodology with the data for the

cyclones obtained from the Indian Meterological Department (IMD). Hurricane Emily [29] formed
and intensified to cyclone status and again fluctuated from moderate to severe cyclone storm
status before weakening and finally dissipating. Our analysis indicates an increase of T number
from 1.5 to 4.5, followed by a subsequent decrease to 3.5, an increase to 6.5 and finally a fairly
stable period with T number of 5.5, followed by another increase to 6.5 and finally, a gradual
decrease. This fluctuation corroborates with the report [29]. Hurricane Andrew [30] also followed
a similar pattern of fluctuations after formation and intensification to storm status and eventually
dissipating. Hurricane Roxanne had a confusing formation [31] and fluctuated frequently
between low intensity and severe cyclone storm status before finally dissipating. Such behaviour
patterns of cyclone storms indicate irregularities and deviations from a model cyclone evolution
pattern, as is true of any natural phenomena. The cyclones had been assigned categories based
on the SSHS scheme at different stages. The T-numbers corresponding to each of these
categories can be obtained from conversion tables and the T-numbers thus obtained give an
indication of the cyclone evolution trend. We compared our results with the T-numbers obtained
from these conversion values. In Table 2, we compare our results with the values obtained from
this cyclone evolution trend (obtained from reports on the Internet [32]) . Table 3 provides
calculations for obtaining the Receiver Operating Characteristics (ROC) and Table 4 provides the
Confusion Matrix for the T-numbers that we have classified versus the T-numbers manually
assigned. This table gives an indication of the true and false classification rates. Figure 8 shows
the ROC curve with TP indicating True Positive and FP indicating False Positive. The Area Under
the Curve of the ROC curve (Figure 5) was 0.8278 indicating an 82.78% agreement with
predicted values.

F
i
g
.
3
(
a
)
F
i
g
.
3
(
b
)
F
i
g
.
3
(
c
)
F
i
g
.
3
(
d
)
FIGURE 3: Images of Ward, Emily, Andrew and Roxanne after image preprocessing in rows 1-4, respec
-tively.
Our proposed methodology falls under the second category. As with other approaches under this
category, we preprocess the images using noise removal, Otsu thresholding, morphological
operations like opening and filling, as appropriate. After preprocessing we use the SHAPE
package for boundary extraction, chain coding, use of the EFD and PCA analysis, after which
comparisons are made between the candidate and prototype (Dvorak template) images. Hence
our matching procedure is based on shape descriptors. It may be mentioned here that, SHAPE
can convert a color image to a binary image, remove noise and perform thresholding before
boundary extraction and subsequent operations that we have used the package for.

T-number Total number of
images matched with
the original T-number
(TP)
Total number of
images
mismatched with
the original T-
number (FP)
Cumulative Rate
TP FP
T1.5 11 1 0.0558 0.0256
T2.5 110 22 0.614 0.564
T3.5 35 9 0.792 0.821
T4.5 18 2 0.883 0.872
T5.5 13 4 0.949 0.974
T6.5 11 1 1.0 1.0
Total 197 39
TABLE 3: Calculation of Receiver Operating Characteristic (ROC).
Predicted Class
Actual
Class
T1.5 T2.5 T3.5 T4.5 T5.5 T6.5
T1.5 11 1 0 0 0 0
T2.5 12 107 5 3 0 0
T3.5 0 3 35 5 1 0
T4.5 0 0 1 15 1 0
T5.5 0 0 2 2 13 1
T6.5 0 1 0 0 0 9
TABLE 4: Confusion Matrix for the Algorithm.
5. DISCUSSIONS AND FUTURE WORK
This paper describes a novel approach to study the evolution of cyclones using both VIS and EIR
satellite images of cyclone cloud intensity patterns. As discussed earlier, there are broadly three
categories of pattern matching analysis of cyclones. The first approach focuses on the extraction
of the eye. Most of the earlier approaches and also some later approaches fall under this
category. The second and third categories involve a segmentation procedure after image pre-
processing to extract cyclone cloud intensity contours. Subsequently, efforts in the second
category attempt to match these images with Dvorak prototypes using soft computing techniques
like neural networks, genetic algorithms, ant colony optimization, etc.,. Another set of
approaches under this category involve generating gradient vectors or angle features at
different points along the contour and matching these features with prototypes. The third category
involves fitting the contours to curves generated from mathematical models (e.g. logarithmic helix,
spiral band, etc.,).

5.1 Comparison with Other Work
The location of the cyclone “eye” is important as the very existence and metamorphosis of the
cyclone is dependent on its presence, and hence, the detection of the eye does play an important
role in cyclone evolution analysis. However, the typical cyclone contour is “comma” shaped and
so the degree of spiralling of the curved band is indicative of the different stages of evolution of
the cyclone and thus, the approaches of the second and third categories provide a clearer picture
of the cyclone evolution. Mathematical models provide exact shapes, but cyclones being natural
phenomena do not always correspond to regular curves. So an empirical image matching
scheme with prototypes could give a good estimate of cyclone evolution trends. Our correct
classification rate of 83% percent compares favorably with the other techniques in all these
categories. Lee and Liu [11] have claimed an overall accuracy of 82% and found that EIR images
give better results because of a better spiral pattern. Their earlier effort [10] yield an overall value
86% for track intensity mining but their efficiency depended on the inter-relationship of successive
pictures. Pao and Yeh [9] claimed a correct classification rate of 82% while locating the center
and contour of the typhoon. Pineros et. al. [14] achieved correlation rates ranging between 82-
86% with the highest being for instances where the maximum hurricane strength was achieved.
Liu et. al. [12] achieved a 10% (72.41%) improvement of human visual justification (62.86%).
The methodology that we have proposed has not been used previously, to the best of our
knowledge. In an earlier attempt [33] we have used a different preprocessing technique involved
a classical edge extraction template followed by erosion and dilation. However, edge detectors
produce broken contours and so we have replaced [34] this earlier methodology with a filling
algorithm to produce closed contours before performing boundary extraction followed by Freeman
chain code implementation that is available in SHAPE. This has improved the results by 16%.
The use of Elliptic Fourier Descriptors has several advantages over Fourier descriptors.
Integration or use of fast Fourier techniques are not required and bounds on the accuracy of the
image contour representation are easy to specify.
EFDs are convenient and Fourier contour representations can be conveniently normalized and is
thus useful for the analysis of well defined 2D contours. Dvorak templates are widely used and
we have also used them as they capture the essence of the intensity patterns effectively. As
EFDs involve the use of many coefficients, PCA is used to reduce the dimensionality. In the
earlier attempt [33] we had used 20 harmonics in the PCAbased classification , but because there
are at most three to five spiral turns, we have used five harmonics, although our results
converged after three harmonics. The degree of banding and thus the evolutionary stage of the
cyclone can thus be described.

Particular of Candidate
and Model image
PCA of Candidate image PCA of model image
The principal component
of the candidate image
Andrew 2 and the model
image EIR(T 1.5) with 5
harmonics.
The principal component
of the candidate image
Emily and the model
image VIS (T1.5) with 5
harmonics.
FIGURE 4: Principal component of candidate images of Hurricanes Andrew and Emily and template images
with which they are matched.
EFDs are convenient and Fourier contour representations can be conveniently normalized and is
thus useful for the analysis of well defined 2D contours. Dvorak templates are widely used and
we have also used them as they capture the essence of the intensity patterns effectively. As
EFDs involve the use of many coefficients, PCA is used to reduce the dimensionality. In the
earlier attempt [33] we had used 20 harmonics in the PCAbased classification , but because there
are at most three to five spiral turns, we have used five harmonics, although our results
converged after three harmonics. The degree of banding and thus the evolutionary stage of the
cyclone can thus be described.
5.2 Future Work
Future work will heve to focus on a clear extraction of the eye and also try to integrate the
preprocessing stage with boundary extraction, chain coding, etc. and to automate the whole
process. This work will have to be extended to larger datasets in order to standardise the
technique for cyclone intensity prediction. Also, a more accurate registration scheme between the
SSHS scheme and Dvorak technique needs to be formulated and designed, in order to provide a
more accurate prediction technique. The methodology will also have to be improved to cater to
situations where the storm interacts with unfavourable environments such as land or wind shear.
The database to be used should also include complicated situations where there are several
cloud structures located within the disturbance, or when the shape of the cloud structures are
elongated.
One of the most challenging problems is to predict the cyclone formation at an early stage of
development, and hence, another long term goal is to incorporate cyclogenesis in this study.
6. ACKNOWLEDGMENTS
The authors are thankful to the University Grants Commission (UGC) Government of India (major
grant no.37-534(09)) for their support. Images of cyclones in the Bay of Bengal and Indian Ocean
were obtained from the Indian Meteorological department, New Delhi, India. Images of hurricanes
and typhoons were obtained from the NOAA website.

FIGURE 5: Data fitted with Receiver Operating Characteristic Curve.
7. REFERENCES
[1] K. Emanuel “A Statistical Analysis of Tropical Cyclone Intensity”, Monthly Weather Review,
128, pp.1139-1152 (2000).
[2] C. C . Chao G. R. Liu, C. Liu , “Estimation of the upper-layer rotation and maximum wind
speed of tropical cyclones via satellite imagery”, Journal of Applied Meteorology and
Climatology , 50(3), pp.750-766 (2011).
[3] V. Dvorak. “Tropical cyclone intensity analysis and forecasting from satellite imagery”, Monthly
Weather Review, .103, pp.420–430 (1975).
[4] V. Dvorak “Tropical cyclone Intensity Analysis Using Satellite Data”, NOAA Technical Report
NESDIS 11, (1984).
[5] J.A. Knaff , D.P. Brown, J. Courtney , G. M. Gallina, J.L. Beven , “An Evaluation of Dvorak
Technique-Based Tropical Cyclone Intensity Estimates”, Weather and Forecasting, 25(5),
1362-1379, (2010).
[6] J.S. Griffin, R.W. Burpee, F. D. Marks, and J. L. Franklin, “ Real Time airborne analysis of
aircraft data supporting operational hurricane forecasting”, Weather and Forecasting, 7,
pp.480-490, (1992).
[7] V. T.Wood, “ A technique for detecting a tropical cyclone centre using a Doppler radar”,
Journal of Atmospheric and Oceanic Technology, 11, pp. 1207-1216, (1994).

[8] L. Tsang , LYyeh , M. Liu, Y.Hsu, “Locating the Typhoon Center from the IR Satellite Cloud
Images”, IEEE International. Conference on System, Man and Cybernetics (SMC 2006) pp.
484-488, (2006).
[9] T. L.Pao, and J.H. Yeh, “ Typhoon locating and reconstruction from the infra-red satellite
cloud image”, Journal of Multimedia, 3, 2, pp. 45-51, (2008).
[10] R. S. T. lee and j n k liu “Tropical cyclone identification and tracking system using
integrated neural oscillatory elastic graph matching and hybrid RBF network track mining
techniques,” IEEE Trans Neural Networks, 11,pp. 680–689, (2000).
[11] R.S. T. Lee , and J.N. K. Liu, “ An Elastic Contour Matching Model for Tropical Cyclone
Pattern Recognition”, IEEE Transactions on Systems Man and Cybernetics-Part B:
Cybernetics, 31, 3, 413-417, (2001).
[12] J.N.K. liu, b. feng , m. wang. and w. luo “Tropical Cyclone forecast using Angle Features and
Time Warping”, International Joint Conference on Neural Networks Sheraton Vancouver Wall
Centre Hotel, Vancouver, BC, Canada, pp-4330-37, (2006).
[13] Q. zhang , l. lai and h. wei “ Continuous space optimized artificial ant colony for real-time
typhoon eye tracking”, IEEE International Conference on Systems, Man and Cybernetics
(SMC) Washington DC: IEEE, pp.1470–1475 , (2007).
[14] M. F. Pineros, E.A. Ritchie, and J.S. Tyo, “ Objective Measures of tropical cyclone structure
and Intensity change from remotely-sensed infra-red data”, IEEE Transactions On
Geosciences and Remote Sensing, 46, 11, pp. 3574-3579, (2008).
[15] K. Y. WONG, C.L., YIP, P.W. LI, W. W. TSANG, “Automatic template matching method for
tropical cyclone eye fix”, Proceedings of the 17th International Conference on Pattern
Recognition(ICPR-2004), Cambridge UK., 3, pp. 650-653, (2004).
[16] C. L.YIP, K.Y. WONG, Efficient and effective tropical cyclone eye fix using genetic
algorithms, Proceedings of the 8th International Conference on Knowledge-Based Intelligent
Information and Engineering Systems (KES-2004), 3213 of Lecture Notes on Artificial
Intelligence, Springer-Verlag, Wellington, pp. 654-660, (2004).
[17] K. Y. Wong, C.L. Yip, and P.W. Li, “A tropical cyclone eye fix using genetic algorithm”,
Expert Systems with Applications 34, 643–656, (2008).
[18] K.Y. Wong and C.L. Yip “Identifying centers of circulating and spiraling vector field patterns
and its applications”. Pattern Recognition, 42, pp. 1371–1387, (2009).
[19]K. Wei , Z. L.Jing , “Spiral band model optimization by chaos immune evolutionary algorithm
for locating tropical cyclones”, Atmospheric Research, 97 (1-2), 266-277, (2010) .
[20]M.A Abidi. and R.C. Gonzalez “Shape Decomposition Using Elliptic Fourier Descriptors",
Proceedings. 18th. IEEE South-east Symposium on System Theory, Knoxville, TN, pp.53-61,
(1986).
[21] Q. I.Guo, F. Guo, J. Shao “Irregular Shape Symmetry Analysis: Theory and Application to
Quantitative Galaxy Classification", IEEE Trans. Pattern Analysis and Machine Intelligence,
Vol. 32, no. 10, pp.1730-1743,( 2010).
[22] N. Otsu “A threshold selection method from gray-level histograms,” IEEE Trans. Systems,
Man, and Cybernetics, vol. 9, no. 1, pp. 62-66, (1979).

[23] H.F reeman “On encoding of arbitrary geometric configurations,” IRE Transactions on
Electronic computers EC 10, pp.260-268, (1961).
[24]H. Iwata and Y. Ukai “SHAPE: A Computer Program Package for Quantitative Evaluation of
Biological Shapes”,Journal of Heredity, 93(5), pp.384-385, (2002).
[25] F.P. Kuhl AND C.R. Giardina “Elliptic Fourier features of a closed contour”, Computer
Graphics and Image Processing, 18, 236–258, (1982).
[26] Y. Yoshioka, H. Iwata, R. Ohsawa, S. Ninomiya “Analysis of Petal Shape Variation of
Primula sieboldii by Elliptic Fourier Descriptors and Principal Component Analysis”, Annals of
Botany 94, pp. 657–664, (2004) .
[27] INDIAN METEOROLOGICAL DEPARTMENT “Hurricane Ward: A Preliminary Report”,
Available at: http://www.imd.gov.in/section/nhac/dynamic/cycrptward.pdf [2009]
[28] NASA” NASA Study Finds 'Pre-Existing Condition' Fueled Killer Cyclone", Available at:
http://www.nasa.gov/topics/earth/features/nargis-20090226.html, (2009).
[29] J. L.Franklin and D. P. Brown “Tropical Cyclone Report: Hurricane Emily”, pp.1-18, (2006).
[30] E. N. RAPPAPORT “Hurricane Andrew”, Weather (49), pp. 51-61, (1992).
[31] L. AVILA L.Preliminary Report Hurricane Roxanne, Available at:
http://www.nhc.noaa.gov/1995roxanne.html
[32] INDIAN METEOROLOGICAL DEPARTMENT (2009) Hurricane Aila: A Preliminary Report,
Available at: http://www.imd.gov.in/section/nhac/dynamic/aila.pdf(2009)
INDIAN METEOROLOGICAL DEPARTMENT (2009) Hurricane Phyan: A Preliminary Report,
Avail-able at: (http://www.imd.gov.in/section/nhac/dynamic/cyclone2008)
[33] NATIONAL HURRICANE CENTRE (2001) Tropical Cyclone Report Hurricane Flossie
Availlable at:http://www.nhc.noaa.gov/2001flossie.html
[34]PASCH AND RICHARD Hurricane Jeanne Preliminary Report, National Hurricane
Centre,(1999) STEWART S. R. Tropical Cyclone Report Hurricane Darby, pp. 1-12, (2010).
[35] I. Dutta and S. Banerjee, “Shape Analysis of Satellite Images of Cyclone” ICCS 2013-
Second International Conference on Computing and Systems”, Burdwan, India, (2013).
[36] I. Dutta, S. Banerjee and M.De, "An Algorithm for Pre-Processing of Satellite Images of
Cyclone Clouds", in press, International Journal of Computer Applications (2013).
[37] V. F. Dvorak, “A technique for the analysis and forecasting of tropical cyclone
intensities from satellite pictures,” unpublished, 1973.

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