Liquid Crystal Image Analysis by Image Descriptors

Guilherme Enoc Egas de Carvalho

, Franklin C

esar Flores

, Fernando Carlos Messias Freire

and Anderson Reginaldo Sampaio

Department of Informatics, State University of Maring

a, Av. Colombo, 5790, 87020-900, Maring

a, PR, Brazil

Department of Physics, State University of Maring

a, Av. Colombo, 5790, 87020-900, Maring

a, PR, Brazil

Keywords:

Image Descriptors, Liquid Crystal.

Abstract:

Liquid crystals are substances with high impact technological, new substances have been discovered and the

properties of these materials need to be examined. When viewed under a microscope using a polarized light

source, different liquid crystal phases will appear to have distinct textures and colors. The use of digital image

processing and computer vision is being initialized in the analysis of these materials. The goal of this work

is to propose methods, based on visual descriptors, which are able to identify phase transitions and classify

phases in liquid crystals from a sequence of images.

1 INTRODUCTION

Most substances are found in the following states:

solid, liquid or gaseous. The process in which a sub-

stance changes from solid to liquid is deﬁned as fu-

sion. Besides it, there is a number of substances into

an intermediate state showing simultaneously physi-

cal properties of liquids and features of crystals. This

state is known as liquid crystalline and these sub-

stances are called as Liquid Crystals (LC). There are

many different types of phases in this state, which can

be distinguished by their different optical properties

(Fig. 1).

When viewed under a microscope using a polar-

ized light source, different liquid crystal phases will

appear to have distinct textures and colors. In gen-

eral, in a phase transition, the images have signiﬁcant

alterations related to optical properties. Such changes

may occur due to several factors such as temperature

and time. Physics researchers study phase transitions

as a way to ﬁnd alternative substances which have de-

sirable properties (Bahadur, 1992).

Figure 1: Examples of liquid crystals at different tempera-

tures.

Light polarizing-microscopy provides a sequence

of images which each image frame is acquired in

a distinct temperature. The physical characteristics

may be indirectly determined by image sequence

analysis (Sampaio and C., 2004). Statistical ap-

proach is a way to do such analysis (Montrucchio

and Strigazzi, 1998). This approach is simple to ap-

ply, however, some phase transitions are not clearly

observed in such approaches, what justiﬁes the design

of more complex techniques.

The goal of this work is the proposal of two meth-

ods to solve problems in liquid crystal research ﬁeld

by application of Visual Descriptors, which are usu-

ally applied to accurate representation of images. Vi-

sual Descriptors may be designed to several computer

vision applications; in this paper, Visual Descriptors

are applied to extract structures from the liquid crys-

tal images in order to make possible the measurement

of features that could characterize phases and transi-

tions.

The ﬁrst proposed method consists in the appli-

cation of Visual Descriptors as phase transition de-

tectors for liquid crystal analysis. This method re-

ceives as input a sequence images of liquid crystal,

makes calculations with visual descriptors and simi-

larity measures and returns a graph where phase tran-

sitions can be identiﬁed. The second one is the re-

trieval of images from a sequence which are closer

to an image parameter, which characteristics are used

as key features for the search, as occurs in a typical

Content-Based Image Retrieval (CBIR) system. The

531

de Carvalho G., Flores F., Freire F. and Sampaio A..

Liquid Crystal Image Analysis by Image Descriptors.

DOI: 10.5220/0004695805310537

In Proceedings of the 9th International Conference on Computer Vision Theory and Applications (VISAPP-2014), pages 531-537

ISBN: 978-989-758-003-1

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

main characteristics extracted are related to color, tex-

ture, spatial relationships and shapes (Snoek, C. and

Worring, M., 2005).

This paper is organized as follows: Section 2

presents some preliminary deﬁnitions. Section 3 in-

troduces the method to detect phase transitions by ap-

plication of Visual Descriptors. Experimental results

are shown in Section 4 and Section 5 concludes the

paper.

2 PRELIMINARY CONCEPTS

Content-based image retrieval (CBIR) systems search

similar images based on their characteristics: their

feature extraction algorithms obtain image proper-

ties using descriptors, and given a similarity function,

they calculate the similarity between two images.

Two important features may be used to describe

an image: color and texture. Color is widely used to

represent an image, it maintains its properties when it

functions as translation, rotation and scaling are ap-

plied the image. Texture is also an important property

for characterization and image recognition, consisting

in a simple assigment of a repeating pattern in which

the elements are arranged (Cess, G., Snoek, M. and

Worring, M. , 2005).

2.1 Color Moments

Color Moments are statistics moments of the distri-

bution probability of the colors and have been used

with success in image retrieval systems, speciﬁcally

when the image contain only one object. The values

of mean (µ), variance (σ

) and standard deviation (σ)

are color moments that have been proven to be efﬁ-

cient and effective in the representation of the colors

distribution in the images (Khokher, A. and Talwar,

R., 2012).

Color Moments descritor recover all the images

whose color compositions are similar to the composi-

tions color image query. However, they do not capture

spatial relationships between areas of the same color,

so its power to differentiate between images is lim-

ited.

Given an image I, of size M × N, the Color Mo-

ments given below

µ =

M ∗ N

∑

i=1

∑

j=1

(i, j)

(1)

σ =

M ∗ N

∑

i=1

∑

j=1

(i, j)

− µ)

(2)

deﬁne, respectively, the mean and the standard devia-

tion. Variance is given by σ

2.2 Color Histogram

The color histogram represents the color distribution

in the image, its mean represents the number of pixels

of each color tone in the image (Lew, M., Sabe, N.,

Djeraba, C. and Jain, R., 2006).

To extract features based on the color histogram,

it is ﬁrst necessary to quantize the image in a certain

amount of color. It is done due the sparseness of the

original color histogram itself. For example, in Fig.

2, the RGB color space (256 × 256 × 256) was quan-

tized in the RGB color space (2 × 2 × 2), thus reduc-

ing the number of possible color combinations. After

having quantized the image in a number of colors, the

histogram is created based on the color of each pixel.

Figure 2: Division of RGB Color Spacer.

2.3 Color Layout Descriptor

Color Layout Descriptor (CLD) is a descriptor de-

signed to capture the spacial distribution of color in

an image. The extraction process of features consists

in four steps (Manjunath B. S. and Sikora, 2002):

Figure 3: Steps of the Color Layout Descriptor.

1. Image partition: the query image is divided into

64 blocks to assure the invariance of scale and res-

olution (a).

2. Selection of representative color for each block of

VISAPP2014-InternationalConferenceonComputerVisionTheoryandApplications

532

the image: a single color is chosen to represent

each block (b).

3. Obtaining coefﬁcients of applying discrete co-

sine transform (DCT): the image icon is converted

from RGB color space to YCbCr color space, then

DCT is applied to each band in the image (Y, Cb

and Cr) resulting in three dimensional arrays of 64

DCT coefﬁcients.

4. Zigzag Scanning of the found coefﬁcients: is ob-

tained three feature vectors by applying a zigzag

scanning on coefﬁcient matrices. The zigzag

scanning aims to group elements of low frequency

(c).

Figure 4: Steps of the Color Layout Descriptor.

2.4 Co-occurrence

Co-Occurrence Matrix is a two-dimensional matrix,

generated from the count of occurrences of spatial

patterns in the neighbourhood of a pixel (Jain, R.,

Kasturi, R. and Schunck, B., 1995) (Sastry, S., Ku-

mari, T., Rao, C., Mallika, K., Lakshminarayana, S.

and Ha Sie Tiong, 2012).

For each of the possible combinations between

the pixel and the neighboring pixel, is created an el-

ement in the co-occurrence matrix, so that the size

of co-occurrence matrix is t × t, where t is the num-

ber of gray scale present in original image. The il-

lustrates better how is the process of building the co-

occurrence matrix.

Note that the value 1 was assigned to the element

(1,3) of the co-occurrence matrix. This value is repre-

senting the number of occurrences of the combination

[1 3] existing in the original image. How this combi-

nation [1 3] occurs only once in the image, is stored

in the element (1,3) the value 1. As for the element

(1,1), was placed the value 2, which symbolizes the

existence of two occurrences of the combination [1 1]

in the original image.

From the co-occurrence matrix, some interesting

characteristics can be obtained. They are: contrast,

correlation, energy and homogeneity.

2.5 Entropy of Gray Scale

Entropy represents the dispersion degree of the gray

levels of an image and can be used to characterize a

Figure 5: Example of Co-occurrence Matrix.

texture of image (Jain, R., Kasturi, R. and Schunck,

B., 1995).

Given a histogram h of an image I, Entropy can be

calculated as:

E =

∑

i=1

h(i) ∗ log

h(i) (3)

2.6 Similarity Measures

Once two feature vectors p and q for the images A and

B, respectively, are computed, it becomes necessary

to calculate the similarity between these two vectors.

Deﬁned as D(p,q) the similarity distance between the

features vectors p and q. If D is equal to zero, this

means that the two images may be identical and if D

is close to zero means that the images are similar.

Some well known equations for calculating the

similarity between two vectors are: Euclidean, Man-

hattan and Minkowski [4, 5 and 6].

D(p,q) =

∑

i=1

(p(i) − q(i))

(4)

D(p,q) =

∑

i=1

|p(i) − q(i)| (5)

D(p,q) =

∑

i=1

|p(i) − q(i)|

1/r

(6)

3 THE PROPOSED METHODS

This Section introduces the method to detect phases

transitions and the method to detect phases in the

analysis of liquid crystal image sequences.

LiquidCrystalImageAnalysisbyImageDescriptors

533

3.1 Phase Transition Detection

The method to detect phase transition receives as in-

put a liquid crystal image sequence and outputs a set

of phase transition temperatures. Let n be the number

of the images in the image sequence. Each frame of

the image sequence is processed by color or texture

visual descriptor. For each frame i, it is extracted a

feature vector V

= hv

,..., v

i that represent the

frame i. It is done for each frame in order to create

an DV = hd

,..., D

i distance vector where, for

each i, d

= D(V

(i−1)

. The elements of DV may

be sequentially considered as values of a one dimen-

sional function. The Fig. 8 to Fig. 12 show the

plotting of DV for the same input liquid crystal im-

age sequence computed by several visual descriptors.

Peaks and valleys for each plotting represents a pos-

sible phase transition. To calculate the values of the

peaks and valleys of the found function, just check

where the ﬁrst derivative of the function is equal to

zero. Since images contain light interference and may

present no uniform results, it was considered an inter-

val ∆

, where the global maximum (or global mini-

mum) in this interval is taken. It is done in order to

avoid to deal with too many roots. Fig. 8 shows the

plot obtained by Color Layout Descriptor.

Fig. 6 shows a ﬂuxogram that summarizes the

method.

3.2 Phase Retrieval by CBIR

The second method aims to identify the phases of a

liquid crystal. This method was based on a CBIR sys-

tem Fig. 7. It receives as input data a liquid crystal

image representing a well deﬁned phase as a search-

ing criterion and also receives an arbitrary liquid crys-

tal image image sequence. The method works as fol-

lows:

1. It is created a features vector V

input

to represent

the input image according to a given Visual De-

scriptor.

2. For each frame i of the input sequence it is com-

puted a features vector V

3. For each vector V

, it is calculated a similarity

measure x

between it and V

input

. Such vector is

given by x

= D(V

input

4. Let X = hx

,..., x

i. Let X

sort

,..., s

i be a sequence where the

elements of X are sorted in a increasing order.

5. If s

= x

, it means that, among all images from

the input image sequence, frame j is the i-th clos-

est frame to the input image criterion. X

sort

gives

the ordering of the frames from input sequence

Figure 6: Fluxogram of the method to detect phase transi-

tion.

Figure 7: The proposed method to identify the phases of

liquid crystal.

according to their similarity to the input criterion.

More, the images from the input sequence which

are more probable to belong to the same phase of

the input image criterion are related to small s

, at

the beginning of the X

sort

4 EXPERIMENTAL RESULTS

The experiments were applied to a known liquid crys-

tal image sequence, acquired from a liquid crys-

tal sample by a well known process (Neto, A.M.F.,

Liebert, L. and Galerne, Y., 1985) in order to produce

VISAPP2014-InternationalConferenceonComputerVisionTheoryandApplications

534

some phases. In a previous paper, this liquid crystal

sequence showed the following phases (A - B - C - D

- A) and was determined, by optical microscopy and

optical birefringence measurements, that the temper-

atures of the phases transitions was: A-B (13.8

◦

C),

B-C (18.6

◦

C), C-D (21.2

◦

C) and D-A’ (40.3

◦

C).

4.1 Experimental Results to Phase

Transition Detection

For the ﬁrst experiment, the Visual Descriptors were

applied to detect the phase transition. The ﬁgures 8

to 12 show the plot of the Visual Descriptor result for

each image of the sequence. The temperatures where

peaks and valleys occurred for each Visual Descriptor

are the ones where probably phase transiitions occurs.

Table I shows the temperatures of each phase transi-

tion found for each visual descriptor. Although some-

what different, all plots in Figures 8 to 12 and data in

Table I show correlation to each other.

The descriptor Co-occurrence showed higher ac-

curacy for detecting the A-B phase transition. All

color descriptors (Color Layout, Color Moments and

Color Histogram) showed the same result for the de-

tection of B-C phase transition, coincides with the real

temperature which is 18.6

◦

C. For the detection of the

C-D transition the descriptors that showed the best re-

sults were the Color Moments and Entropy. In the last

phase transition, D-A’, the descriptor that found phase

transition temperature was of the Entropy. Although

they found different temperatures for the transitions,

all descriptors found the phase transitions with a small

margin of error.

Figure 8: Color Layout Descriptor result.

4.2 Experimental Results to Phase

Retrieval

The second experiment was applied to three samples

Figure 9: Color Moments result.

Figure 10: Entropy result.

Figure 11: Co-Occurrence result.

of the liquid crystal sequence. Was chosen an image

that belongs to phase B, another image that belongs

to phase C and ﬁnally one that belongs to phase D.

In the experiment of the ﬁrst sample, the selected

image is in the temperature of 15.0C

◦

C , it has 49 rel-

evant images that are between 13.8

◦

C and 18.6

◦

C. In

the second sample, the selected image is in the tem-

LiquidCrystalImageAnalysisbyImageDescriptors

535

perature of 19.5

◦

C and it has 36 relevant images that

are between the temperatures of 18.5

◦

C and 21.2

◦

In the last sample, the selected image is in the tem-

perature of 30.0

◦

C and it has 185 relevant images that

are between the temperatures of 21.2

◦

C and 40.3

◦

One way to rank the visual descriptors is using the

functions of Precision and Recall. To calculate the

Precision, is necessary to consider the value n which

means how many images must be retrieved from the

database. The results of the experiments are shown in

Tables II, III and IV.

Precision =

#(retrieved relevant images)

#(retrieved images)

(7)

Recall =

#(retrieved relevant images)

#(relevant images in collection)

(8)

5 CONCLUSIONS

This paper introduces two methods for liquid crystal

image sequences processing. One of them is applied

to detect phase transitions in such sequences and the

other one classiﬁes the phases based on a input im-

age which criterion is deﬁned by its known phase, or-

dering frames according to the similarity to the input

criterion.

Both methods use Visual Descriptors. Color and

texture descriptors showed to be very efﬁcient to ex-

tract information from the complex structures, in or-

der to make easier the proposed tasks.

For the method to detect phase transition, all the

descriptors exhibited good results. The experiments

showed that all visual descriptors found the phase

transitions with high accuracy, since they found tran-

sition temperature values close to the real measured

ones. Colors descriptor had better precision to some

phases transition and texture descriptor were better

for others. For phase transition D-A’, the texture de-

scriptors found values closer to the real value. The

phase transition B-C was best identiﬁed by color de-

scriptors. For the other transitions, all visual descrip-

tors presented very approximate answer to real value.

In the experiment for phase retrieval the color de-

scriptors showed better results. For n equals to 10,

color descriptors classify all phases with 100% of

Precision. The calculation of Recall function showed

that is recovered at least 59% of all relevant images

when the color descriptor is used. Texture descriptors

didn’t show good results as the color descriptors, with

exception to identiﬁcation of the phase D.

In a future work, it is possible to combine the two

methods presented in this paper for best results. Once

discovered phase transitions and how many phases a

liquid crystal possesses, is possible, from a database

of known liquid crystal image sequences, to classify

these phases and the temperature of each found phase

transition.

REFERENCES

Bahadur, B. (1992). Liquid Crystals - Applications and

uses. World Scientiﬁc Pub Co Inc.

Cess, G., Snoek, M. and Worring, M. (2005). Multimodal

video indexing: A review of the state-of-the-art. Mul-

timedia Tools and Applications, 25:5–35.

Jain, R., Kasturi, R. and Schunck, B. (1995). Machine Vi-

sion, chapter 7. McGraw-Hill.

Khokher, A. and Talwar, R. (2012). Content-based image

retrieval: Feature extraction techniques and applica-

tion. International Journal of Computer Applications,

pages 356–361.

Lew, M., Sabe, N., Djeraba, C. and Jain, R. (2006).

Content-based multimedia information retrieval: State

of the art and challenges. ACM Transactions on Mul-

timedia Computing, Communications, and Applica-

tions.

Manjunath B. S., Salembier, P. and Sikora, T. (2002). Intro-

duction to MPEG-7. John Wiley and Sons.

Montrucchio, B., S. A. and Strigazzi, A. (1998). A new

image processing method for enhancing the detection

sensitivity of smooth transitions in liquid crystals. Liq-

uid Crystals, 24(6):841–852.

Sampaio, A., P. A. and C., V. (2004). Investigation of uniax-

ial and biaxial lyotropic nematic phase transitions by

means of digital image processing. Molecular Crys-

tals and Liquid Crystals, 408(1):45–51.

Sastry, S., Kumari, T., Rao, C., Mallika, K., Lakshmi-

narayana, S. and Ha Sie Tiong (2012). Transition tem-

peratures of thermotropic liquid crystals fromthe local

binary gray level cooccurrencematrix. Hindawi Pub-

lishing Corporation, 24:9.

Snoek, C. and Worring, M. (2005). Multimodal video in-

dexing: A review of the state-of-the-art. Multimedia

Tools and Application, 25:5–35.

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APPENDIX

Table 1: Experiment with the sample temperature 15.0

◦

Descriptor Precision (n=10) Precision (n=20) Recall

Color Layout 100% 100% 66.7%

Color Moments 100% 100% 63.9%

Entropy 30% 40% 61.1%

Co-occurrence 70% 70% 72.2%

Color Histogram 100% 100% 63.9%

Table 2: Experiment with the sample temperature 19.5

◦

Descriptor Precision (n=10) Precision (n=30) Recall

Color Layout 100% 80% 99.5%

Color Moments 100% 66.7% 96.8%

Entropy 50% 30% 82.2%

Co-occurrence 32% 30% 26.7%

Color Histogram 100% 66.7% 59.2%

Table 3: Experiment with the sample temperature 30.0

◦

Descriptor Precision (n=10) Precision (n=100) Recall

Color Layout 100% 100% 99.6%

Color Moments 100% 100% 96.8%

Entropy 100% 95% 82.2%

Co-occurrence 100% 96% 88.1%

Color Histogram 100% 100% 91.9%

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