=Paper=
{{Paper
|id=Vol-1424/Paper6
|storemode=property
|title=Rough-Fuzzy Granularity in the Study of Optical Phenomena
|pdfUrl=https://ceur-ws.org/Vol-1424/Paper6.pdf
|volume=Vol-1424
|dblpUrl=https://dblp.org/rec/conf/ijcai/PraP15
}}
==Rough-Fuzzy Granularity in the Study of Optical Phenomena==
https://ceur-ws.org/Vol-1424/Paper6.pdf
Rough-Fuzzy Granularity in the study of optical phenomena
Ana Lucia Dai Pra, Lucía Isabel Passoni
Faculty of engineering, National University of Mar del Plata, Mar del Plata, Argentina
daipra@fi.mdp.edu.ar
Abstract a suitable resolution and in stable conditions [Rabal and
Braga, 2008].
Granular computing deals with information
In ecography images, the speckles are a nuisance that is
representation in the form of a number of entities
desired to diminish to improve recognition and resolution
or information granules. Information granules are
made up of a collection of entities, usually of [Damerjiana et al., 2014], [Hiremath et al., 2013] .
numeric level, joined due to their similarity, In both cases, laser and ultrasound, a stable speckle pattern
functional adjacency, indistinguishability, is achieved when the scatterers don´t move however when
coherence or alikeness. The granular computing is the sample has certain activity it is translated to the
associated to sets concepts, such as fuzzy sets, scatterers movement, the dynamic of the speckle pattern is
rough sets, intervals. used to evaluate the scatterer movements.
In this work is considered the application of In this work we propose using a method based on rough-
Rough-Fuzzy Granularity to the detection of fuzzy granular computing to detect regions of interest in
optical phenomena in registered videos. Basically ecographies and Speckle image stack and also in single
these phenomena are dynamic laser speckle and frames, since each of them would allow detecting different
ecography videos. types of features. Then, temporal and spatial granularity is
. analyzed.
.
1 Introduction
2 Methodology
In granular computing the information is grouped in entities
that fulfill conditions of similarity, being the granules, 2.1 Granular Computing
conceptual entities that emerge as a direct consequence of In granular computing the information is grouped in entities
the quest for the identification of abstract objects and its that fulfill conditions of similarity, being the granules,
processing [Zadeh, 1970], [Pedrycz, 2001], [Yao, 2004]. conceptual entities that emerge as a direct consequence of
The fuzzy sets and rough sets are a suitable way to define the quest for the identification of abstract objects and its
information granules. processing.. The fuzzy sets and rough sets are a suitable way
The identification of information granules is context to define granules.
dependent and is expected that achieve two intuitive In the signal processing, the information granules contribute
requirements: Justifiable granularity and Semantic to condensing a signal and represent it as a set of temporal
meaningfulness. For numeric data, the requirement of granules through an abstraction mechanism that synthesizes
Justifiable granularity is quantified by counting the number the information. This representation preserves the granules
of data falling within the bounds of the granule, and the identity in spite of some small fluctuations occurring within
requirement of semantic meaningfulness is quantified by the the experimental data [Bargiela and Pedrycz, 2003] . This
length of the granule [Wang et al., 2015]. type of condensation moves the signal from the numeric
The dynamic laser speckle and ecography videos level up to the symbolic processing layer. The granules size
exhibit special characteristics. and quantity implies a level of abstraction that is achieved
Speckle is a phenomenon that allows to detect activity in (figure 1).
several objects through the lighting with laser beams. In spatial granulation the individual pixels of an image are
Speckle generate an interference pattern formed by coherent arranged into larger entities and processed as such or density
radiation of a medium containing many sub-resolution pixels with determined characteristic are analyzed in small
scatterers in move. In order to register the phenomenon, windows. In small windows, the image is built with pixels
successive images can be obtained with CCD cameras with computed as the sum of elements quantity belonging to the
same fuzzy concept in a slide window of NxN, where the
pixel is in the left-upper side. Thus, the image does not lose defining its possible attributes, the subsets X ⊆ U and B⊆
resolution, only it loses an edge of N-1 pixels (figure 2). A, and an equivalence class [x] B which defines a relation in
which elements in X are indiscernible from each other by
attributes from B, a rough set is defined by the sets
{x∈U:[x] B ⊆ X} and {x∈U:[x] B ∩ X ≠ ∅} which are
denominated as B-lower approximation and B-upper
approximation of X in B respectively. These rough sets are
denoted as BX and B X respectively. The objects in BX are
certainly members of B and the objects in B X are possibly
members in B [Pawlak, 1982], [Pawlak and Skowron,
2007]. If B is a fuzzy attribute, the sets are rough-fuzzy sets
[Jensen, 2002]
To define the fuzzy-rough regions for each Ck concept,
image intensity histogram is analyzed to find an equitable
distribution for the number of pixels that will correspond to
Figure 1. Temporal Fuzzy Granulation each lower approximation and boundary region (figure 3).
To granulate a signal TS(x,y) of length n, corresponding to the
(x,y) pixel, successions of equal equivalence classes [i] Ck are
considered (upper approximation). A granule ends when an
12 Dark
granules
equivalence class membership is zero.
9 Medium
granules
12 Light
granules
Figure 2. Spatial Fuzzy Granulation
2.2 Selection of Fuzzy-Rough sets
The theory of fuzzy sets, that permits the handling of
vagueness and overlapped concepts, makes easy the
adequate definition of intensity grains as they are inherent in Figure 3. Rough Parameters selection
speckle phenomena. By definition [Zadeh, 1965], [Dubois
and Prade, 1980], given a Universal set U of elements ui , a 1 if TS ( x , y ) ( j −1) C = 1 and TS ( x , y ) ( j ) C = 0
Gr( x , y ) ( j , k ) = k k (1)
fuzzy set A∈U is defined by pairs of elements (ui, µA(ui)), 0 in other case
where µA(ui) is a real value in [0,1] that represent the with j =1, n and k =1,2,3
membership degree of ui to A. In this case, the U set is given
by intensity values I(x,y) ∈ [0,255], and the fuzzy set are The Temporal Rough-Fuzzy Granularity (TRFG) is com-
defined by membership functions µ Ck(I(x,y)), with C ∈ puted as the granule quantities Gr in j= n time for k equiva-
{dark, medium, light} conceptual sets that define lence classes. Eq (1) and (2)
characteristics of the intensity pixels. These fuzzy sets
facilitate the interpretation of subjective terms with 3 n
indefinite limits. TRFG( x , y ) = ∑ ∑ Gr( x , y ) (i , j ) / n (2)
A rough set is an approximation of a vague concept by a k =1 j = 2
pair of precise concepts. Rough sets are based on the fact
that an object cannot always be defined in precise form The Rough-Fuzzy spatial granularity (SRFG) is computed as
(crisply) inside a category on the basis of the value of its the relative pixels quantities corresponding to equivalence
attributes. classes [i] Ck in a window of m*m, where P(x,y) indicate a
Formally a rough set is expressed as: pixel. Eq (3)
Given an information system S = (U,A), with U the
universal set defining all the objects to consider, the A set
3 m m the inspection of biological, physical and / or chemical
SRFG( x , y ) = ∑ ∑ ∑ [P(x + i , y + j )]Ck / (m * m ) (3) processes [Todorovich et al., 2013].
k =1 i = 0 j = 0
The computed pixel value will be greater when the window 3.2 Ecography
pixels belong to the boundary regions (the pixel belongs to Usually, speckles observed in ultrasound images are only an
more than one fuzzy concept). This feature could be artifact, a nuisance that is desired to diminish to improve
interpreted as corresponding to the blurring of moving recognition and resolution. In that direction most efforts
regions. were directed. To improve the performance of that
technique, the instruments are usually provided with filters
that smooth slow speckle motions effects, thus avoiding the
3 Experiments dynamics that constitute speckle.
3.1 Speckle In both cases, laser and ultrasound, a stable speckle pattern
Speckle is an optical phenomenon that takes place when a is achieved when the scatterers don´t move, therefore the
beam of coherent light (laser) illuminates an object with a dynamic of the speckle pattern is used to evaluate the
surface that is rough in comparison with the wave length. scatterer movements.
Light is scattered in all directions and an interference pattern Activity measurement has shown a noticeable increase in
of granular aspect, called ‘speckle pattern’ can be observed research interest in the last few years. Laser speckle patterns
on a screen. When the object under study presents some show dynamic behavior when one or more mechanisms act
type of activity, such as biological specimens or certain on the observed sample, such as: Doppler Effect, diffusion,
physical phenomena, the particles of the surface move and optical polarization activity [Briers, 2007].
the speckle pattern changes over time. This change permits
the detection and segmentation of different activity degrees
in a diversity of phenomena, allowing us to analyze paint 4 Coments and results
drying time, imperceptible bruises in fruits, viability of
Figure 4 a) shows a speckle patterns of a corn seed.. Figure
seeds, bacteria mobility, endosperm phase proportions, etc.
4 b) shows the identification of vital region of the seed
[Rabal and Braga, 2008], [Briers, 2007].
(radicle and embryo). It´s important in the agricultural trade.
Stacks of records of successive images are obtained with
CCD cameras with a suitable resolution and in stable
conditions. The variation of each pixel value over time,
considered as a time series, can be analyzed by applying
different technologies of signal processing to obtain values
that describe its behavior. The set of the values or
descriptors obtained in every pixel generates an image
whereby it is possible to detect regions with different
characteristics.
Many of the methods has been studied to analyze dynamic
speckle patterns require a high number of images to obtain
good results. In some cases, the time of evolution of the
analyzed activity is not known a priori and changes inside
the time required for the register are lost. Also, records
taken beyond the end of the studied events reduce the
efficacy of the analysis because of the recording of assumed
activity that has already finished, changed or reduced. Non-
stationary phenomena cannot be detected. a) b)
require the register of images stack where the time history Figure 4. Corn seed
of each pixel is analyzed as a time series [Rabal and Braga,
2008]. Less frequent, single frame estimation techniques,
such as local spatial contrast measurements [Briers, 2007]
have been reported and used in actual applications with the
advantages of being able to follow non-stationary processes.
The temporal granular computing has been applied to obtain
descriptors in dynamic speckle, it provided satisfactory
results in the detection of regions with different activity
characteristic [Dai Pra et. al, 2009], besides, can perform
almost real-time analysis of unquestionable importance in
across a dynamic monitoring, optimizing the strategy
Figure 5. Painted coin ventilatoria during the general anesthesia. The processing of
the video would allow the quantification of the re-aeration
Figure 5 shows the result of the processing of a coin with a and of the loss of pulmonary aeration, in order to contribute
coat of fresh paint. The zones with relief have more activity to not subjective elements in the interpretation of results.
and this allows to visualize the different reliefs of the coin.
This experiment is very useful in the study of times of dried
of paintings.
Figure 6 a) shows a ecography of eye tumor. Figure 6b) is
the result of a temporal process, a semi posterior oval region
with, seemingly, light dots in the middle that can be
estimated could be blood vessels of neo-vascularization
(Doppler effect), making very simple the differentiation
between both pathologies.
Figure 6c) is the result of a spatial process, retina can be
seen that cannot be perceived in the other images.
Figure 7. Pulmonar ecography
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