Efﬁcient Classiﬁcation of Digital Images based on Pattern-features

Angelo Furfaro

and Simona E. Rombo

DIMES, University of Calabria, Italy

DMI, University of Palermo, Italy

Keywords:

Image Classiﬁcation, Bidimesional Pattern Extraction, Irredundant Pattern.

Abstract:

Selecting a suitable set of features, which is able to represent the data to be processed while retaining the

relevant distinctive information, is one of the most important issues in classiﬁcation problems. While different

features can be extracted from the raw data, only few of them are actually relevant and effective for the

classiﬁcation process. Since relevant features are often unknown a priori, many candidate features are usually

introduced. This degrades both the speed and the predictive accuracy of the classiﬁer due to the presence of

redundancy in the feature candidate set. We propose a class of features for image classiﬁcation based on the

notion of irredundant bidimensional pair-patterns, and we present an algorithm for image classiﬁcation based

on their extraction. The devised technique scales well on parallel multi-core architectures, as witnessed by the

experimental results that have been obtained exploiting a benchmark image dataset.

1 INTRODUCTION

Image classiﬁcation is an active research ﬁeld and va-

rious classiﬁcation techniques, based on supervised

and on unsupervised techniques or on a mix of them,

appeared in the literature. Surveys on the topic can

be found in (Bosch et al., 2007; Lu and Weng, 2007;

Nanni et al., 2012).

Traditional approaches use low-level image featu-

res, such as color or texture histograms. Other techni-

ques rely on intermediate representations, made of lo-

cal information extracted from interesting image pa-

tches referred to as keypoints (Bosch et al., 2007).

Image keypoints are automatically detected using va-

rious techniques, and then represented by means of

suitable descriptors. Keypoints are usually clustered

based on their similarity, and each cluster is inter-

preted as a “visual word”, which summarizes the lo-

cal information pattern shared among the belonging

keypoints (Yang et al., 2007). The set of all the vi-

sual words constitutes the visual vocabulary or code-

book. For classiﬁcation purposes, an image is then

represented as a histogram of its local features, which

is analogous to the bag-of-words model for text do-

cuments. Examples of commonly exploited keypoint

detectors are: Difference of Gaussian (DoG) (Lowe,

2001), Sample Edge Operator (Berg et al., 2005),

Kadir-Brady (Kadir and Brady, 2001). Feature des-

criptors are often based on SIFT (Scale Invariant Fe-

ature Transform) (Lowe, 1999).

Like in many other classiﬁcation problems, the re-

levant features to be employed are not known a priori.

Therefore, various candidate features can be introdu-

ced, many of which are either partially or completely

irrelevant/redundant to the target concept (Dash and

Liu, 1997). A relevant feature is neither irrelevant nor

redundant to the target concept; an irrelevant feature

does not affect the target concept in any way, and a

redundant feature does not add anything new to the

target concept (John et al., 1994). In this work, we

analyze a special kind of features for image classiﬁ-

cation, based on the concept of bidimensional irre-

dundant pair-patterns.

Roughly speaking, bidimensional irredundant

pair-patterns represent approximate repetitions bet-

ween pairs of images in an input training set. In more

detail, given two images I

and I

, one can superim-

pose each rectangular sub-portion of I

with each rec-

tangular sub-portion of I

, keeping only those pieces

of the two images that match. When all the possi-

ble repeated portions between I

and I

are conside-

red, also taking into account sub-regions that are si-

milar but not identical, the number of such features

can grow exponentially with the size of I

and I

, and

many of the extracted patterns are irrelevant and/or

redundant.

Suitable notions of maximality and irredundancy

have been introduced for digital images (Apostolico

Furfaro, A. and Rombo, S.

Efﬁcient Classiﬁcation of Digital Images based on Pattern-features.

DOI: 10.5220/0006955500930099

In Proceedings of the 5th International Conference on Physiological Computing Systems (PhyCS 2018), pages 93-99

ISBN: 978-989-758-329-2

et al., 2008) and successfully exploited for both image

compression in (Amelio et al., 2011) and image clas-

siﬁcation (Furfaro et al., 2013), showing to be useful

in encoding the relevant information from input ima-

ges, by reducing their representation. However, all

such approaches work by extracting repetitions from

a single input image, whereas for classiﬁcation pur-

poses the goal is that of singling out useful repetitions

able to characterize a set of images, representing a

class.

A ﬁrst contribution of the research work presen-

ted here is that of extending the notions of maxima-

lity and irredundancy introduced in (Apostolico et al.,

2008) for pairs of images. In particular, the main idea

is that of eliminating all the extracted pair-patterns

that are redundant with respect to the other ones in

the set of candidates. The notion of redundancy here

is related to the occurrence of patterns in the images

of a class, since if several patterns occur on the same

class, then only the most informative ones will be kept

into account and they will be used as features for the

classiﬁcation process.

As a second contribution, we propose an image

classiﬁcation approach based on the extraction of

such bidimensional pair-patterns. In particular, gi-

ven an input training set of images already classiﬁed,

the irredundant pair-patterns are extracted and used

to build a suitable codebook. After feature selection,

image classiﬁcation is then performed based on the

K-Nearest Neighbour approach. The algorithm has

been implemented according to the principles of pa-

rallel computing, in order to use efﬁciently the mo-

dern multi-core architectures.

We tested the proposed approach on a benchmark

image dataset (ZuBud (Shao et al., 2003)) and the pre-

liminary results show that it is able to reach high va-

lues of accuracy.

The paper is organized as follows. Section 2 il-

lustrates some preliminary notions, while in Section

3 the proposed classiﬁcation algorithm is described

in detail. In Section 4 we show some preliminary

results we obtained on real datasets, also comparing

them with those returned by other methods proposed

in the literature. Finally, Section 5 draws some con-

clusive remarks.

2 PRELIMINARY NOTIONS

A digitized image can be represented as a rectangular

array I of N = m × n pixels, where each pixel i

i j

is a

character (typically, encoding an integer) over an alp-

habet Σ, corresponding to the set of colours occurring

into I (see Figure 1).

(a)

[m,n]

. . . i

(b)

Figure 1: (a) A digitized image (Lena). (b) The correspon-

ding image I over the alphabet of colours Σ = {c

, c

, ..., c

}

(each element i

i j

represents a pixel of Lena with a speciﬁc

colour c

∈ Σ).

We are interested in ﬁnding a compact descriptor

for a set of images S

= {I

, I

, . . . , I

}, able to cap-

ture the common features of the images in the set. To

this aim, we search for the repetitive content among

, I

, . . . I

under the assumption that if a small block

of such images is sufﬁcently repeated in S

, then it

represents a feature that is characteristic for the set.

Such repeated blocks can be not necessarily identi-

cal, but somewhat identical unless some pixel, due to

different shades or lightness in the original pictures.

Thus, in addition to the solid characters from Σ, we

also deal with a special don’t care character, deno-

ted by ‘∗’, that is a wildcard matching any character

in Σ ∪ {∗}. Don’t cares are useful in order to take

into account approximate repetitions. We say that an

image P deﬁned on Σ ∪ {∗} occurs in a larger image

I if P[i, j] = I

[h + i − 1, k + j − 1], for some position

[h, k] in I and for all the positions [i, j] in P.

Given a pair of images I

and I

, both of size m ×n

and such that I

, I

∈ S

, a bidimensional pair-pattern

is an extended image P of size m

× n

such that:

1. m

≤ m and n

≤ n;

2. there is at least one solid character adjacent to

each edge of P;

3. there exist positions [h

, k

] in I

and [h

, k

] in I

such that P occurs in both I

and I

The notion of bidimensional pair-pattern extends

that of 2D motif already introduced in (Apostolico

et al., 2008) and applied to digital images in (Amelio

et al., 2011; Furfaro et al., 2017). The main difference

here is that the bidimensional pair-pattern (referred to

simply as pattern in the following) is extracted from

PhyCS 2018 - 5th International Conference on Physiological Computing Systems

pairs of images, whereas the 2D motif represents re-

petitions occurring in the same image.

When approximate occurrences are taken into ac-

count, and patterns with don’t cares are thus conside-

red, the number of all the possible patterns that one

can extract from an input image can grow drastically,

often becoming exponential in the size of the input

image. In order to limit such a growth, suitable no-

tions of maximality and irredundancy have been pro-

posed for bidimensional patterns (Apostolico et al.,

2008; Rombo, 2009; Rombo, 2012). Since such noti-

ons concern patterns extracted from only one image,

we extend them here for pairs of images. To this aim,

given a pattern P occuring in some of the images in

(we say that P is covered on S

), its occurrence list

= {1, 2, . . . , k} is made of the indices of those ima-

ges {I

, I

, . . . , I

} in S

where P occurs.

Maximal Pattern. Let P = P

, P

, . . . , P

be a set

of patterns covered on S

, and let L

, L

, . . . , L

be their occurrence lists, respectively. A pattern P

maximal in P if and only if there exists no pattern P

∈

P , j 6= i, such that P

occurs in P

and |L

| = |L

In other words, P

cannot be substituted by P

without

loosing some of the P

occurrences in S

Irredundant Pattern. A pattern P

that is maximal

in P , having occurrence list L

in S

, is also irre-

dundant in P if there not exist any maximal pattern

∈ P , j = 1, . . . , h, such that P

occurs in P

and

= L

∪ L

∪ . . . ∪ L

, up to some offsets.

3 THE CLASSIFICATION

ALGORITHM

This section describes the proposed image classiﬁca-

tion procedure whose pseudo-code is reported in Al-

gorithm 1.

The algorithm takes in input an image dataset S

, I

, . . . , I

}, which is a priori partitioned into h

classes C

, C

, . . . , C

, and a test image I for which

the algorithm will predict the membership class. For

each image in the input dataset, the set of irredun-

dant bidimensional pair-pattern motifs is extracted by

overlapping it with all the other images in its class, as

described by the extraction procedure (PATTERNEX-

TRACTION) reported in Algorithm 2. The overall set

made of the extracted motifs constitutes the codebook

D. Then, for each image I

, we build an array w

, ha-

ving as many entries as the codebook size. w

is the

histogram of the occurrences of the codebook patterns

into I

, i.e. w

[i] is the number of occurrences of the

motif m

in the image I

The REMOVEBORDER procedure, invoked at line

12 of Algorithm 2, removes from the input pattern

those border zones made up of only don’t cares.

In order to classify a test image I, its histogram w

with respect to the codebook pattern is computed, as

for the training set images.

The ﬁnal step, which actually outputs the classiﬁ-

cation label for I, uses the well-known classiﬁcation

algorithm k-Nearest Neighbour (k−NN). This step is

applied by calculating all the distances between each

array w

and the array w obtained from the image that

has to be classiﬁed. The output class is that having

the larger consensus among the k images that score

the lowest values for the distances from I.

Algorithm 1: Classiﬁcation algorithm.

Require: set S

of l images of size m × n images par-

titioned in h classes C

, C

, . . . , C

; a test image I;

an integer k;

Ensure: the label x of the class predicted for I

/* training phase */

1: D

2: for each class C

in C

, C

, . . . , C

3: B

=PATTERNEXTRACTION(C

)

4: D = D ∪ B

5: end for

6: for each image I

in S

7: let w

be an empty array of |D| integer values

8: for each motif m

in D

9: w

[i] =COMPUTEOCCURRENCES(m

)

10: end for

11: end for

/* testing phase */

12: let w be an empty array of |D| integer values

13: for each motif m

in D

14: w[k] = COMPUTEOCCURRENCES(m

,I)

15: end for

16: let E be an empty array of l real values

17: for each image I

in S

18: E[ j] = dist(w

, w)

19: end for

20: sort E in increasing order

21: let S be the set of the ﬁrst k elements in E

22: return the label x of the most popular class in S

Efﬁcient Classiﬁcation of Digital Images based on Pattern-features

Algorithm 2: Extraction of irredundant patterns.

Require: set S

of l images of size m × n

Ensure: set I

of irredundant patterns of S

1: I

2: for each image I

in S

3: for each image I

6= I

in S

4: for each position [i

, j

] in I

5: for each position [i

, j

] in I

6: extract a pattern P

such that

7: if I

, j

] 6= I

, j

] then

8: P

[i, j] = ∗

9: else

10: P

[i, j] = I

, j

]

11: end if

12: P

=REMOVEBORDER(P

)

13: I

= I

∪ P

14: end for

15: end for

16: end for

17: end for

18: for each pattern P in I

19: compute the occurrence list of P in S

20: end for

21: I

= I

\ {all the redundant patterns in I

}

3.1 Distance Notions

An important aspect in classiﬁcation algorithms is the

choice of the distance notion employed to measure

the similarity among objects. This choice may have

in some cases a great impact on the algorithm perfor-

mances. As discussed in the next section, the pro-

posed classiﬁcation technique has been tested with

different deﬁnitions of the distance functions. Some

of them are normalized versions of classical distance

functions which take into account also the standard

deviation of the training samples for each dimensions.

In particular, we used: the Euclidean distance and its

normalized version, the Hamming distance, and a nor-

malized Manhattan distance.

The formal deﬁnitions of these functions are re-

ported in Table 1, where s

l−1

∑

i=1

[k] − w[k])

i.e. the variance of the k

dimension, w[k] =

∑

i=1

[k], i.e. the mean value for the k

dimen-

sion, and δ(x, y) =



1 if x = y

0 otherwise.

3.2 Algorithm Parallelization

The algorithm has been implemented according to the

principles of parallel computing. Some details about

Table 1: Used distances.

Euclidean

, w

) =

∑

k=1

[k] − w

[k])

Normalized Euclidean

, w

) =

∑

k=1

[k]−w

[k])

Hamming

, w

) =

∑

k=1

δ (1 − δ(w

[k], 0), δ(w

[k], 0))

Normalized Manhattan

, w

) =

∑

k=1

[k]−w

[k]|

Start execution

PATTERNEXTRACTION(C

) PATTERNEXTRACTION(C

)

dist(w,w

)

COMPUTEOCCURRENCES(m

)

dist(w,w

) dist(w,w

)

...

COMPUTEOCCURRENCES(m

,I) COMPUTEOCCURRENCES(m

|D|

,I)

...

COMPUTEOCCURRENCES(m

|D|

)

...

COMPUTEOCCURRENCES(m

)

...

COMPUTEOCCURRENCES(m

|D|

)

...

Assing class to image I

...

training phase

testing phase

Figure 2: Parallel execution of Algorithm 1.

the implementation are provided below.

Both training and testing phases have been pa-

rallelized. In particular, a pool of n

core

+ 1 working

threads has been created, where n is the number of

available cores on the underlying architecture. Each

iteration of the for loops can be transformed into a

separate task, which can be submitted for execution

and accomplished by a worker thread. In particular,

regarding the for loop at line 3, for each class we ge-

nerate a single task consisting in the execution of the

PATTERNEXTRACTION procedure on the relevant test

images; similar considerations hold regarding the for

loop of line 6, where a single task is the execution

of the COMPUTEOCCURRENCES procedure on each

pair made of a pattern and training image.

As for the testing phase, the for loop of line 13

is parallelized like it has been done for that of line

6. Finally, the computation of the distances among

PhyCS 2018 - 5th International Conference on Physiological Computing Systems

Figure 3: Images from the ZuBud dataset.

the histogram of a test image and those of the training

images (line 17) is performed in parallel as well.

4 EXPERIMENTAL RESULTS

This section describes the experimental campaign that

has been performed in order to test and analyze the re-

sults of the proposed image classiﬁcation algorithm.

The algorithm has been implemented in Java. A stan-

dard benchmark dataset, the ZuBuD dataset, which is

described by the next subsection, has been used. The

classiﬁer performances have been measured from two

points of view: in terms of its accuracy and in terms of

scalability of its parallel execution. In particular, the

experiments have been executed on a machine with

an i7 processor with 2.00 Ghz per core, and 8GB of

RAM.

4.1 The ZuBuD Dataset

The ZuBuD (Zurich Building Image Database) (Shao

et al., 2003) is a famous collection of images, often

used to test classiﬁcation algorithms. The dataset is

freely available, and it is considered a standard in the

literature to test this kind of classiﬁers. It consists of a

collection of photos that have been done to 201 buil-

dings of Zurich. For each building, the training set

contains ﬁve pictures, each of which represents the

building from a different point of view. Each image

in the training has a size of 640 × 480 pixels: in total,

there are 1005 images in the training set. Then, we

have the test set, that consists of 115 photos of buil-

dings. These images have a size of 320 × 240 pixels,

and represent some of the buildings contained into the

training set in various angulations and various points

100

20 40 60 80 100 120 140 160 180 200

Accuracy (%)

Training classes

Classification accuracy vs. distance

Euclidean

Normalized euclidean

Normalized Manhattan

Hamming

Figure 4: Accuracy.

Table 2: Accuracy vs. distance (201 classes).

Distance Accuracy

Euclidean 71.30%

Normalized euclidean 78.26%

Normalized Manhattan 75.65%

Hamming 72.17%

of view. In general, the photos have numerous cha-

racteristics of heterogeneity: in fact, they have been

taken with two cameras and in different periods time

of the year. The only condition consistent between all

photos relating to a same building are the conditions

of illumination, which remain almost identical.

4.2 Accuracy Analysis

The algorithm has been tested with an increasing

number of training classes and with various kinds

of distances. This allows us to study how the accu-

racy evolves with the increasing of the number images

and, consequently, of the extracted patterns. Figure 4

shows how the accuracy tends to decrease with the in-

crease of the training set size till 100 classes, then it

increases and settles down to about 70%.

As it can be seen from Table 2, the best score

has been achieved with the Normalized Euclidean dis-

tance, which with 201 classes scored 78.26% of accu-

racy, i.e 90 test images out of 115 were correctly clas-

siﬁed.

4.3 Scalability

In this kind of algorithms performance is a crucial as-

pect, especially with big datasets. As explained in

Section 3.2, the classiﬁer was parallelized both in the

training phase and in the testing phase: this allows us

to use efﬁciently the modern multicore architectures.

Efﬁcient Classiﬁcation of Digital Images based on Pattern-features

1.5

2.5

3.5

1 2 3 4 5 6 7 8 9

Speed up factor

Executing threads

Speed-up factor chart

Speed-up

Figure 5: Speed up.

We also did a work of optimization on all of the data

structures used during the execution. However, there

is no guarantee that all of the real world machines on

which the algorithm will run have at their disposal

the same number of physical cores. Accordingly, it

should be noted as the performance evolve in relation

to varying the number of threads that are running si-

multaneously on the machine in question: this aspect

is summarized in the speed-up plot of Figure 5. The

results are related to an experiment conducted with 10

training classes.

In this speed-up factor chart we can see how the

increase of number of threads, running simultane-

ously on the machine, have a good effect on the exe-

cution time. Clearly, beyond a certain number, i.e.,

that of the physical processors, there are no further

considerable improvements. The machine where the

experiments were performed is equipped with 8 cores

and by using a pool of 8 threads we reached a factor

speed-up of nearly 4.

5 CONCLUDING REMARKS AND

DISCUSSION

This paper presented an image classiﬁcation techni-

que based on bidimensional motifs. The analysis of

the experimental results, suggests that this technique

is effective and obtains good performances both in

terms of accuracy and of scalability. We must not

however lose sight of the enormous complexity that

the classiﬁcation problem presents inherently, especi-

ally as it regards the search space that we can explore

in order to improve the accuracy of classiﬁcation. In

fact, at present, it is possible to customize the classi-

ﬁer in a considerable number of parameters, each of

which can assume a range of values potentially very

high. In some cases, the wrong choice of these pa-

rameters can also degenerate performance at an ex-

tent as to make the execution times unacceptable. In

this sense, research is responsible for identifying si-

tuations where the instrument maximizes percentage

of correctly classiﬁed images with reasonable perfor-

mances. As regards the implementation, the actual

classiﬁer version runs in a maximally efﬁcient on a

single machine with multi-core architecture: one of

the steps for the future might be to offer an implemen-

tation that can deliver computing in cluster machines

or distributed environments, for example in cloud sce-

narios. In this way, we may improve timing perfor-

mance and be able to experience the behavior of the

classiﬁer in further complex scenarios. To be taken

into account is also the positive inﬂuence that has had

the introduction of distance normalization: this aspect

has led a substantial improvement in the accuracy of

the algorithm, and is indeed a solid starting point for

future research. It might also be interesting to try to

replace the ﬁnal classiﬁcation technique, currently k-

NN, with other types of classiﬁers coming for exam-

ple from the pool of statistical ones. Another open

question is to see how non-exact chromatic matching

is inﬂuential on the technique. Moreover, suitable in-

variants, such as rotations and/or translations, can be

considered in the 2D basis generation, by extending

the proposed approach to this aim. Finally, a compari-

son with more recent techniques for image classiﬁca-

tion (Chan et al., 2015; Kumar et al., 2017; Maggiori

et al., 2017) will be object of our investigation.

ACKNOWLEDGEMENTS

The authors are grateful to Michele Bombardieri for

his help in the implementation of a preliminary ver-

sion of the software presented here. Moreover, their

research has been partially supported by a project ﬁ-

nanced by INDAM titled “Elaborazione ed analisi di

Big Data modellati come graﬁ in vari contesti appli-

cativi”, under the program GNCS 2018.

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