=Paper=
{{Paper
|id=Vol-3006/10_regular_paper
|storemode=property
|title=Texture classification in aerial photographs using multiscale and multilayer complex networks
|pdfUrl=https://ceur-ws.org/Vol-3006/10_regular_paper.pdf
|volume=Vol-3006
|authors=Margarita N. Favorskaya,Angelina N. Zhukovskaya
}}
==Texture classification in aerial photographs using multiscale and multilayer complex networks==
https://ceur-ws.org/Vol-3006/10_regular_paper.pdf
Texture classification in aerial photographs using
multiscale and multilayer complex networks
Margarita N. Favorskaya1 , Angelina N. Zhukovskaya1
1
Reshetnev Siberian State University of Science and Technology, Krasnoyarsk, Russia
Abstract
Texture classification using oriented complex networks considers the functional connections between
topological elements and simulates the complex textures more accurately. In contrast to the classical
spatial texture analysis, we offer a novel function of weights in complex networks and a classification
method that takes into account the scaling and color of textures. For this, three complex networks
represented R, G and B components are built, which provide invariance of color aerial photographs
obtained at different times. Comparison of the classification results using the proposed multiscale
complex networks and conventional texture analysis based on a statistical approach is given. Also we
extended this approach on color aerial photographs using multilayer structure of complex network.
Keywords
Texture classification, complex networks, multilayer structure, multiscale invariance, aerial photograph.
1. Introduction
Texture analysis is a fundamental problem in computer vision tasks. Due to the fact that this
is a constant research field since the 1960s, many different approaches have been developed
that does not prevent from looking for new views on an old problem [1]. Any visible object
of the real world has its own textural features at a certain scale, associated with local spatial
variations such as color, orientation and intensity depending on lighting conditions. There are
many definitions of texture in literature, which are employed in several areas. The main reason
is that natural textures have a wide range of the properties, for example, from regularity to
randomness, from homogeneity to heterogeneity. Such properties cannot be described in a
unified manner. Depending on the task, texture is considered as primitives with specific spatial
distributions [2], as a stochastic, possibly periodic, two-dimensional image field [3] or as simple
color patterns. Nevertheless, spatial homogeneity, meaning statistical stationarity, is the most
important property of texture, leading directly to self-similarity and texture interpretation as a
fractal structure.
Extraction of texture features is usually performed at the initial stages of visual data process-
ing that makes this procedure important from the point of view of future results. Conventional
methods of texture analysis are grouped into four categories, such as statistical, spectral, struc-
tural and model-based methods. Recently, alternative approaches based on learning techniques
have been developed. These approaches include bag-of-visual-words, cellular automata and
SDM-2021: All-Russian conference, August 24–27, 2021, Novosibirsk, Russia
" favorskaya@sibsau.ru (M. N. Favorskaya); zhukowskaya.angelina@yandex.ru (A. N. Zhukovskaya)
© 2021 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073 CEUR Workshop Proceedings (CEUR-WS.org)
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Margarita N. Favorskaya et al. CEUR Workshop Proceedings 74–83
complex networks. The use of complex networks (CNs) is one of the interesting and rapidly
developing areas, when a texture is interpreted as a graph with certain topological properties
and binary connections. This interpretation makes it possible to simulate the physical properties
of natural textures.
The structure of this paper is as follows. In Section 2, the evolution of texture analysis
methods is briefly reviewed. Section 3 describes the main propositions of CNs. The proposed
method based on multiscale CNs is presented in Section 4. Further, the dataset and experimental
results are reported in Section 5. Section 6 concludes the paper.
2. Evolution of texture analysis methods
Investigations in texture analysis began in the 1960s and continue to this day, because texture, as
an inherent property of objects in the real world, is a determining factor in both the classification
and modeling. Statistical texture analysis is one of the earliest methods based on estimating
ordinal statistical moments, calculating gray-level co-occurrence matrices, and applying local
binary patterns (LBPs). It should be noted that the use of LBPs proposed in the 1990s is a fast
way to classify textures with fairly good results. This family of methods has led to numerous
modifications, some of which have became difficult to implement [4]. Spectral methods are
based on the calculation of Gabor filters, wavelet transforms and other spectral methods. In
structural methods, texture is considered as a combination of small elements called textones
that form a spatially structured pattern. These methods often use morphological decomposition.
Model methods involve the construction of complex mathematical models and the estimation of
their parameters, for example, fractal models and stochastic models based on Markov networks.
In addition to conventional approaches, alternative innovative methods are being developed
based on the analysis of feature points, discriminant local features, cellular automata, deep
neural networks and complex networks. Often these approaches use feature dictionaries in the
form of bag-of-visual-words (BOVW). The main advantage of the methods based on the theory
of complex networks is related to their ability to map relationships between structural elements
of a texture. However, the reduction of the dimensionality of features and the search for new
ways to build complex networks remain an area of interest.
The deterministic tourist walk method, which belongs to the agent-based category, can be
considered as a predecessor of CNs in texture analysis [5]. An agent visits pixels in accordance
to predefined deterministic rule and memory size. Each walk included the transient part, where
the agent walked freely, and the attractor in the form of a sequence of pixels, repeated during
the walk. The description of texture was the joint distribution of transient times and attractor
periods. Hereinafter, texture analysis using a combination of graph theory and partially self-
avoiding deterministic walks was proposed by the same authors in [6]. First, an image was
represented in the form of a regular graph. Then the regular graph was transformed into a
graph with different properties and transitivity, which revealed different texture properties. The
texture descriptor was presented as a histogram.
A combination of CNs and LBPs was introduced in [7]. The proposed local spatial pattern
mapping (LSPM) method transformed CNs at different radial distances to LBPs, followed by
concatenation of histograms, as is done in classification using conventional LBPs. The LSPM
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Margarita N. Favorskaya et al. CEUR Workshop Proceedings 74–83
method described the uniformity of texture primitives and examined three Euclidean radial
distances of LSPM. Experiments have confirmed that the classification results were highly
dependent on a predefined set of thresholds during CNs construction.
In [8], the fusion of BOVW and CNs methods called BoVW-CN was proposed. This approach
allowed to describe the keypoints of the image through a texture-based focus. Parameters such
as mean centrality, number of communities, average degree, transitivity, average minimum
path, motifs (small patterns of interconnections), and connectivity histogram were calculated
for a limited number of salient points in the image, assuming that salient points fully reflect the
properties of the texture.
Ribas et al. [9] proposed a combination of CNs and randomized neural networks (RNN) to
obtain a texture description. First, a texture is simulated as a directed CN. Second, RNN is
trained with information from the modeled CNs in order to consider the topological properties
of the texture. The outputs of RNN provide texture signature. This method has demonstrated
robustness to rotation of texture images.
CNs find their application not only in texture analysis, but also in image segmentation, when
a cluster of nodes is related with image segmentation. The fundamental limitation of image
segmentation based on CNs due to the excessive numbers of nodes in the network is overcome
by the concept of super-pixels [10]. Mourchid et al. [11] proposed a framework that used a
weighted region adjacency graph to represent an image as a network, where regions represented
nodes in the network. This framework was based on community detection algorithms in graphs
because networks are growing exponentially in size, variety and complexity.
From a brief literature review, we see that CNs are used in combination with other interesting
techniques aimed at achieving invariance properties. The paper proposes a texture classification
method for aerial photographs based on the use of complex networks calculated for various
scales and refined the final classification.
3. Complex networks
Currently, the theory of complex networks is used in many fields, such as physics, sociology,
biology, mathematics, computer science, medicine, ecology, linguistics, and others. Complex
networks can be defined as graph structures with statistical mechanisms that give them an
interdisciplinary nature. Complex networks demonstrate the flexibility and versatility of repre-
senting natural structures, including dynamic topology changes. In linguistics, CNs are suitable
for automatic summarization due to strong correlation between the metrics of such networks
and important text features. In [12], CNs were applied to select sentences for an extractive sum-
mary. The nodes of such CN corresponded to sentences, while the edges connected sentences
that had common meaningful nouns. In computer vision, most of the problems are related to
feature extraction and topological characteristics. In this sense, the CN-based descriptors can
be used to classify objects and solve the recognition problems [13]. When describing a texture
in terms of CNs, pixels are considered as nodes, and the connections between nodes determine
the similarity. The main assumption is that different textures have different topologies of such
networks, which are characterized by their own connectivity parameters. Such parameters are
used as features in the classification of textures.
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Let us define a texture as a two-dimensional pixel structure. In grayscale images, each
pixel has an intensity value, which is an integer in the range 𝑔 = 0, . . . , 𝐿, 𝐿 = 255. Let
𝐼(𝑥, 𝑦) = 𝑔, 𝑥 = 1, . . . , 𝑀 and 𝑦 = 1, . . . , 𝑁 be the intensity of the pixel with coordinates
(𝑥, 𝑦) in image 𝐼. Let us build a graph 𝐺 = (𝑉, 𝐸), in which each pixel 𝐼(𝑥, 𝑦) is a node
𝑣𝑥,𝑦 ∈ 𝑉 and connections between two pixels 𝐼(𝑥, 𝑦) and 𝐼(𝑥′ , 𝑦 ′ ) are defined by an undirected
edge 𝑒 ∈ 𝐸, 𝑒 = (𝑣𝑥,𝑦 , 𝑣𝑥′ ,𝑦′ ), where Euclidian distance is no more that radius 𝑟:
𝐸 = 𝑒 = 𝑣𝑥,𝑦 , 𝑣𝑥′ ,𝑦′ ∈ 𝐸|𝑑𝑖𝑠𝑡 𝑣𝑥,𝑦 , 𝑣𝑥′ ,𝑦′ ≤ 𝑟 ∧ 𝐼(𝑥, 𝑦) < 𝐼(𝑥′ , 𝑦 ′ ) , (1)
{︀ (︀ )︀ (︀ )︀ }︀
where 𝑑𝑖𝑠𝑡(𝑣𝑥,𝑦 , 𝑣𝑥′ ,𝑦′ ) is an Euclidian distance between two pixels, defined by following ex-
pression: √︀
𝑑𝑖𝑠𝑡(𝑣𝑥,𝑦 , 𝑣𝑥′ ,𝑦′ ) = (𝑥 − 𝑥′ )2 + (𝑦 − 𝑦 ′ )2 .
Each edge has a weight 𝑤(𝑒) computed by (2):
|𝐼(𝑥, 𝑦) − 𝐼(𝑥′ , 𝑦 ′ )|
𝑤(𝑒) = 𝑑𝑖𝑠𝑡2 (𝑣𝑥,𝑦 , 𝑣𝑥′ ,𝑦′ ) · 𝑓 2 ∀𝑒 = (𝑣𝑥,𝑦 , 𝑣𝑥′ ,𝑦′ ) ∈ 𝐸. (2)
𝐿
Weights are often normalized to the range [0, 1] for two cases 𝑟 = 1 and 𝑟 > 1. In literature,
we can find different functions 𝑤(𝑒), for example [9]. We suggest this function in the form
of (3).
|𝐼(𝑥, 𝑦) − 𝐼(𝑥′ , 𝑦 ′ )|
⎧
⎪
⎨ if 𝑟 = 1,
𝑤(𝑒) = 2
𝐿 ′ ′ (3)
⎩ 𝑑𝑖𝑠𝑡 (𝑣𝑥,𝑦 , 𝑣𝑥′ ,𝑦′ ) − 𝑟 · |𝐼(𝑥, 𝑦) − 𝐼(𝑥 , 𝑦 )| if 𝑟 > 1.
⎪
2𝑟2 𝐿
As one can see, the multiplier 𝐹
𝑑𝑖𝑠𝑡2 (𝑣𝑥,𝑦 , 𝑣𝑥′ ,𝑦′ ) − 𝑟
𝐹 = (4)
2𝑟2 · 𝐿
is a constant for different values 𝑟. Thus, we can pre-calculate these values and store them in a
special matrix. According to (4), value 𝐹 increases with a larger value 𝑟. We can interpret (4) as
an inverse filter with a minimum value at 𝑟 = 1.
Note that the network constructed according to (1)–(3) has the same number of connections,
in other words such network is a regular graph. A regular graph is not a complex network and
requires further transformations. The simplest transformation is to use the threshold value 𝑡
for the original set of edges 𝐸 in order to form a subset 𝐸𝑡 ⊆ 𝐸, where each edge 𝑒 ∈ 𝐸𝑡 has a
weight 𝑤(𝑒) equal to or less than the value 𝑡. As a result of this transformation, a new network
𝐺𝑡 = (𝑉, 𝐸𝑡 ) is formed, which is an intermediate stage in the evolution of the network:
𝐸 * = {𝑒 ∈ 𝐸|𝑤(𝑒) ≤ 𝑡} (5)
Figure 1 depicts an example of creating a complex network using a sliding window with sizes
7 × 7 pixels.
Due to the wide variety of textures, it is difficult to say immediately which values of 𝑟 and 𝑡
will be the best in terms of CN stability. Thus, the learning process of CN is an experimental
selection of these parameters. By applying a set of threshold values 𝑡, 𝑡 ∈ 𝑇 , to the original
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a b c
Figure 1: Creating complex network: a — original image as the nodes in the graph; b — edges of the
nodes, 𝑟 < 3; c — complex network, 𝑡 < 0.11.
network 𝐺, we can study the behavior of texture properties based on calculations of statistical
features. The degree (connectivity) of a node 𝑣 determines the number of edges connected to this
node. Knowing the degree, we can build a histogram and calculate the mean, contrast, energy,
and entropy. These features have a significant role in the description of the texture because
they describe local properties (at the level of neighboring nodes) and global properties (at the
level of histogram). Moreover, it is possible to simulate the dynamic behavior of a complex
network by transforming the original network and then calculating its specific properties [14].
Typically, texture signatures are evaluated using Linear Discriminant Analysis (LDA). The
LDA method is a supervised learning method and, therefore, requires a preliminary determina-
tion of the number of classes. However, other classifiers are also used, for example, based on
distance metrics or histogram analysis by transforming a complex network into local spatial
patterns [7].
Various modifications of complex networks are known, for example, CNs for the catego-
rization of textures, dynamic texture recognition, face recognition, texture classification using
BOVW, etc.
4. Proposed method for texture classification
The developed method of texture classification takes into account different image scales. Scale
invariance is achieved by building a pyramid of images in such a way that the texture is analyzed
by sliding windows of sizes 31 × 31, 15 × 15 and 7 × 7 pixels. Also we chose the values of
parameters r and t during the CN learning. Aerial photographs are high resolution images,
thus the number of extracted texture samples will be sufficient for supervised learning. During
testing, parameters such as mean 𝑀 , contrast 𝐶, energy 𝐸 and entropy 𝐻 are calculated for
each analyzed patch using (6)–(9), where 𝑧𝑖,𝑗 is the intensity value, 𝑝(𝑧𝑖,𝑗 ) is the number of
pixels with values 𝑧𝑖,𝑗 , 𝑀 is the size of the sliding window in one direction, 𝐿 is the number of
intensity levels, 𝐿 = 255.
𝑀 ∑︁𝑀
1 ∑︁
𝑀= 𝑧𝑖,𝑗 , (6)
𝑀 ×𝑀
𝑖=1 𝑗=1
∑︁ 𝐿−1
𝐿−1 ∑︁
𝐶= 2
𝑝(𝑧𝑖,𝑗 )𝑧𝑖,𝑗 , (7)
𝑖=0 𝑗=0
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𝐿−1
∑︁ 𝐿−1
∑︁
𝐸= 𝑝2 (𝑧𝑖,𝑗 ), (8)
𝑖=0 𝑗=0
𝐿−1
∑︁ 𝐿−1
∑︁
𝐻=− 𝑝(𝑧𝑖,𝑗 ) log2 𝑝(𝑧𝑖,𝑗 ). (9)
𝑖=0 𝑗=0
One of the interesting but difficult to calculate texture parameters is the fractal dimensionality.
The main idea is to verify that CNs consist of self-repeating patterns at all scales, using fractal
methodologies. This is a special issue for further investigation. Note that fractal dimensionality
is a distinctive feature of natural and man-made objects.
Analysis of color aerial photographs leads to triple increase in the number of features in RGB
color space. In this case, we build multilayer CNs close to the approach presented in [15].
Aerial photographs, as a rule, contain a limited number of textures. Therefore, the classifi-
cation stage can be simplified using the Minkowski distance [16] or the maximum likelihood
method as an estimation function. The study is aimed at comparing the results of texture
classification in the spatial domain with and without the factor of scale invariance of aerial
photographs.
5. Experimental results
Since we could not find a publicly available aerial texture dataset, we used 12 video sequences
obtained from a dataset “Drone Videos DJI Mavic Pro Footage in Switzerland” [17] and aerial
photographs from dataset “Aerial Textures” [18]. The dataset “Drone Videos DJI Mavic Pro
Footage in Switzerland” can be applied to a variety of computer vision tasks and has no ground-
truth labels. This dataset includes 18 short video sequences in various natural environments
with and without people present. The total size is 1.71 GB. We used frames from 6 video
sequences. Dataset “Aerial Textures” is a library, which consists of 145 high quality textures in
extremely high resolution of up to 400 million pixels, suitable for general usage, and includes
images of roads, cross road walks, fields and pavements at different times of season and frozen
water features. This library provides photorealistic texturing of large areas with close views.
We used about 40 high resolution photographs from “Aerial Textures Field Summer” and “Aerial
Textures Road Summer”. The total size of “Aerial Textures JPG, Field Summer” and “Aerial
Textures JPG, Road Summer” is 10.9 GB. The main parameters of video sequences and aerial
photographs are depicted in Table 1.
We created our own dataset as a set of texture patches belonging to the classes “Forest”,
“Meadow”, “Field”, “Road”, “Mountains”, “River”, “Sand”, and “Sky”. Each class includes 40–
60 patches, thus our dataset is balanced. The total number of patches is 420 patches of 192 ×
192 pixels, which were divided into training set and test set as 70% and 30%, respectively.
Examples of patches are depicted in Figure 2.
Texture analysis was performed in “The R Project for Statistical Computing”. The used sliding
windows had sizes 31 × 31, 15 × 15 and 7 × 7 pixels. During the experiments, we adapted
the parameters of 𝑟 and 𝑡 (see Figure 1) for each scale and each class. Such manual setting is a
disadvantage of using CNs. However, this approach is suitable for solving the problem with
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Table 1
Main parameters of test frames and photographs.
Drone Videos DJI Mavic Pro Footage in Switzerland Aerial Textures
Number
Caption First frame Resolution Caption Photograph Resolution
of frames
AET
Berghouse
1280 × 720 1073 FIELD 8000 × 8000
Leopard.mp4
Summer 03
AET
Bluemlisal
1280 × 720 957 FIELD 8000 × 6000
Flyover.mp4
Summer 10
AET
Isles of
1280 × 720 899 FIELD 12000 × 10000
Glencoe.mp4
Summer 20
AET
DJI_0501.mov 3840 × 2160 232 ROAD 10000 × 1700
Summer 33
AET
DJI_0574.mov 3840 × 2160 928 ROAD 16000 × 9000
Summer 45
AET
DJI_0596.mov 3840 × 2160 1015 ROAD 12000 × 6000
Summer 55
a b
c d
e f
g h
Figure 2: Examples of patches from eight classes: “Forest”, “Meadow”, “Field”, “Road”, “Mountains”,
“River”, “Sand”, “Sky” (a–h respectively).
limited classes. Since textures belonging to the same class are not homogeneous, the structures
of CNs are different for different scaling. We calculated mean 𝑀 , contrast 𝐶, energy 𝐸 and
entropy 𝐻 for three scales and three color components (R, G and B) for each class of texture
using CNs based on the training set. For classification, we used the Minkowski distance.
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We compared our results with the conventional texture analysis based on a statistical approach
similar to texture analysis done in [19] using normalized energy 𝐸𝑛 , relative smoothness 𝑅𝑚
and normalized entropy 𝐻𝑛 . The formulae for estimating normalized homogeinity 𝐸𝑛 , relative
smoothness 𝑅𝑚 and normalized entropy 𝐻𝑛 are provided by (10)–(12).
𝐿−1
∑︁ 𝐿−1
∑︁ ⧸︁
𝐸𝑛 = 𝑝2 (𝑧𝑖,𝑗 ) log2 𝐿, (10)
𝑖=0 𝑗=0
−𝑙𝑜𝑔𝑅 if 𝑅 > 0
{︂
1
𝑅=1− , 𝑅𝑚 = , (11)
𝐿−1 ⧸︁ 10 if 𝑅 = 0
2 2
∑︀
1+ (𝑧𝑖 − 𝑚) 𝑝(𝑧𝑖 ) (𝐿 − 1)
𝑖=0
(12)
⧸︀
𝐻𝑛 = 𝐻 log2 𝐿.
Table 2
Comparative results of texture classification.
The conventional texture analysis The proposed CNs analysis
Class Size of patch
Mean TR, % Mean HTER, % Mean TR, % Mean HTER, %
7×7 94.02 6.87 96.12 4.65
Forest 15 × 15 95.32 5.79 97.02 3.84
31 × 31 95.92 5.68 97.81 3.07
7×7 92.96 7.17 94.26 5.85
Meadow 15 × 15 93.52 7.59 96.76 4.72
31 × 31 93.36 6.61 96.90 4.15
7×7 94.46 6.11 95.28 5.84
Field 15 × 15 94.98 5.89 96.41 4.92
31 × 31 95.02 5.64 97.08 4.98
7×7 95.98 5.08 95.65 5.85
Road 15 × 15 96.32 4.23 97.16 3.70
31 × 31 96.46 4.01 97.89 3.24
7×7 97.24 3.97 98.41 3.05
Mountains 15 × 15 98.02 3.72 98.92 2.39
31 × 31 98.32 3.02 99.08 2.27
7×7 94.02 6.52 93.20 8.08
River 15 × 15 94.19 5.19 93.48 6.83
31 × 31 95.22 4.05 95.91 4.25
7×7 84.91 14.82 86.90 13.96
Sand 15 × 15 85.44 14.39 88.23 11.02
31 × 31 87.28 10.04 88.82 11.49
7×7 90.54 9.71 89.29 10.86
Sky 15 × 15 91.49 8.19 90.02 9.62
31 × 31 92.18 7.87 92.73 7.39
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For texture classification was used artificial neural network of direct propagation with three
hidden layers. The comparative results are shown in Table 2, where TR is True Recognition and
HTER is Half Total Error Rate, which combines the False Rejection Rate (FRR) and the False
Acceptance Rate (FAR).
The results presented in Table 2 show that the CNs approach classifies the homogeneous
textures close to statistical approach. This can be explained by the fact that CNs build almost
regular graphs on homogeneous textures. Mean TR values are in the ranges 84.91–98.32 and
87.29–99.08 for conventional texture analysis and proposed CNs analysis, respectively (in Table 2,
the best true recognition results are highlighted in bold). Images with explicit fractal structures
provide the best recognition accuracy. In our case, there are “Mountains” and “Forest”. Also
good results were achieved due to the color differences of the class samples in this limited
dataset, despite the available color variations within the same class. The main advantages of our
approach are the ability to reflect the physical nature of textures and low computational costs
at the training step due to the use of simple metrics for classification. Multiscaling increases the
recognition accuracy slightly and decreases the HTER values in a statistical sense, primarily
due to the fractal properties of natural textures.
6. Conclusions
In this research, we study the application of CNs theory for texture classification in aerial
photographs. We propose a new function for calculating the weights of the edges and introduce
a CN training based on multiscale and multilayer properties. For experiments, own dataset was
created from the video sequences “Drone Videos DJI Mavic Pro Footage in Switzerland” and
photographs of the “Aerial Textures”. It includes a set of texture patches belonging to the classes
“Forest”, “Meadow”, “Field”, “Road”, “Mountains”, “River”, “Sand”, and “Sky”. The conducted
experiments show that despite the CNs approach classifies the natural textures close to statistical
approach, the proposed CNs reflect the physical nature of textures and have low computational
costs at the training step due to the use of simple metric for classification (Minkowski distance).
In general, the results of true recognition are 1–3% higher compared to conventional texture
analysis.
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