Wavelet Transform for the Analysis of Convolutional Neural Networks in
Texture Recognition
Joao Batista Florindo
Institute of Mathematics, Statistics and Scientific Computing, University of Campinas,
Rua S
ergio Buarque de Holanda, 651, Cidade Universit
aria ”Zeferino Vaz”,
Distr. Barao Geraldo, CEP 13083-859, Campinas, SP, Brazil
Convolutional Neural Networks, Wavelet Transform, Multiscale Analysis, Fractal Theory, Texture
Convolutional neural networks have become omnipresent in applications of image recognition during the last
years. However, when it comes to texture analysis, classical techniques developed before the popularity of
deep learning has demonstrated potential to boost the performance of these networks, especially when they
are employed as feature extractor. Given this context, here we propose a novel method to analyze feature
maps of a convolutional network by wavelet transform. In the first step, we compute the detail coefficients
from the activation response on the penultimate layer. In the second one, a one-dimensional version of local
binary patterns are computed over the details to provide a local description of the frequency distribution.
The frequency analysis accomplished by wavelets has been reported to be related to the learning process of
the network. Wavelet details capture finer features of the image without increasing the number of training
epochs, which is not possible, in feature extractor mode. This process also attenuates over-fitting effect at the
same time that preserves the computational efficiency of feature extraction. Wavelet details are also directly
related to fractal dimension, an important feature of textures and that has also recently been found to be related
to generalization capabilities. The proposed methodology was evaluated on the classification of benchmark
databases as well as in a real-world problem (identification of plant species), outperforming the accuracy of
the original architecture and of several other state-of-the-art approaches.
In the last years, convolutional neural networks
(CNN) have been successfully employed in a vari-
ety of tasks in computer vision, including image clas-
sification (Krizhevsky et al., 2017), object recogni-
tion (Ren et al., 2017), image segmentation (Chen
et al., 2018), video analysis (Ng et al., 2015), etc.
Among such tasks, an important topic that also has
benefited from CNNs is texture recognition (Cim-
poi et al., 2016). Besides theoretical developments,
CNN-based algorithms have also been applied to sev-
eral real-world problems in which texture images play
fundamental role, such as in medicine (Shin et al.,
2016), remote sensing (Zhu et al., 2017), face recog-
nition (Taigman et al., 2014), and others.
Despite the great performance of classical CNN
architectures in texture recognition, it has been also
shown that other strategies can leverage the power of
those neural networks, either increasing the classifi-
cation accuracy or reducing computational require-
ments for training of the learning model. In par-
ticular, traditional texture representations that have
been successful in the years before the populariza-
tion of deep learning have been recently rediscovered
and combined with CNNs in hybrid models that have
demonstrated interesting capabilities. A remarkable
example is deep filter banks (Cimpoi et al., 2016),
that use convolutional feature maps as local descrip-
tors and classical encodings like Fisher vectors and
“bag-of-visual-words”. In (Ji et al., 2020), the au-
thors obtain high classification accuracy and perfor-
mance by introducing constraints and compression
techniques associated to local binary patterns (LBP)
(Ojala et al., 2002) to a convolutional/recurrent neu-
ral network. In (Anwer et al., 2018), LBP maps are
combined with the original image at different stages
of the CNN improving the recognition capacity. In T-
CNN (Andrearczyk and Whelan, 2016), CNN feature
Florindo, J.
Wavelet Transform for the Analysis of Convolutional Neural Networks in Texture Recognition.
DOI: 10.5220/0010866700003124
In Proceedings of the 17th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2022) - Volume 4: VISAPP, pages
ISBN: 978-989-758-555-5; ISSN: 2184-4321
2022 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
maps are also interpreted as filter banks and an energy
measure is established to provide feature vectors for
image representation. We should also mention here
the “handcrafted” CNN descriptors, that use CNN-
like architectures, but associated with pre-defined fil-
ter banks. Examples are NmzNet (Vu et al., 2017),
ScatNet (Bruna and Mallat, 2013), PCANet (Chan
et al., 2015), etc.
In this context, we propose the use of wavelet
transforms as a technique for the analysis of CNN
feature maps. Following ideas like those devel-
oped in (Cimpoi et al., 2016), we apply the wavelet
transform over the penultimate fully-connected layer
of the CNN. In the following, we calculated one-
dimensional binary patterns (Tirunagari et al., 2017)
of the detail signal to form the final texture repre-
sentation. The frequency distribution of the neu-
ral response, here described by wavelet transform, is
known to be related to the learning evolution (Ra-
haman et al., 2019). Injecting such complementary
information to the image descriptors has potential to
be very beneficial to a more robust representation.
Furthermore, using the different radii for binary pat-
terns ensures a second layer of multiscale analysis
over localized frequencies. Together, these transfor-
mations of the activation response are capable of ex-
pressing the localized frequency at multiple scale lev-
els, capturing a complete mapping of the CNN both
in frequency and spatial domain.
The proposed methodology was assessed on the
classification of four benchmark data sets: KTHTIPS-
2b (Hayman et al., 2004), FMD (Sharan et al., 2009),
UIUC (Lazebnik et al., 2005), and UMD (Xu et al.,
2009). It was also applied to a practical problem, that
of identifying Brazilian plant species based on the leaf
surface texture (Casanova et al., 2009). The results
are competitive with the state-of-the-art on texture
recognition and suggest our proposal as a promising
approach for practical purposes, especially for smaller
datasets where the use of CNN as a feature extractor
is more appropriate.
2.1 Motivation
An interesting result obtained by theoretical studies
on neural networks is that low frequencies (global
viewpoint) are learned before high frequencies (fine
details) along the training epochs (Rahaman et al.,
2019). The reader can check, for example, Figure 2 in
(Ronen et al., 2019) for an intuition. Evidences sug-
gest that such “learning guided by frequency” phe-
nomena, confirmed both theoretically for toy mod-
els and empirically on realistic deep neural networks,
does not occur by chance and that it could be ex-
plored further. In particular, if frequencies are im-
portant during the training, it makes sense to imagine
that they are relevant at the output of the network as
well. Given that the training usually stops after a fixed
number of cycles, it is expected that the distribution of
frequencies in the output response of the network is
tightly related to the distribution on the input (image
in our case). On the other hand, it is also well known
in image processing and analysis that frequency anal-
ysis provides an alternative complementing viewpoint
of the original spatial representation. This same infor-
mation however has not been sufficiently explored on
the network response.
Fourier transform is the most well known tool for
frequency analysis and would be a natural candidate
for the same analysis on neural networks. Neverthe-
less, a simple observation of the response distribution
makes it clear how the information conveyed drasti-
cally varies depending on the observed region of the
signal. This is a consequence both of the random ini-
tialization and the complexity of the neural network
function. In this context, wavelet analysis is more
suitable as it supports the spatial localization together
with the frequency. We have in this way a more com-
plete description of the frequency distribution on the
network. Furthermore, the energy of wavelet details
is known to be directly related to the fractal dimen-
sion of the signal (Mallat, 2008). Besides being an
important feature in texture analysis (Xu et al., 2009),
recent studies have also established connections be-
tween such dimension and the generalization perfor-
mance of neural networks (Simsekli et al., 2020).
Figure 1 shows the wavelet scalograms and fre-
quency distribution at the penultimate layer of a CNN,
for three clearly different textures: an irregular pro-
file T1 (“pebbles”), a homogeneous texture T2 (“fur”)
and an artificial periodic material T3 (“corduroy”). At
the bottom we see the average energy contributed by
each frequency in each texture. T3 spectrum is more
balanced, not surpassing the magnitude of the other
samples with localized peaks. This corresponds to
moderate contribution of a larger band of frequencies
and is consequence of the multiscale regularity, corre-
sponding to multiple frequencies arising. For T1 and
T2, they alternate their influence in each frequency
region. T2 has two wide peaks around 0.1 and 0.25,
whilst T1 concentrates around 0.15 and 0.45. Such
shift to lower frequencies in T2, when compared with
T1, is a consequence of the regular patterns in T1,
even though we do not have the same homogeneity
presented by T3 now.
Wavelet Transform for the Analysis of Convolutional Neural Networks in Texture Recognition
T1 T2 T3
0 100 200 300 400 500
0 100 200 300 400 500
0 100 200 300 400 500
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Figure 1: Three types of textures: irregular (T1), natu-
ral regular (T2), and artificially periodic (T3). Below we
have the wavelet scalograms of each texture and the aver-
age magnitude on the frequency range.
Such remarkable behavior naturally points out
to the possibility of exploring wavelet decomposi-
tion of neural network responses. The combina-
tion of wavelets with neural networks has in fact
been explored in the literature (Zhang and Benveniste,
1992; Alexandridis and Zapranis, 2013; Fujieda et al.,
2017). These works, however, usually focus on intro-
ducing new trainable elements into the network archi-
tecture. Here we opt for a significantly simpler strat-
egy of applying multi-resolution wavelets to the net-
work activation response, which besides having sim-
pler implementation, allows for more in-depth studies
in the future on how such responses are affected by
frequency response (a more elaborated version of the
analysis in Figure 1).
2.2 Implementation
Based on these assumptions, the proposed method
relies on the processing of the activation responses
of neurons at the penultimate fully-connected layer.
Here we use the VGGVD architecture as in (Cimpoi
et al., 2016). Each image is processed by the already
trained neural network outputting a vector of real val-
ues at that layer. Such vector is therefore processed
by a composite operator formed by a combination of
a discrete wavelet transform (Mallat, 2008) and local
binary patterns in their 1D version, as described in
(Tirunagari et al., 2017).
In the following we calculate the detail coeffi-
cients d
. In discrete domain they can be obtained
(n), j j
, (1)
where j is the decomposition level, M is the length of
y and φ and ψ are the wavelet functions. These coeffi-
cients can be easily obtained in any modern scientific
programming language. Here we use symlet4 wavelet
functions (Mallat, 2008). Two levels of decomposi-
tion are employed here yielding the vectors d
In the next step, those detail vectors are linearly
combined with a predefined weight α:
(1 α)ds(y) + αd
if 0 α 1,
(2 α)ds(d
) + (α 1)d
if 1 α 2,
where ds is a downsampling function (here using a
lowpass Chebyshev Type I infinite impulse response
filter of order 8). The downsampling operation is nec-
essary to make the combined vectors to have the same
Finally, the descriptors are given by applying 1D
LBP with radius r over D
). (3)
The proposed method essentially explores two
complementary fundamental viewpoints of the tex-
ture neural activation: the frequency and spatial dis-
tribution. At the same time it benefits from all the
machinery of CNNs and their capacity of extracting
features in highly complex hierarchical organizations.
The efficient local description provided by LBP over
the high frequency distribution captured by wavelet
details has the effect of providing a detailed map of
finer details in the output CNN function. According to
studies like (Rahaman et al., 2019), this corresponds
VISAPP 2022 - 17th International Conference on Computer Vision Theory and Applications
precisely to characteristics learned in more advanced
stages of the CNN. On the other hand, frequency do-
main is not restrict to a well-localized point on the
loss surface, such that this type of analysis ends up
being less susceptible to over-fitting than simply us-
ing a very large number of epochs in the CNN model.
We assess the performance of the proposed method
in texture recognition over four benchmark datasets
(KTHTIPS-2b (Hayman et al., 2004), FMD (Sharan
et al., 2009), UIUC (Lazebnik et al., 2005), and UMD
(Xu et al., 2009)) and an application to the identifi-
cation of Brazilian plant species (database 1200Tex
(Casanova et al., 2009)).
KTH-TIPS2b database is composed by 4752 color
images of 11 different materials (classes). Unlike
classical texture databases, that are focused on visual
appearance, here each target group may contain sub-
stantially different images. This is particularly chal-
lenging mainly for classical local patch approaches
like LBP and bag-of-visual-words. Each material is
further divided into 4 samples, each sample corre-
sponding to particular settings of illumination, scale
and perspective. Here we adopt the most challeng-
ing protocol of training on 1 sample of each class and
testing on the remaining 3 samples.
FMD is also a material-based dataset. Comprises
10 classes with 100 color images per class and the
training/testing protocol is a random split with 50%
for training and 50% for testing, which is repeated 10
times to provide statistical measures.
UIUC and UMD, on the other hand, are typical
texture-based databases. Both comprise 25 classes
with 40 grayscale samples in each class. Both are also
collected under non-controlled conditions and share
variations in scale, illumination and viewpoint. The
most remarkable differnce is in resolution: whereas
UIUC has smaller images with size 640 ×480, UMD
images has resolution 1280 ×960.
1200Tex (Casanova et al., 2009) is a database of
color texture images acquired by scanning the leaf
surface of 60 species of Brazilian plants. The ob-
jective is to identify the respective species. A com-
mercial scanner is used and conditions of illumina-
tion, pose and scale are strictly controlled. For each
class (species) we have 60 image samples, each one
corresponding to a non-overlapping window with size
128 ×128. The training/testing split is the same one
used in UIUC and UMD, i.e., 50% for training and
50% for testing.
For the classification we employed linear discrim-
inant analysis (Bishop, 2006), mainly for its ease of
interpretation and no need for tuning a large number
of hyper-parameters. Given the high number of fea-
tures, we also applied principal component analysis
(Bishop, 2006). The number of components was de-
fined by cross-validation over the training set.
Figure 2 shows the classification accuracies on the
compared databases when parameters r and α are var-
ied. In general, we observe that r = 0, i.e., the direct
use of wavelet transform is a good choice in most sce-
narios. Nevertheless, some significant boost was ob-
tained in KTH and UIUC by using r = 2 and r = 3,
respectively. It can also be noticed that r = 2 and r = 3
are in general preferred over r = 1. Another interest-
ing point is that the best performance is achieved usu-
ally for α 1.0, which corresponds to the first level
of detail coefficients. Actually, we verified the accu-
racy for higher levels but no gain was obtained. Table
2 lists the best accuracies for each LBP radius, also
confirming the effectiveness of using r = 0.
Tables 1 and 2 present the accuracies compared
to state-of-the art results published in the literatures
on the same databases and using the same protocol.
We separate KTH, FMD, UIUC, and UMD (bench-
mark data sets) from 1200Tex (application) due to
the comparatively reduced number of results for the
later in the literature. In both cases we notice the
proposed descriptors outperforming several state-of-
the-art methods, including advanced CNN-based so-
lutions. This is more evident in the most challenging
databases, i.e., KTH, FMD and 1200Tex. Even when
the proposed descriptors were surpassed in a few sit-
uations in UMD and UIUC databases, they achieved
higher accuracy in the other ones.
In summary, the presented results corroborate our
expectations of an improved performance of CNNs
when associated to the wavelet representation. The
details coefficient were capable of extracting a fine-
grained description of the image, but avoiding over-
fitting due to the non-localized behavior of frequency
distribution. Altogether, this was the rationale behind
a more complete CNN representation for the texture
image, that was responsible for more robust descrip-
tors and, as a consequence, higher classification accu-
racies in general.
Wavelet Transform for the Analysis of Convolutional Neural Networks in Texture Recognition
0 0.5 1 1.5 2
Accuracy (%)
r = 0 r = 1 r = 2 r = 3
0 0.5 1 1.5 2
Accuracy (%)
r = 0 r = 1 r = 2 r = 3
0 0.5 1 1.5 2
Accuracy (%)
r = 0 r = 1 r = 2 r = 3
0 0.5 1 1.5 2
Accuracy (%)
r = 0 r = 1 r = 2 r = 3
0 0.5 1 1.5 2
Accuracy (%)
r = 0 r = 1 r = 2 r = 3
Figure 2: Accuracies of the proposed method for different hyperparameters on the texture databases. Even though r = 0 works
fine in most cases, LBP improved the accuracy in more complicated scenarios, e.g., in KTHTIPS-2b textures.
This work presented a new method for texture recog-
nition extracting wavelet details from the penultimate
layer of a CNN. Such coefficients were also subjected
to LBP analysis to improve even further its ability of
capturing the complexity of a visual texture.
The performance of the proposal was evaluated
in terms of accuracy on the classification of bench-
mark datasets and on a practical problem of identi-
fying plant species using the leaf surface texture. In
this tasks, the proposed method outperformed several
state-of-the-art approaches for texture recognition, at-
testing its potential as a powerful representation for
texture images.
The success of the proposed methodology can be
expected and explained in theoretical terms by a novel
perspective over the CNN offered by the localized fre-
quency analysis of wavelets. Detail coefficients de-
scribe fine-grained characteristics of the image at the
same time that frequency domain prevents over-fitting
as the feature is not exactly localized in space.
J. B. Florindo gratefully acknowledges the financial
support of S
ao Paulo Research Foundation (FAPESP)
(Grant #2020/01984-8) and from National Council
for Scientific and Technological Development, Brazil
(CNPq) (Grants #306030/2019-5 and #423292/2018-
VISAPP 2022 - 17th International Conference on Computer Vision Theory and Applications
Table 1: Accuracies for different databases: KTHTIPS-2b, FMD, UIUC, and UMD. Several state-of-the-art approaches are
outperformed by the proposed method.
VZ-MR8 (Varma and Zisserman, 2005) 46.3 22.1 92.9 -
LBP (Ojala et al., 2002) 50.5 - 88.4 96.1
VZ-Joint (Varma and Zisserman, 2009) 53.3 23.8 78.4 -
BSIF (Kannala and Rahtu, 2012) 54.3 - 73.4 96.1
CLBP (Guo et al., 2010a) 57.3 43.6 95.7 98.6
/VAR (Ojala et al., 2002) 58.5 - 84.4 95.9
PCANet (NNC) (Chan et al., 2015) 59.4 - 57.7 90.5
RandNet (NNC) (Chan et al., 2015) 60.7 - 56.6 90.9
ScatNet (NNC) (Bruna and Mallat, 2013) 63.7 - 88.6 93.4
DeCAF (Cimpoi et al., 2014) 70.7 60.7 94.2 96.4
SIFT + BoVW (Cimpoi et al., 2014) 58.4 49.5 96.1 98.1
FC-CNN VGGM (Cimpoi et al., 2016) 71.0 70.3 94.5 97.2
FC-CNN AlexNet (Cimpoi et al., 2016) 71.5 64.8 91.1 95.9
FC-CNN VGGVD (Cimpoi et al., 2016) 75.4 77.4 97.0 97.7
RAMBP (Alkhatib and Hafiane, 2019) 68.9 46.8 94.8 98.6
H2OEP (Song et al., 2021) 64.2 - - -
SWOBP (Song et al., 2020) 66.4 - - -
SLGP (Song et al., 2018b) 53.6 - - -
LBPC (Singh et al., 2018) 50.7 - - -
LETRIST (Song et al., 2018a) 65.3 - 97.7 98.8
(Pan et al., 2019) - - 92.2 93.5
(Pan et al., 2019) - - 95.2 94.2
DSTNet (Florindo, 2020) 61.0 - 93.6 98.5
2D-LTP (Xiao et al., 2019) - 49.0 - -
Proposed 77.2 77.7 98.1 99.0
Table 2: State-of-the-art accuracies for 1200Tex. Outper-
forming computationally intensive methods like FV-CNN
is a remarkable achievement.
Method Accuracy (%)
LBPV (Guo et al., 2010b) 70.8
Network diffusion (Gonc¸alves et al., 2016) 75.8
FC-CNN VGGM (Cimpoi et al., 2016) 78.0
FV-CNN VGGM (Cimpoi et al., 2016) 83.1
Gabor (Casanova et al., 2009) 84.0
FC-CNN VGGVD (Cimpoi et al., 2016) 84.2
SIFT + BoVW (Cimpoi et al., 2014) 86.0
FV-CNN VGGVD (Cimpoi et al., 2016) 87.1
DSTNet (Florindo, 2020) 79.3
Proposed 88.2
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