=Paper= {{Paper |id=Vol-3074/paper16 |storemode=property |title=Gated Local Adaptive Binarization using supervised learning |pdfUrl=https://ceur-ws.org/Vol-3074/paper16.pdf |volume=Vol-3074 |authors=Javier Fumanal Idocin, Juan Uriarte, Borja De la Osa, Francesco Bardozzo, Javier Fernández,Humberto Bustince |dblpUrl=https://dblp.org/rec/conf/wilf/Fumanal-IdocinU21 }} ==Gated Local Adaptive Binarization using supervised learning== https://ceur-ws.org/Vol-3074/paper16.pdf

Gated Local Adaptive Binarization using Supervised
Learning
Javier Fumanal-Idocin1 , Juan Uriarte1 , Borja de la Osa1 , Francesco Bardozzo2 ,
Javier Fernández1 and Humberto Bustince1
1
Estadística, Informática, Matemáticas, Public University of Navarre
2
Neuronelab, DISA-MIS, University DegliStudy di Salerno

Abstract
Image thresholding is one of the most popular problems in image processing. However, changes in
lightning and contrast in an image can cause trouble for the existing algorithms that use a global thresh-
old for all the image. A solution for this problem is the adaptive thresholding, in which an image can
have different thresholds for different parts of the image. Yet, the problem of choosing the most suitable
threshold for each region of the image is still open. In this paper we present the Gated Local Adaptive
Binarization algorithm, in which we choose the most appropriate threshold for each region of the image
using a logistic regression. Our results show that this algorithm can effectively learn the most appropri-
ate threshold in each situation, and beats other adaptive binarization solutions for a standard dataset in
the literature.

Keywords
Fuzzy logic, Image Thresholding, Image Processing, Aggregation functions

1. Introduction
Image processing ins one of the most important research topics in the computer science areas [1,
2, 3]. Many problems have been studied in this area, like classification [4, 5, 6] and segmentation
of different objects in an image [7]. One of the most researched topics in image processing is
image thresholding [8, 9], also called image binarization, which consists of discriminating the
objects in an image from the background.
The most popular binarization algorithm is the Otsu algorithm [10], and many other popular
algorithms have been proposed [11, 12, 13]. All of these algorithms work by establishing a
global threshold for the whole image. However, this strategy results in poor performance when
there are changes in the lightning and contrast of the image. In that case, the same threshold
cannot adapt itself to the different conditions in the image.
Adaptive thresholding was proposed in [14] as a mean to solve this problem, by choosing a
different threshold for the different parts of the image. This algorithm works by precomputing

WILF 2021: International Workshop on Fuzzy Logic and Applications
" javier.fumanal@unavarra.es (J. Fumanal-Idocin); juan@losuriarte.es (J. Uriarte);
borjajose.delaosa@unavarra.es (B. d. l. Osa); fbardozzo@unisa.it (F. Bardozzo); fcojavier.fernandez@unavara.es
(J. Fernández); bustince@unavara.es (H. Bustince)
~ https://fuminides.netlify.app/ (J. Fumanal-Idocin)
0000-0002-0644-1355 (J. Fumanal-Idocin); 0000-0003-0199-6623 (F. Bardozzo)
© 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)
the integral image from the original one, and sliding a 3 × 3 window through all integral image,
where each window will use a different threshold according to its own characteristics. The
Adaptive thresholding was further developed in [15]. In that work, the authors focused on
the possible improvements using aggregation functions, and proposed a new generalization
of the Sugeno integral. Indeed, aggregation functions [16] have been successfully used in
many decision making problems [17, 18], brain computer interface classification tasks [19, 20],
community detection [21] and other image processing tasks [22, 23, 24, 25].
However, there were some limits in the improvements of the algorithm proposed in [15],
as the fusion processes are limited by the quality of the data to fuse with the tested integrals.
In this work we propose a new algorithm to perform dynamic thresholding, the Gated Local
Adaptive Binarization (GLAB), that uses supervised learning to improve the results obtained by
other adaptive algorithms, based on a “gated” fusion process [26]. We also present a series of
extensions to the FLAT algorithm using other aggregation functions to compare to our newly
developed GLAB.
The rest of this paper goes as follows: Section 2 describes the algorithm proposed in [15], the
different aggregation functions used to extend it, and the proposed GLAB. Section 3 describes
our experiments and illustrates the results obtained. Finally, Section 4 details our conclusions
for this work and future lines of research.

2. Methods
In this section we discuss the Fuzzy Local Adaptive Thresholding (FLAT) algorithm, and the
proposed Enhanced Local Adaptive Thresholding.

2.1. Fuzzy Local Adaptive Thresholding
The FLAT algorithm was proposed by Bardozzo et al. in [15] to improve the results of the local
Adaptive thresholding algorithm proposed in [14] using a new generalization of the Sugeno
integral. The FLAT algorithm consist of computing the fuzzy integral image of the original
image, and then perform the Adaptive binarization on the computed integral image.

2.2. Computing the fuzzy integral image
To compute the Fuzzy Integral Image, 𝐹𝐴 , we first compute the integral image 𝑆, using the
formula:
𝑆(𝑥, 𝑦) = 𝑝(𝑥, 𝑦) + 𝑆(𝑥, 𝑦 − 1) + 𝑆(𝑥 − 1, 𝑦) − 𝑆(𝑥 − 1, 𝑦 − 1) (1)
where 𝑝 is the original image, and with convention 𝑆(0, ·) = 0 and 𝑆(·, 0) = 0. Then, we
compute the 𝐹𝐴 as follows:

𝐹𝐴 (𝑥, 𝑦) = 𝐴(𝑆(𝑥, 𝑦), 𝑆(𝑥, 𝑦 − 1), 𝑆(𝑥 − 1, 𝑦), 𝑆(𝑥 − 1, 𝑦 − 1)) (2)
where 𝐴 is an aggregation function. The best result obtained in [15] was obtained using the
following Sugeno-like integral:
𝑛
∑︁
(3)
(︀ )︀
𝐴= 𝑥𝜎(𝑖) · 𝜇(𝐸𝑖 )
𝑖=1

where 𝑥𝜎 is a permutation of 𝑥 such that 𝑥𝜎𝑖 < 𝑥𝜎𝑖 +1 for 𝑖 ∈ {1, . . . , |𝑥|}, 𝐸𝑖 = {(𝑖), . . . , (𝑛)}
and 𝜇(𝐸𝑖 ) is a fuzzy measure [27] that follows the expression:

|𝐸𝑖 |
𝜇(𝐸𝑖 ) = (4)
𝑛

2.3. Computing adaptive binarization
We compute the threshold for each window of size 𝑎𝑖 × 𝑎𝑗 , usually a 3 × 3. For each of these
windows we do as follows:
1. Compute the area of the window:

𝑝𝑎𝑟𝑒𝑎 = 𝑎𝑖 × 𝑎𝑗 (5)

2. Compute the area in the fuzzy integral image:

𝑝𝑠 = 𝐹𝐴 [𝑦1 , 𝑥1 ] − 𝐹𝐴 [𝑦0 , 𝑥1 ] − 𝐹𝑎 [𝑦1 , 𝑥0 ] + 𝐹𝐴 [𝑦0 , 𝑥0 ] (6)

3. Compute the threshold using the ratio:
𝑝𝑠
𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 = (7)
𝑝𝑎𝑟𝑒𝑎
where 𝑥0 , 𝑥1 , 𝑦0 , 𝑦1 are the corners of the window. So, for each pixel we compute the corre-
sponding threshold using the 𝑎1 × 𝑎2 window where that pixel is the center, cropped in the
case of the borders of the image.

2.4. Gated Local Adaptive Thresholding
The Gated Local Adaptive Thresholding (GLAB) is a modification of the FLAT algorithm in
which the final threshold is computed using a logistic regression, using the values in the 𝑎1 × 𝑎2
window as an input vector, 𝐼, we compute the resulting threshold using the expression:

𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 = 𝜎(𝑊 𝐼 + 𝑏) (8)

where 𝑊 is the weight vector and 𝑏 the bias to learn respectively, and 𝜎 is the logistic
function.
Figure 1: The dataset of 9 images used for this experimentation.

2.5. Evaluation Metrics
As a evaluation metric, we have used the 𝐹1 score, comparing the obtained thresholding solution
with the ground truth label for each image. The 𝐹1 score is computed using the following
formulas, using the concepts of precision and recall:

𝑇 𝑟𝑢𝑒𝑃 𝑜𝑠𝑖𝑡𝑖𝑣𝑒
𝑃 𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 = (9)
𝑇 𝑟𝑢𝑒𝑃 𝑜𝑠𝑖𝑡𝑖𝑣𝑒 + 𝐹 𝑎𝑙𝑠𝑒𝑃 𝑜𝑠𝑖𝑡𝑖𝑣𝑒
𝑇 𝑟𝑢𝑒𝑃 𝑜𝑠𝑖𝑡𝑖𝑣𝑒
𝑅𝑒𝑐𝑎𝑙𝑙 = (10)
𝑇 𝑟𝑢𝑒𝑃 𝑜𝑠𝑖𝑡𝑖𝑣𝑒 + 𝐹 𝑎𝑙𝑠𝑒𝑁 𝑒𝑔𝑎𝑡𝑖𝑣𝑒
𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 * 𝑟𝑒𝑐𝑎𝑙𝑙
𝐹1 = 2 (11)
𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 + 𝑟𝑒𝑐𝑎𝑙𝑙

3. Experimentation
In this work we have taken the image thresholding dataset taken from [28], that consists of 9
different images in grayscale with ground-truth labels for each pixels. We show the images in
Figure 1.
We studied the effect of different global threshold in the FLAT algorithm, in order to study
the relevance of this parameter in the FLAT algorithm, and then, we studied the performance of
the FLAT and GLAB algorithm for the images displayed in Figure 1.

3.1. Studying different thresholds in Fuzzy Local Adaptive Thresholding
First, we studied how setting different fixed threshold could impact the performance of the
FLAT algorithm. This is contrary to the local nature of the FLAT algorithm, but is representative
of the performance of the integral image-based thresholding for the global image, and can give
us an intuition of the expected changes in performance when changing the threshold value.
('Image ', '6') ('Image ', '7') ('Image ', '8')
1.0 1.0 1.0

0.8 0.8 0.8

0.6 0.6 0.6
Fscore

Fscore

Fscore
0.4 0.4 0.4

0.2 0.2 0.2

0.0 0.0 0.0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Threshold Threshold Threshold

Figure 2: Performance for different FLAT executions using different threshold values for different ag-
greagtion functions.

Algorithm Agg. Img. 1 Img. 2 Img. 3 Img. 4 Img. 5 Img. 6 Img. 7 Img. 8 Img. 9 Img. 10 Average
Sugeno 0.56 0.58 0.93 0.77 0.55 0.28 0.53 0.77 0.92 0.89 0.68
Choquet 0.82 0.89 0.98 0.78 0.76 0.29 0.68 0.79 0.93 0.89 0.78
FLAT C𝐹1 ,𝐹2 0.56 0.58 0.93 0.77 0.55 0.28 0.53 0.77 0.93 0.89 0.68
F-Sugeno 0.56 0.58 0.93 0.77 0.55 0.28 0.53 0.77 0.93 0.89 0.68
CF 0.81 0.89 0.98 0.78 0.76 0.29 0.66 0.79 0.93 0.89 0.78
Sugeno 0.53 0.52 0.67 0.77 0.55 0.29 0.53 0.77 0.93 0.89 0.66
Choquet 0.98 0.88 0.97 0.98 0.96 0.90 0.97 0.95 0.93 0.89 0.95
GLAB C𝐹1 ,𝐹2 0.53 0.52 0.67 0.77 0.55 0.29 0.53 0.77 0.93 0.89 0.66
F-Sugeno 0.53 0.52 0.67 0.77 0.55 0.29 0.53 0.77 0.93 0.89 0.66
CF 0.97 0.87 0.96 0.98 0.95 0.28 0.96 0.95 0.93 0.89 0.87

Table 1
Results for all the images in the dataset and the average performance for the FLAT and GLAB algorithm,
using different aggregation functions to construct the Fuzzy Integral Image.

Some of the results of this study are illustrated in Figure 2. We can determine that there is an
evident impact in the chosen threshold for each image, and that for the different combinations of
aggregations and images tested, the optimal threshold seem to vary a lot, which is an indication
of the suitability of the GLAB to optimize the threshold for each one.

3.2. Results of Gated Local Adaptive Thresholding
To train and evaluate the performance of the GLAB we first computed the fuzzy integral image
of each of the original images. Then, we divided each image and the corresponding fuzzy
integral image in non-overlapping windows of 3 × 3. Finally, we split the 80% of the images to
train the model and the rest to evaluate the performance of the GLAB.
In Table 1 we show the results for the GLAB and FLAT algorithms for the evaluation windows
corresponding to each image. We found results to be much higher than those obtained using
the FLAT, and that the best case was using the Choquet integral to construct the fuzzy integral
image, and then using the GLAB to perform the binarization.
4. Conclusions and Future Lines
In this work we have presented the Gated version of the FLAT algorithm, the GLAB. The GLAB
computes the local threshold from each image using a logistic regression that learns the most
appropriate threshold for each region of the image. We found the results using GLAB to be
superior to the FLAT algorithm, and the GLAB constructing the fuzzy integral image using the
Choquet integral.
Future research shall study the use of further aggregation functions, and to study the use of
the GLAB algorithm in a Convolutional Neural Network.

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