2D Geometric Shapes Dataset - For Machine Learning and Patte - 2020 - Data in BR

Data in Brief 32 (2020) 106090
Contents lists available at ScienceDirect
Data in Brief
journal homepage: www.elsevier.com/locate/dib
Data Article
2D geometric shapes dataset – for machine

learning and pattern recognition
Anas El Korchi∗, Youssef Ghanou∗
University Moulay Ismail of Meknes, Morocco
a r t i c l e i n f o a b s t r a c t
Article history: In this paper, we present a data article that describes a

Received 5 July 2020 dataset of nine 2D geometric shapes, and each shape is
Accepted 22 July 2020 drawn randomly on a 200 × 200 RGB image. During the gen-
Available online 25 July 2020 eration of this dataset, the perimeter and the position of each
shape are selected randomly and independently for each im-
Keywords:
age. The rotation angle of each shape is chosen randomly
Geometric shapes dataset
for each image within an interval between -180° and 180°,
Machine learning
Pattern recognition
as well as the background colour of each image and the fill-
Classification synthetic dataset ing colour of each shape are selected randomly and indepen-
dently.
The published dataset is composed of 9 classes of data, and
each class represent a type of geometric shape (Triangle,
Square, Pentagon, Hexagon, Heptagon, Octagon, Nonagon, Cir-
cle and Star). Each class is composed of 10k generated im-
ages. This paper also includes a GitHub URL to the generator
source code used for the generation, which can be reused to
generate any desired size of data.
The proposed dataset aims to provide a perfectly clean
dataset, for classification as well as clustering purposes. The
fact that this dataset is generated synthetically provides the
ability to use it to study the behaviour of machine learn-
ing models independently of the nature of the dataset or the
possible noise or data leak that can be found in any other
datasets. Moreover, the choice of a 2D geometrical shape
dataset provides the ability to understand as well to have
good knowledge of the number of patterns stored inside each
data class.
∗
Corresponding authors.
E-mail addresses: anaselkorchi@gmail.com (A.E. Korchi), youssefghanou@yahoo.fr (Y. Ghanou).
https://doi.org/10.1016/j.dib.2020.106090
2352-3409/© 2020 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license.
(http://creativecommons.org/licenses/by/4.0/)
2 A.E. Korchi and Y. Ghanou / Data in Brief 32 (2020) 106090
© 2020 The Author(s). Published by Elsevier Inc.

This is an open access article under the CC BY license.
(http://creativecommons.org/licenses/by/4.0/)
Specifications Table
Subject Computer vision and pattern recognition

Specific subject area Automatically generated 2D geometric shapes dataset that contains nine types
of shapes (Triangles, Squares, Pentagons, Hexagons, Heptagons, Octagons,
Nonagons, Circles and Stars)
Type of data Image
How data were acquired The geometric shapes were generated by using the turtle library and the
Python programming language.
Data format Raw
Parameters for data collection Each geometric shape was drawn on a 200 × 200 pixel image, and each shape
has a random background colour, random filling colour, a random position
inside the image, an arbitrary rotation angle between -180° and 180°, and a
random perimeter under the condition that the drawn shape must be fully
visible inside the containing image.
Description of data collection Each geometric shape was drawn 10 0 0 0 times under the conditions described
above, and each image was saved into a PNG image.
Data source location Institution: University Moulay Ismail of Meknes
City: Meknes
Country: Morocco
Data accessibility Direct URL to data: https://data.mendeley.com/datasets/wzr2yv7r53/1
Data generator source code:
https://github.com/elkorchi/2DGeometricShapesGenerator
Value of the Data
• The simulated dataset can be used to train machine learning models to perform geometric
shape recognition tasks.
• This dataset could be useful for researchers studying the overfitting of machine learning
models [2] since the classification of the images inside this dataset can only be performed
with a model that focuses on pattern detection [1] instead of memorization.
• This dataset could be useful for researchers to benchmark and test any regularization tech-
niques that can be applied to machine learning models or any other approach that can help
to avoid the overfitting.
• This dataset consists of a set of images containing random drawn geometrical shapes, which
provides a clean dataset from any data leak that would influence the benchmark of any ma-
chine learning model.
1. Data Description
The presented dataset is a set of 90k RGB images of a fixed resolution 200 × 200 pixel. This
specific resolution aims to provide the minimum space where we can draw the geometric
shapes with different positions and different sizes inside the image. Taking into consideration
that high-resolution images require more computation power for machine learning models dur-
ing the training phase, which may make the published dataset less useful as a benchmarking
dataset. Each image contains one of the following polygon shapes: Triangles, Squares, Pentagons,
Hexagons, Heptagons, Octagons, Nonagons, Circles and Stars. 10k images were generated for each
shape (Fig. 1). Each image is saved in a PNG file. The name of each file is composed of two sec-
tions: [Type of polygon shape drawn inside the image]_[UUID].png.
A.E. Korchi and Y. Ghanou / Data in Brief 32 (2020) 106090 3
Fig. 1. CNN architecture used for recognition and classification of geometric shapes. Conv 2D + BN denotes a convolu-
tional layer with Batch Normalization [3].
Examples:
• Triangle_6f1d8142–2a58–11ea-8f1b-c869cd928de6.png
• Square_6f22e600–2a58–11ea-a950-c869cd928de6.png
• Pentagon_6f22e998–2a58–11ea-9fc2-c869cd928de6.png
• Hexagon_6f22eb64–2a58–11ea-818b-c869cd928de6.png
• Heptagon_6f22ecd8–2a58–11ea-82eb-c869cd928de6.png
• Octagon_6f22f118–2a58–11ea-944f-c869cd928de6.png
• Nonagon_6f22f318–2a58–11ea-bf89-c869cd928de6.png
• Circle_6f22f4d8–2a58–11ea-beb7-c869cd928de6.png
• Star_6f22f654–2a58–11ea-b6fc-c869cd928de6.png
The background colour of each image, the filling colour of each shape, the rotation angle of
each shape, the position of each shape inside the image, as well the perimeter of each shape is
generated randomly and independently.
2. Experimental Design, Materials, and Methods
The generation program was developed using the Python programming language and the Tur-
tle library to draw geometric shapes inside each image as well we have used the NumPy library
to generate all the random parameters that we have used during the generation. The generation
program receives as an input the number of desired samples per each shape as well as the path
of the storage directory where the generated images will be stored. The goal of the tool is to
generate a set of labelled images that contains 2D geometric shapes.
Each image is generated with the following parameters:
• A fixed image size of 200 × 200 pixel

• A random background colour: the background colour is generated randomly by using the
function numpy.random.randInt(0, 255, 3). This function generates three random integers
from the discrete uniform distribution in the half-open interval of 0 and 255. Each number
represent respectively, the RGB values that construct the background colour. We ignore the
possibility that the background colour may be different or close to the filling colour as we
consider it as a normal task for a machine learning model, to be able to identify the drawn
shape with a filling colour close to the background colour.
• A random filling colour of each shape: the filling colour of each shape is generated by using
the same setting described in the generation of the background colour. Note that the genera-
tion of the filling colour is independently from the generation of the background colour (we
4 A.E. Korchi and Y. Ghanou / Data in Brief 32 (2020) 106090
Table 1
Statistical description of the generated dataset.
Shape Minimal perimeter Maximal perimeter Minimal Maximal Number of

(pixel) (pixel) area(pixel) area (pixel) samples
Triangle 51.96 389.71 129.90 7 307 10 000

Square 56.57 424.26 20 0.0 0 11 250 10 000
Pentagon 58.78 440.84 237.76 13 374.23 10 000
Hexagon 60.00 450.00 259.80 14 614.18 10 000
Heptagon 60.75 455.58 272.00 15 300.06 10 000
Octagon 61.23 459.22 282.84 15 909.90 10 000
Nonagon 61.56 461.73 289.25 16 270.56 10 000
Circle 62.83 471.24 314.16 17 671.46 10 000
Star 126.29 947.18 112.26 6 314.46 10 000
ignore the very low probability that the background colour would be the same as the filling
colour).
• A random rotation angle between -180° and 180°
• A random shape perimeter
• A random shape position inside the containing image
The perimeter and the position of each shape inside each image are selected as the following.
• First, we select the radius of the circumscribed circle of the drawn shape randomly, and
this selection is performed within the interval of 10 and 75 (pixels), which ensures that the
drawn shape may have a random perimeter between the interval of 10 and 75. Also, it gives
that the smallest possible shape may be circumscribed by a circle with a radius = 10 pixel,
and the largest possible shape may be circumscribed by a circle with a radius = 75 pixel. In
Table 1 we show the minimal possible perimeter of each shape the maximal possible perime-
ter for each shape, the minimal possible area of each shape and the maximal possible area
of each shape based on the parameters described above.
• Then, in the function of the selected radius value, we choose the position of the centre of the
circumscribed circle of the drawn shape inside the image randomly, the position is selected
under the condition that all the drawn shape must be fully visible inside the image.
• And finally, we draw the shape in the function of the centre and position of its circumscribed
circle. Note that the circumscribed circle of the shape is used only to draw the shapes, and
it is not visible in the generated images (Fig. 2).
All the parameters described above are generated for each sample independently and identi-
cally. All the random values are selected by using the Numpy function numpy.random.randInt,
which generates a defined number of random values from the uniform discrete distribution in
the half-open interval specified in the function call arguments.
3. A Use Case Example with Convolutional Neural Networks
This dataset could be used to train a convolutional neural network to perform geometric
shape recognition and classification. To do so, this dataset must be divided into two separate
sets of data a training dataset and a testing dataset, the selection of samples that composes
each collection of data is made randomly:
• A training dataset which consists of 40% of samples of the original dataset

• A testing dataset which consists of 60% of samples of the original dataset
The architecture of the convolutional neural network is defined as the following: 7 convo-
lutional layers and one fully connected layer, which represents the output layer of the neural
network. Each convolutional layers is illustrated with a parametrized number of filters a batch
A.E. Korchi and Y. Ghanou / Data in Brief 32 (2020) 106090 5
Fig. 2. Samples from the generated dataset, each row contains examples that belong to the same geometric shape.
normalization layer [3] an activation function, and a max-pooling layer follows each convolu-
tional layer. Fig. 1 shows the convolutional neural network architecture that can be used on this
dataset.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal rela-
tionships which have, or could be perceived to have, influenced the work reported in this article.
References
[1] M.Douglas Hawkins, The problem of overfitting, J. Chem. Inf. Comput. Sci. 44 (2004) 1–12.
[2] M Bishop, Christopher, Pattern recognition and Machine Learning, Springer, 2006.
[3] S. Ioffe, C. Szegedy, Batch normalization: accelerating deep network training by reducing internal covariate shift, in:
Proceedings of the 32nd International Conference on Machine Learning, Lille, France, ICML, 2015, pp. 448–456. 6-11
July 2015, 2015.

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Data in Brief 32 (2020) 106090

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/dib

2D geometric shapes dataset – for machine

Article history: In this paper, we present a data article that describes a

© 2020 The Author(s). Published by Elsevier Inc.

Subject Computer vision and pattern recognition

Value of the Data

2. Experimental Design, Materials, and Methods

• A ﬁxed image size of 200 × 200 pixel

Shape Minimal perimeter Maximal perimeter Minimal Maximal Number of

Triangle 51.96 389.71 129.90 7 307 10 000

3. A Use Case Example with Convolutional Neural Networks

• A training dataset which consists of 40% of samples of the original dataset

Declaration of Competing Interest

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