features for SVM classification are line intersections
points and dot products between the Hough-detected
lines, as described in Section 2.3. Due to non-linearity
of the data, a RBF Kernel, depending on a parameter
γ, is used to increase the accuracy rate. See Section 4
for technical details and values.
3.2 Convolutional Neural Network
Classification Convolutional Neural Network is a
Deep Learning method (Krizhevsky et al., 2012; de
Rezende et al., 2018) which generally consists of
three main parts (see Figure 6 as an example): an in-
put layer part, where the image is given to the clas-
sifier, a feature extraction (or a hidden layer) part,
and a classification part that uses fully connected lay-
ers (i.e. each neuron of a layer is connected to ev-
ery neurons of the following layer). This overall net-
work provides as an output the probability values for
an input image to belong to each of the classes. In
this work two classes are considered, CoT and SPT.
CNN have shown unequalled performances in image
classification. Such performances are mainly due to
the learning of the hidden network from a huge num-
ber of images. Indeed, a feature extraction network
is classically composed of a sequence of layers, each
one containing bias addition, convolution filters, ac-
tivation function (Rectified Linear Unit, ReLu), and
pooling operation.
We choose to use a transfer-learning procedure
with a pre-modeled and pre-trained network, specif-
ically the GoogLeNet architecture (Szegedy et al.,
2015). The architecture and huge quantity of parame-
ters of the first two parts of this CNN network which
compute image characteristics (e.g. bias, coefficients
of the convolution filters) remained unchanged. Only
the parameters of the third fully connected layer part
were estimated and tested using our dataset, which is
one of the main advantages of using such a network.
For this estimation, we used the DL Matlab toolbox
1
.
All parameters of SVM and CNN are provided in
Section 4.
4 CLASSIFICATION RESULTS
This section presents the classification results ob-
tained on lines, segmented images (see Section 2.2),
and 2-D cross-sections of raw tomographic images.
The considered datasets are as follows:
• 360 segmented binary images (130 from CoT
1
https://it.mathworks.com/help/deeplearning/ref/
trainnetwork.html
sherds and 130 from SPT sherds), used for SVM
and CNN classification.
• 460 grey-scale images (230 from CoT sherds and
230 from SPT sherds), used for CNN classifica-
tion.
Note that the dataset of segmented images is smaller
than the dataset of tomographic images, because the
pore segmentation process can produce empty images
(dark images, which correspond to a slice where no
pores were detected).
As Figure 2 (first line) shows, the CoT experimen-
tal sherds usually have a squared shape, while the SPT
ones are round-shaped. Since this shape is not rel-
evant for manufacturing characterisation, it may in-
duce bias in the classification. To avoid this phe-
nomenon, only the central part of each grey-scale im-
age is considered in the experiments (see Figure 7).
Whatever the classification methods and the input
data, the learning step is performed on 80% of the
dataset and the remaining 20% are used for testing.
4.1 Results with Support Vector
Machine
As mentioned in Section 3.1, a cost parameter C and
the Kernel parameter γ must be tuned in order to pre-
vent under- or over-fitting phenomena. A grid search
is performed to determine the optimal values of these
parameters. From these multiple tests, C was set to
100 and γ to 10. The dataset is randomly shuffled
1000 times and different learning and testing sets are
picked for each run. The prediction accuracy results
averaged over 1000 runs on 72 test images are shown
in Table 1.
4.2 Results with Convolutional Neural
Network
The second method we consider is the classification
by CNN, first on segmented images, and then on raw
images.
As presented in Section 3.2, we use a transfer-
learning procedure with GoogLeNet network which
requires three-dimensional 224 × 224 × 3 images as
inputs; the images are thus resized accordingly. As
the images of our dataset are either binary or grey-
scale, each image is replicated three times to obtain
the desired form. The training and validation set is
composed by 80% of the images of each dataset (more
precisely, 64% of the dataset is used for training and
16% for validation), while the testing set is composed
by the remaining 20% of the images.
The CNN classifier was tested multiple times with
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