3D Object Classification Using Deep Learning and Phase-only Digital Holography

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Abstract
In this paper, we present a deep CNN-based approach for multi-class classi ication of three-dimensional (3-D) objects using phase-only digital
holographic information. The 3-D objects considered for the multi-class (four-class) classi ication task are ‘triangle-square’, ‘circle-square’, ‘square-
triangle’, and ‘triangle-circle’. The 3-D object ‘triangle-square’ is considered for Class-1 and the remaining 3-D objects ‘circle-square’, ‘square-circle’, and
‘triangle-circle’ are considered for Class-2, Class-3, and Class-4. The digital holograms of 3-D objects were created using the two-step Phase-Shifting
Digital Holography (PSDH) technique and were computationally post-processed to obtain phase-only digital holographic data. Subsequently, a deep CNN
was trained on a phase-only image dataset consisting of 2880 images to produce the results. The loss and accuracy curves are presented to validate the
performance of the model. Additionally, the results are validated using metrics such as the confusion matrix, classi ication report, Receiver Operating
Characteristic (ROC) curve, and precision-recall curve.
Deep Learning-based Multi-
class Three-dimensional
(3-D) Object Classification
using Phase-only Digital
Holographic Information
Uma Mahesh RN1
* and L Basavaraju2
1
Associate Professor, Dept of CSE (AI and ML), ATME College of Engineering,
Mysore-570028, India
2
Professor, Dept of ECE, ATME College of Engineering, Mysore-570028, India
*Correspondence: Uma Mahesh RN, Associate Professor, Dept of CSE (AI and ML),
ATME College of Engineering, Mysore-570028, India, Email: mahivit72@gmail.com
Research Article
Introduction
Deep learning, a branch of arti icial intelligence (AI),
encompasses various deep neural networks, including
Convolutional Neural Network (CNN), AlexNet, Visual
Geometry Group (VGG) Networks, U-Net, Y-Net, and
Convolutional Encoder-Decoder Network models. These
networks have been utilized in various digital holographic
applications, including focus prediction [1], depth prediction
[2], image segmentation [3], hologram reconstruction [4], 3-D
object binary classi ication [5], 3-D object binary regression
[6,7], 3-D object multi-class classi ication and multi-output
regression [8-10], and phase unwrapping [11]. Digital
holography is an optical imaging technique that records 3-D
information about an object using an electronic sensor such
as a Charge-Coupled Device (CCD) or Complementary Metal
Oxide Semiconductor (CMOS) sensor. The hologram recorded
using a CCD sensor is numerically reconstructed to obtain a
complex-valued image containing both intensity and phase
information. This phase (depth) information can be utilized for
AI-based supervised learning techniques such as classi ication
and regression tasks. Classi ication is a supervised learning
technique that de ines the decision boundary between the
input data and the target labels. The classi ication technique
produces output as discrete labels. In this study, multi-class
(four-class) classi ication of 3-D objects was performed using
a deep CNN. A CNN is a deep neural network that consists of
distinct layers for feature extraction and classi ication. The
feature extraction component includes multiple convolutional
and pooling layers. The convolutional layer performs a
convolution operation between the input and the kernel to
produce a feature map. This feature map is then processed
through the pooling layer to reduce its dimensionality. The
classi ication component comprises fully connected layers
and an output layer to generate the inal results. Zifei Li, et al.
[12] introduced a deep CNN for binary classi ication of speckle
patterns acquired from multi-mode iber. Priscoli, et al. [13]
explored both machine learning and deep learning techniques,
including Principal Component Analysis (PCA), Multi-Layer
Perceptron (MLP), and CNN, for binary classi ication of cancer
cells in micro luidics. Additionally, Lam, et al. [14] proposed
a deep CNN for hologram classi ication of occluded and
deformable objects, addressing holograms contaminated with
speckle noise. Cheng, et al. [15] introduced a deep CNN tailored
Article Information
Submitted: June 27, 2024
Approved: July 08, 2024
Published: July 09, 2024
How to cite this article: Uma Mahesh RN, Basavaraju L.
Deep Learning-based Multi-class Three-dimensional (3-D)
Object Classi ication using Phase-only Digital Holographic
Information. IgMin Res. July 09, 2024; 2(7): 550-557. IgMin
ID: igmin216; DOI: 10.61927/igmin216; Available at:
igmin.link/p216
Copyright: © 2024 Uma Mahesh RN, et al. This is an open
access article distributed under the Creative Commons
Attribution License, which permits unrestricted use,
distribution, and reproduction in any medium, provided the
original work is properly cited.
Keywords: Deep Convolutional Neural Network (CNN);
Multi-class classi ication; Phase-Shifting Digital Holography
(PSDH); Digital hologram

TECHNOLOGY July 09, 2024 - Volume 2 Issue 7
DOI: 10.61927/igmin216
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ISSN
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for pattern classi ication of digital holographic data. Zhang,
et al. [16] developed a deep CNN speci ically for classifying
marine plankton from digital holograms. Zhu, et al. [17]
proposed an automated method for classifying microplastics
in digital holographic data using deep learning and generative
adversarial networks. The current study presents a multi-class
(four-class) classi ication of 3-D objects, speci ically ‘triangle-
square’, ‘circle-square’, ‘square-triangle’, and ‘triangle-circle’,
utilizing phase-only digital holographic information acquired
from the Phase-Shifting Digital Holography (PSDH) technique
through deep CNN. The primary distinction between this work
and prior studies [12-17] lies in the utilization of deep CNN
for multi-class (four-class) classi ication of 3-D objects based
on phase-only digital holographic data acquired via phase-
shifting digital holography. The results of the classi ication task
are delineated in terms of loss and accuracy curves to validate
the proof of concept. Furthermore, the work is validated with
results including the confusion matrix, classi ication report,
Receiver Operating Characteristic (ROC) curve, and precision-
recall curve. Classifying phase images entails the classi ication
of 3-D objects using deep CNN. The major contribution of
this paper is this is the irst work reported to perform a four-
class classi ication of 3-D objects using phase-shifting digital
holographic data.
Methodology
Figure 1 depicts a block diagram illustrating the
CNN architecture employed for multi-class (four-class)
classi ication of 3-D objects utilizing a phase-only image
dataset. The CNN takes the input as the phase-only image of
size 512 × 512 from the digital hologram. The CNN depicted in
Figure 1 comprises four convolutional and four pooling layers
in the feature extraction stage, followed by fully connected and
output layers in the classi ication stage. In the convolutional
layer, the input phase image undergoes convolution with
a kernel to generate the feature map. The output of the
convolutional layer is determined by
  ( )
( )
0
0
t
k k
t
Z P H X B
mn pq pq
pq m
n

 



(1)
In the above eqn. (1),
 
k
Z pq represents the output feature
map and Xpq
represents the input phase image. ( )
k
Hmn
represents kernel coef icients, k represents the number
of kernels, t represents the kernel size, P represents the
activation function, and Bpq
represents bias. The number of
kernels in the convolutional layer is k = 8,16,32,64. The size of
the kernel is t = 5 × 5. The activation function P represents the
recti ied linear unit (ReLU) activation function that is present
in convolutional and fully connected layers. The output of the
convolutional layer is then fed into the pooling layer, where the
Max-Pooling2D technique is applied to further decrease the
dimensionality of the feature map. The output of the pooling
layer is determined by
Ypq =
Xpq
(2)
In the above eqn. (2), Ypq
represents the output feature
map and Xpq
represents the input. The output of the inal
pooling layer is lattened and subsequently passed to the fully
connected layer. The output of the fully connected layer is
determined by
( )
1
t
Y P W X B
p mn p p
p

 
 (3)
In the above eqn. (3), Yp
represents the output of the fully
connected layer, Bp
represents the bias, P represents the
ReLU activation function, Wmn
represents weight values, Xp
represents the one-dimensional (1-D) data obtained through
the lattening layer, and t represents the number of neurons.
The output of the inal pooling layer is 28 × 28 × 64. The
number of neurons selected in the fully connected layer is t
= 64. The output of the fully connected layer is forwarded to
the output layer. In the output layer, a subset of four neurons
is selected from the sixty-four neurons, utilizing the softmax
activation function to generate the inal output. The equation
for the softmax activation function is expressed as
exp( )
exp( )
1
M K
Q t
K
Xt
n

 
(4)
In the above eqn. (4), Qk
represents the output, Mk
represents the input, and t represents several neurons.
Dataset preparation
For the four-class classi ication task, the following four
Figure 1: Block diagram of Convolutional Neural Network (CNN).
Figure 1: Block diagram of Convolutional Neural Network (CNN).

DOI: 10.61927/igmin216
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3-D objects were included: ‘triangle-square’, ‘circle-square’,
‘square-triangle’, and ‘triangle-circle’. These objects were
distributed among four distinct subclasses: Class-1, Class-2,
Class-3, and Class-4. Speci ically, the 3-D object ‘triangle-
square’ was designated as belonging to Class-1. Following
the classi ication scheme, the subsequent 3-D object, ‘circle-
square’, was assigned to Class-2. Similarly, the 3-D object
‘square-triangle’ was allocated to Class 3. Finally, the last
3-D object, ‘triangle-circle’, was designated as belonging to
Class-4. The 3-D object ‘circle-square’ was structured such
that the circular feature resided prominently in the irst
plane, while the square feature was distinctly positioned in
the subsequent plane. Each plane is separated by various
distances d1
, and d2
respectively. The remaining three 3-D
objects were constructed similarly, with the distinction that
different features were allocated to the irst and second planes,
respectively. Two phase-shifted holograms of 00
and 900
were formed at the camera plane and these holograms were
post-processed to obtain a complex-valued image containing
intensity and phase information using a two-step phase-
shifting digital holography (PSDH) technique. The holograms
and reconstructed intensity/phase images are of size 1024
× 1024. The intensity and phase images were reconstructed
at both distances. In Figure 2a, a schematic representation of
the 3-D object volume ‘triangle-square’, belonging to Class-1,
is depicted, illustrating the distribution of information across
both the irst and second planes. Additionally, Figure 2a
illustrates the geometry for digital hologram recording from
two-step phase-shifted plane reference waves.
The digital holograms of four different 3-D objects
namely ‘triangle-square’, ‘circle-square’, ‘square-triangle’, and
‘triangle-circle’ belonging to four-different sub-classes were
further rotated in steps of 0.5° separately forming a dataset of
2880 holograms. Similarly, the reconstructed intensity/phase
images obtained from the two-step Phase-Shifting Digital
Holography (PSDH) technique were also rotated in steps of
0.5° to form a dataset of 2880 images separately for intensity
and phase information. For the multi-class classi ication (four-
class classi ication) of 3-D objects, only phase information
was taken into account. The dataset, comprising 2880 phase
images, was divided into training, validation, and test sets,
containing 2160 (75%), 432 (15%), and 288 (10%) images,
respectively. for the training of the deep CNN, the size of the
phase image considered was 512 × 512 from 1024 × 1024.
The deep CNN was trained for 50 epochs on the phase-only
image dataset using an Adam optimizer with a learning rate of
0.0007, while categorical cross-entropy was employed as the
loss function. The implementation of the deep CNN was carried
out in a TensorFlow environment using Python programming.
Figure 3 displays samples of three reconstructed phase images
corresponding to 3-D objects, namely ‘triangle-square’, ‘circle-
square’, and ‘triangle-circle’, which belong to Class-1, Class-2,
and Class-4, respectively.
Results and discussions
The deep CNN was trained on a batch of 54 images from the
training set and a batch of 24 images from the validation set of
the phase-only image dataset in a single epoch. Subsequently,
each epoch was iteratively iterated over 40/18 steps on the
training/validation sets to complete the training process.
Figure 4 illustrates the loss/accuracy curves obtained from
the training/validation sets after completing the training for
50 epochs on the phase-only image dataset.
From Figure 4a, it can be said that the training loss is
decreasing and the validation loss is luctuating. After the
completion of the training for ifty epochs, the training loss
Figure 1: Schematic of the geometry for the recording of the digital hologram of 3-D object volume with different features in the irst and second planes and
separating distances z =10 cm and d = 2 cm. (a) triangle-square. BS: beam splitter CCD: charge-coupled device.

DOI: 10.61927/igmin216
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c
Figure 3: Reconstructed phase-only images of 3-D objects (a) circle-square (b) triangle-circle (c) triangle-square.
a b
Figure 4: Loss and accuracy curves on training/validation sets for phase-only image dataset (a) loss (b) accuracy.
is 0.0015and the validation loss is 0.5771. So it can be said
that the training loss is lower compared to the validation loss.
Next from Figure 4b, it can be said that the training accuracy
is increasing initially and then becomes constant. i.e. training
accuracy increases initially till around ten epochs and then
becomes constant around 1.00 after 10 epochs and remains
at a value of 1.00 till 50 epochs. The validation accuracy
increases in the beginning till around 10 epochs and then
starts luctuating around 0.80 after 10 epochs. So it can be
observed that from Figure 4b, the training accuracy is greater
than the validation accuracy i.e. the margin between the
training accuracy and validation accuracy is more. So it can
be said that the deep CNN model is Over itting on the phase-
only image dataset for the four-class classi ication task. The
deep CNN model was tested using 24 phase-only images from
the test set. Furthermore, the performance of the four-class
classi ication task is illustrated by a multi-class confusion
matrix. This matrix shows the number of images correctly
and incorrectly classi ied for each class. Figure 5 presents the
confusion matrix for the four classes, as obtained from the
Deep CNN model on the phase-only image dataset. The multi-
class classi ication task can be done for any number of classes.
Here, four classes have been considered for the multi-class
classi ication task. In general, n classes can be considered to
perform multi-class classi ication tasks.

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From Figure 5, it can be observed that the confusion matrix
is represented for the four classes on the phase-only image
dataset obtained from the deep CNN model. For Class-1, 22
images are predicted as FALSE and 2 as TRUE. For Class-2, 16
images are predicted as FALSE and 8 as TRUE. For Class-3,
17 images are predicted as FALSE and 7 as TRUE. Finally, for
Class-4, 17 images are predicted as FALSE and 7 as TRUE.
For Class 1, 22 images are recognized as true positive (TP),
2 images are recognized as true negative (TN), and inally 0
images are recognized as false positive (FP) and false negative
(FN) respectively. For Class 2, 11 images are recognized as
true negative (TN), 8 images as true positive (TP), 5 images
as false positive (FP), and 0 images as false negative (FN)
respectively. For Class 3, 17 images are recognized as true
negative (TN), 3 images are recognized as true positive (TP),
4 images are recognized as false negative (FN), and 0 images
as false positive (FP) respectively. For Class 4, 17 images are
recognized as true negative (TN), 6 images are recognized as
true positive (TP), 1 image as false negative (FN), and 0 images
as false positive (FP) respectively. The performance metrics
namely accuracy, positive predictive value (PPV), sensitivity,
and F1-Score are calculated for all four classes namely Class 1,
Class 2, Class 3, and Class 4 for both TRUE and FALSE classes.
The metric accuracy is calculated by taking the ratio of the
sum of true positives and true negatives to the sum of true
positives, true negatives, false negatives, and false positives
respectively. The metric positive predictive value is calculated
by taking the ratio of true positives to the sum of true positives
and false positives respectively. The metric sensitivity is
calculated by taking the ratio of true positives to the sum of
true positives and false negatives respectively. The metric
F1-score is calculated by taking the ratio of the sum of twice
of true positives to the sum of twice of true positives, false
positives, and false negatives respectively. The metric mean
squared error is calculated by taking the squared difference
between ground truth and predicted values. The metric mean
absolute error is calculated by taking the difference between
the ground truth and the predicted values. The classi ication
report from the deep CNN model for all four classes on the
phase-only image dataset is shown in Table 1.
Table 1 highlights that the deep CNN model achieves higher
accuracy for Class 1 compared to the other classes, with perfect
(unity) values for Positive Predictive Value (PPV), sensitivity,
and F1-score in both the FALSE and TRUE classes. The macro
average is computed by averaging these metrics across TRUE
and FALSE classes, while the weighted average combines
macro and micro averages. For Class 1, the deep CNN model
achieves unity values for both macro and weighted averages.
In Class 2, the model demonstrates higher sensitivity but
lower PPV for the TRUE class, and conversely, lower sensitivity
and higher PPV for the FALSE class. The macro average results
in the value of 0.81 for positive predictive value (PPV), 0.84
for sensitivity, and 0.79 for F1-score labels respectively. The
weighted average results in the value of 0.87 for PPV, 0.79
for sensitivity, and 0.80 for F1-score labels respectively. The
metrics mean squared error (MSE) and Mean Absolute Error
(MAE) for the TRUE class are 0.12, and 0.12 for Classes 1 and 2
respectively. The deep CNN model has Classes 3 and 4 exhibits
Figure 5: Multi-Class Confusion Matrix on Phase-only image dataset obtained from
Deep CNN Model.

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a pattern where PPV is higher but sensitivity is lower for the
TRUE class compared to the FALSE class. In Class 3, the macro
average results in the value of 0.90 for positive predictive value
(PPV), 0.71 for sensitivity, and 0.75 for F1-score labels. The
metric weighted average results in the value of 0.87 for PPV,
0.83 for sensitivity, and 0.81 for F1-score labels respectively.
The mean square error (MSE) and Mean Absolute Error (MAE)
values are 0.33, and 0.33 for Class 3 in the TRUE Class. In Class
4, the macro average results in the value of 0.97 for positive
predictive value (PPV), 0.93 for sensitivity, and 0.95 for F1-
score labels. The weighted average results in equal values for
PPV, sensitivity, and F1-score labels respectively. i.e. 0.96 for
PPV, sensitivity, and F1-score. The mean squared error and
mean absolute error results in the values of 0.42, and 0.42 for
Class 4 in the TRUE Class. Furthermore, the performance of
the multi-class classi ication task is depicted using Receiver
Operating Characteristic (ROC) curves and PPV-sensitivity
characteristic curves in Figure 6. These curves illustrate how
well the deep CNN model distinguishes between TRUE and
FALSE classes, assessed by the area under the curve (AUC)
metric.
From Figure 6, it is evident that the deep CNN model
has a higher AUC value for Class 1 compared to the other
classes. Figure 7 displays the Positive Predictive Value (PPV)
– sensitivity characteristic curve for all four classes obtained
from the deep CNN model on the phase-only image dataset.
From Figure 7, it can be observed that the deep CNN model
has higher sensitivity and lower positive predictive value for
Class 4. Class 1 exhibits perfect positive predictive value and
sensitivity on the phase-only image dataset from the deep
CNN model. Classes 2 and 3 exhibit lower Positive Predictive
Value (PPV) and higher sensitivity as depicted in Figure 7.
Table 1: Classi ication Report obtained from Deep CNN model on phase-only image dataset.
Label
Positive Predictive Value
(PPV)
Sensitivity F1-Score Support
Mean Square Error
(MSE)
Mean Absolute Error
(MAE)
Class 1
Not 1 (FALSE class) 1.00 1.00 1.00 22
1 (TRUE class) 1.00 1.00 1.00 2 0.12 0.12
Accuracy 1.00 24
Macro average 1.00 1.00 1.00 24
Weighted average 1.00 1.00 1.00 24
Label
(PPV)
Mean Square Error
(MSE)
Mean Absolute Error
(MAE)
Class 2
Not 1 (FALSE class) 1.00 0.69 0.81 16
1 (TRUE class) 0.62 1.00 0.76 8 0.12 0.12
Accuracy 0.79 24
Macro average 0.81 0.84 0.79 24
Label
(PPV)
Mean Square Error
(MSE)
Mean Absolute Error
(MAE)
Class 3
Not 1 (FALSE class) 0.81 1.00 0.89 17
1 (TRUE class) 1.00 0.43 0.60 7 0.33 0.33
Accuracy 0.83 24
Macro average 0.90 0.71 0.75 24
Label
(PPV)
Mean Square Error
(MSE)
Mean Absolute Error
(MAE)
Class 4
Not 1 (FALSE class) 0.94 1.00 0.97 17
1 (TRUE class) 1.00 0.86 0.92 7 0.42 0.42
Accuracy 0.96 24
Macro average 0.97 0.93 0.95 24
Figure 6: ROC curve obtained from deep CNN model on phase-only image dataset.

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Conclusion
This paper presents a deep CNN-based approach for multi-
class object classi ication, speci ically focusing on a four-class
classi ication task using phase-only digital holographic data
obtained from phase-shifting digital holography (PSDH).
The study involves four distinct 3-D objects: triangle-square,
circle-square, square-triangle, and triangle-circle. Digital
holograms of these objects are generated using a two-step
PSDH technique and subsequently processed computationally
to derive phase-reconstructed images. The dataset comprises
2880 phase-only images, which are utilized to train a deep CNN
for classi ication purposes. The effectiveness of the proposed
approach is demonstrated through various evaluation metrics.
Loss and accuracy curves are presented to validate the ef icacy
of the model during training. Furthermore, results such as the
confusion matrix, Receiver Operating Characteristic (ROC)
curves, and Positive Predictive Value (PPV)-sensitivity curves
are provided to substantiate the performance of the deep CNN
in multi-class classi ication tasks using phase-shifting digital
holographic data. This study underscores the application
of deep learning as a modern and effective methodology for
classifying 3-D objects based on phase-only holographic
information. In the future, the deep CNN model can be used
for live-cell images in the different forms of digital holographic
information to perform binary classi ication and multi-class
classi ication tasks.
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