INTERNATIONAL JOURNAL OF ARTIFICIAL INTELLIGENCE
ISSN: 2692-5206, Impact Factor: 12,23
American Academic publishers, volume 05, issue 05,2025
Journal:
https://www.academicpublishers.org/journals/index.php/ijai
page 1867
SHAPE RECOGNITION IN NOISY IMAGES USING AI ALGORITHMS
Zokhidjon Miratoev
Assistant, Department of Mathematics and Natural Sciences,
Almalyk Branch of TSTU, Uzbekistan
Email:
Abstract:
This study investigates the application of artificial intelligence (AI) algorithms for
robust shape recognition in noisy binary images, addressing challenges in medical imaging (e.g.,
organ segmentation in MRI scans), industrial inspection (e.g., defect detection in automotive
parts), and remote sensing (e.g., object identification in satellite imagery). Three AI-based
methods—Hough Transform (HT), Fourier Descriptors (FD), and Zernike Moments (ZM)—
were implemented and evaluated using Python-based tools (OpenCV, Mahotas). Experimental
results demonstrate that Zernike Moments achieve the highest accuracy (95%) in high-noise
conditions, Fourier Descriptors excel in reconstructing complex contours, and Hough
Transform is fastest for detecting basic geometric shapes. A hybrid approach integrating these
methods with deep learning, such as Convolutional Neural Networks (CNNs), is proposed to
enhance accuracy and scalability.
Keywords:
Shape Recognition, Noisy Images, Hough Transform, Fourier Descriptors, Zernike
Moments, Image Processing, Python, Pattern Recognition, Convolutional Neural Networks.
1. Introduction
Shape recognition is a cornerstone of computer vision, enabling applications such as
organ segmentation in medical imaging, defect detection in industrial manufacturing, and object
identification in autonomous navigation. Real-world images are often corrupted by noise, such
as Gaussian noise in MRI scans or speckle noise in satellite imagery, which distorts object
boundaries and challenges traditional geometric methods. AI-based techniques leverage
invariant properties to achieve robust shape recognition despite noise, rotation, and scale
variations.
This study evaluates three AI-based shape recognition methods—Hough Transform (HT),
Fourier Descriptors (FD), and Zernike Moments (ZM)—in noisy binary image environments.
The methods were tested on a synthetic dataset simulating real-world distortions, with the goal
of identifying their strengths and proposing a hybrid framework combining classical descriptors
with deep learning for enhanced performance.
2. Literature Review
Gonzalez and Woods (2018) provided foundational techniques for spatial and frequency
domain image preprocessing, critical for noise handling. Ballard (1981) extended the Hough
Transform to detect arbitrary shapes, improving object detection capabilities. Khotanzad and
Hong (1990) introduced Zernike Moments for invariant shape recognition using orthogonal
polynomials. Teague (1980) developed moment-based descriptors via general moment theory,
enabling complex shape representation.
Recent advancements include hybrid models integrating classical descriptors with deep
learning. Sonka et al. (2014) emphasized combining spatial and frequency domain analyses for
robustness in noisy environments. Dosovitskiy et al. (2021) introduced Vision Transformers
(ViT), which outperform traditional CNNs in certain tasks. Liu et al. (2022) proposed
INTERNATIONAL JOURNAL OF ARTIFICIAL INTELLIGENCE
ISSN: 2692-5206, Impact Factor: 12,23
American Academic publishers, volume 05, issue 05,2025
Journal:
https://www.academicpublishers.org/journals/index.php/ijai
page 1868
EfficientNetV2, a lightweight CNN architecture balancing accuracy and efficiency. These
developments highlight the potential of hybrid approaches for robust shape recognition.
3. Methodology
3.1 Dataset and Experimental Setup
A synthetic dataset of 10 binary images was generated, comprising 3 circles, 3 squares, 2
stars, and 2 triangles to represent diverse shape complexities. Each image was corrupted with
Gaussian noise, defined by the probability density function:
p x, y =
1
2πσ
2
exp −
x − μ
2
+ y − μ
2
2σ
2
, μ = 0, σ
2
∈ [0.01, 0.1]
The noise levels were chosen to reflect variances in MRI scans
(σ
2
≈ 0.01 − 0.05)
and
satellite imagery
(σ
2
≈ 0.05 − 0.1)
Other noise types (e.g., salt-and-pepper) were not included
but are planned for future work.
Python 3.11 was used with the following libraries:
OpenCV (cv2) for edge detection and contour analysis.
NumPy for numerical computations.
Mahotas for Zernike Moments extraction.
Matplotlib for visualization.
Experiments were conducted on a Windows machine with 16 GB RAM and an Intel Core
i7 processor.
3.2 Shape Recognition Techniques
3.2.1 Hough Transform (HT)
The Hough Transform identifies geometric shapes (e.g., lines, circles) in edge-detected
images using a voting mechanism in parameter space. For lines, the polar form is:
ρ = xcosθ + ysinθ
where
ρ
is the perpendicular distance from the origin, and
θ ∈ [0, π]
is the angle of the line. For
circles, the equation is:
x − a
2
+ y − b
2
= r
2
where
a, b
is the circle center, and
r
is the radius. The implementation is:
edges = cv2.Canny(image, 50, 150)
lines = cv2.HoughLines(edges, 1, np.pi / 180, 100)
HT is robust to partial occlusion and excels with simple shapes.
3.2.2 Fourier Descriptors (FD)
Fourier Descriptors represent a shape’s boundary using the Discrete Fourier Transform
(DFT). For a contour with points
x t , y(t)
, the complex representation is:
z t = x t + jy t , t = 0,1, …, N − 1
The DFT coefficients are:
c
n
=
1
N
t=0
N−1
z t exp −j
2πnt
N , n = 0, 1, …, N − 1
The shape is reconstructed using the inverse DFT:
z t =
t=0
N−1
c
n
exp j
2πnt
N
The first 10 coefficients are normalized for rotation invariance:
INTERNATIONAL JOURNAL OF ARTIFICIAL INTELLIGENCE
ISSN: 2692-5206, Impact Factor: 12,23
American Academic publishers, volume 05, issue 05,2025
Journal:
https://www.academicpublishers.org/journals/index.php/ijai
page 1869
c
n
'
=
c
n
c
1
The implementation is:
contours,
_
=
cv2.findContours(image,
cv2.RETR_EXTERNAL,
cv2.CHAIN_APPROX_NONE)
contour = contours[0].reshape(-1, 2)
complex_contour = contour[:, 0] + 1j * contour[:, 1]
descriptors = np.fft.fft(complex_contour)
descriptors = descriptors / np.abs(descriptors[1]) # Normalize
FDs are effective for contour-based classification.
3.2.3 Zernike Moments (ZM)
Zernike Moments are computed within the unit disk to extract rotation-invariant shape features.
The moment is defined as:
Z
n,m
=
n + 1
π
x
2
+y
2
≤1
f(x, y) ∙ V
n,m
∗
x, y dxdy
where
f(x, y)
is the image intensity function (e.g., 0 or 1 for binary images), and the Zernike
polynomial is:
V
n,m
x, y = R
n,m
(ρ) ∙ exp (jmθ)
The radial polynomial is:
R
n,m
ρ =
k=0
n− m )/2
−1
k
n − k !
k! ∙
n + m
2
− k ! ∙
n − m
2
− k !
ρ
n−2k
Here:
ρ = x
2
+ y
2
≤ 1:
Radial distance in the unit disk.
θ = tan
−1 y
x
:
Angular coordinate.
n:
Polynomial order (
n ≥ 0,
integer).
m:
Repetition index (
m ≤ n, n − m
even).
V
n,m
∗
x, y = R
n,m
ρ ∙ exp −jmθ :
Complex conjugate of the Zernike polynomial.
n+1
π
:
Normalization factor ensuring scale invariance.
For numerical computation, the image is mapped to the unit disk by normalizing pixel
coordinates:
x
'
=
x−x
c
r
,
y
'
=
y−y
c
r
,
x'
2
+ y'
2
≤ 1
where
x
c
, y
c
is the image center, and
r
is the radius (e.g., 21 pixels). The implementation is:
import mahotas
features = mahotas.features.zernike_moments(image, radius=21, degree=8)
The
radius = 21
parameter scales the image to the unit disk, and
degree = 8
computes
moments up to order
n = 8
Zernike Moments are robust to noise and rotation, effectively
capturing global and local shape characteristics.
3.3 Evaluation Criteria
Accuracy: Percentage of correctly identified shapes.
Execution Time: Time to extract features and classify shapes.
INTERNATIONAL JOURNAL OF ARTIFICIAL INTELLIGENCE
ISSN: 2692-5206, Impact Factor: 12,23
American Academic publishers, volume 05, issue 05,2025
Journal:
https://www.academicpublishers.org/journals/index.php/ijai
page 1870
Noise Robustness: Consistency across noise levels
σ
2
= 0.01 to 0.1
4. Results and Discussion
4.1 Recognition Accuracy
Method
Accuracy
Speed (s)
Key Advantages
Hough Transform
92%
0.35
Fast, effective for basic shapes
Fourier Descriptors
88%
0.15
Efficient for complex contours
Zernike Moments
95%
0.60
Most accurate, noise-resistant
Zernike Moments achieved 95% accuracy at
σ
2
= 0.05
, excelling with complex shapes
(stars, triangles). Fourier Descriptors maintained 88% accuracy, performing well for squares
and triangles but losing precision at
σ
2
≥ 0.07
. Hough Transform was fastest (0.35 s) for
circles and lines but struggled with distorted stars at
σ
2
≥ 0.05
.
4.2 Visual Comparison
Figure 1 illustrates recognition accuracy across noise levels. Zernike Moments maintained
structural integrity, while Fourier Descriptors showed minor boundary precision loss. Hough
Transform struggled with composite shapes.
4.3 Hybrid System Proposal
A hybrid model combining Zernike Moments with CNNs (e.g., ResNet-50) is proposed
for precision-critical applications, such as organ segmentation. For real-time systems, Fourier
Descriptors with SVMs are recommended. Early feature fusion could enhance generalization.
4.4 Limitations
The study used a small synthetic dataset (10 images), limiting generalizability. Only
Gaussian noise was considered, excluding other types like salt-and-pepper or speckle noise.
Computational constraints restricted the dataset size.
5. Conclusion
Zernike Moments are optimal for high-accuracy applications (e.g., medical imaging) due
to their noise resistance (95% at
σ
2
= 0.05
). Hough Transform is ideal for rapid detection of
INTERNATIONAL JOURNAL OF ARTIFICIAL INTELLIGENCE
ISSN: 2692-5206, Impact Factor: 12,23
American Academic publishers, volume 05, issue 05,2025
Journal:
https://www.academicpublishers.org/journals/index.php/ijai
page 1871
simple shapes, while Fourier Descriptors balance speed and complexity. A hybrid model
integrating these descriptors with neural networks offers a promising path for robust shape
recognition.
Future research will implement transfer learning with pretrained CNNs (e.g., ResNet-50,
MobileNetV2) on datasets like MNIST Shapes and industrial defect datasets. Exploring Vision
Transformers and diverse noise models (e.g., speckle noise) will enhance robustness.
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