Page 44 - IJOCTA-15-4

Kazemi et al. / IJOCTA, Vol.15, No.4, pp.578-593 (2025)
this method, providing links to variational princi- contain valuable diagnostic or interpretive infor-
ples from geometry that tend to favor structural mation. As an example, in the medical imaging
fidelity. field, the subtle anatomical features in the image
(i.e., blood vessels or tissue boundaries) need to
5. Comparison between tension field be preserved and no artifact should be introduced
and α−tension field in image in the denoising process. Additionally, the term
2
processing ∇I(∇ | ∇I | ) in the 2-tension field illustrates
how the higher-order gradient information can be
In this section, we compare the tension field to
integrated. This minute change, which reacts to
the nonlinear α-tension field with α = 2, referred
linear differences in the strength of the gradient, is
to as the 2-tension field. This comparison is a lens
what enables the model to automatically amplify
on the math formulations, properties, and usages
or damp specific features so that the native image
in image processing. The behavior of each op-
structure is maintained while still considering the
erator is illustrated in a figure to further clarify
issue of noise.
this comparison. After this, we display the algo-
rithm that is used to make a comparison between
the tension field and the 2-tension field of a 2D The strong mathematical background of the
image. 2-tension field is shown from a theoretical point
Equation (7) demonstrated that tension field of view by the connection between the 2-tension
of 2D image I satisfies τ(I) = ∆(I), where ∆ is field and geometric variational principles. This
the Laplacian operator. This field is crucial for provided a framework, which naturally balances
recognizing rapid intensity changes (edges, cor- smoothness with structure accuracy (key for good
ners). The tension field is useful to highlight such image processing), as can be seen in Figure 2.
running levels; however, it suffers from one major In contrast to traditional methods, which rely on
flaw, which is its high sensitivity toward the uni- static or piecewise -linear weighting techniques,
form regions, thereby making it prone to noise. the 2-tension field reacts according to the spa-
This problem occurs because the tension field in- tial characteristics of the image, proving versatile
fers isotropic smoothing across the whole image and adaptable in differing scenarios. By dynam-
pixel-wise, failing to differentiate between the ac- ically adjusting based on local conditions, such
tual substantive parts of the image and simple as textures and other fine transitions, it can pro-
noise. Thus, while the tension field is good at vide high efficiency with no unwanted artifacts.
basic edge detection, it can fail to find a balance Moreover, the versatility of the equation allows
between preserving important features while elim- it to be tailored for particular applications, such
inating unwanted artifacts when used alone. as medical imaging, where preserving fine details
In contrast, the 2-tension field defined in equa- is critical. In brief, the 2-tension field repre-
tion (16) takes it a step further with the use sents a significant leap in image processing, pro-
of higher-order terms, allowing it to dynamically viding computationally speedy solution for de-
throttle the tension field according to the gra- noising, edge retention, and features enhancement
dient norm | ∇I |. The first term of (16) dy- tasks.
namically adjusts the diffusion coefficient based
on the local gradient magnitude, and the second
term incorporates higher-order gradient informa- Figure 2 consists of eight images that illus-
tion. This inherently adaptive process protects trate, step by step, how the tension field and
those regions with high-edge structures, thus re- each term of the 2-tension field are applied to
taining their structural integrity. This minimizes the input image. It also compares the perfor-
the risk of over-smoothing in areas where noisy mance of the tension field and the 2-tension field
images are, while also letting through areas that on a well-known benchmark in image processing,
are less affected (i.e., relatively smooth) in order highlighting their respective strengths and limi-
to help smooth out the final image. Through an tations. Image (a 1 ) is the original image used as
intelligent trade- off between these effects, the 2- input for both operators. Some features of | ∇I | 2
tension field achieves the best performance across are demonstrated in Image (a 2 ) which influences
both feature preservation and noise cancellation edge detection. On the other hand, Image (b 1 )
tasks. shows the output of the tension field as it not only
Adaptive modulation can be very significant efficiently detects edges but also amplifies noise
for practical applications such as medical imaging. in smooth regions due to its isotropic smooth-
In this use case, it is important to retain fidelity ing properties. To explore the 2-tension field in-
in fine-scale structures and edges, which typically depth, we evaluate every term of τ 2 (I) and show
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