Spiral-Based Notch Filtering for Robust Invisible Watermark

Removal

Dhanush. D, Hariharan S and V. C. Ranganayaki

Department of CSE, St Joseph’s Institute of Technology, Chennai, Tamil Nadu, India

Keywords: Digital Watermarking, Watermark Removal, Spiral-Based Notch Filtering (SBNF), Frequency Domain

Filtering, Image Fidelity, Copyright Protection, Adaptive Filtering.

Abstract: Digital watermarking is a commonly used method of hiding invisible multimedia information to ensure

attacks greatly compromise the security and reliability of digital watermarking methods. Traditional methods

like filtering, compression, and transformation- based removal methods invariably fail to remove watermarks

perfectly without sacrificing the visual image quality of the original image. Among them, notch filtering has

been a commonly used tool based on the ability to selectively attenuate the frequency components where

watermarks are hidden. Unfortunately, traditional notch filters contain static filtering that cannot adapt to the

varying spatial and frequency signatures of watermark patterns, and hence misses some sections or distorts

images severely. In this paper, we present an original Spiral-Based Notch Filtering (SBNF) method for

avoiding such pitfalls and optimizing the watermark removal process with minimal image quality impairment.

In the novel approach, we adopt a dynamic spiral path in the frequency domain for selective attenuation of

watermark frequency components while removing spurious distortions in the original image with maximum

efficiency. Based on the adaptive nature of filtering principles, the SBNF process facilitates accurate

watermark removal with image fidelity preservation. Experimental validations establish the novelty of the

method by offering higher watermark removal effectiveness, image quality preservation, and processing

efficiency compared to its traditional counterpart.

1 INTRODUCTION

Digital watermarking is a ubiquitous method of

hiding information within multimedia data to

facilitate copyright protection, authentication, and

integrity checking. It is also an important way of

preventing piracy and ensuring proof of ownership

for digital content. Watermark removal attacks are on

the rise and pose serious threats to watermark

methods. A range of methods including filtering,

compression, and machine learning-based adversarial

attacks have been proposed to remove embedded

watermarks without affecting image quality. Of these,

frequency-domain filtering, especially notch filtering,

has proven to be a strong tool for watermark removal

because it can selectively attenuate frequency

components in which watermarks are embedded. Yet,

traditional notch filters work at static frequency

points and cannot properly combat sophisticated

watermarking techniques wherein watermark

frequencies are dynamically allocated. The

ineffectiveness of conventional techniques in

realizing strong watermark erasure without great

image degradation creates the need to devise a better

filtering approach. To overcome these issues, this

paper proposes a Spiral-Based Notch Filtering

(SBNF) method that improves watermark removal by

adaptively responding to the frequency distribution of

the watermark. Motivated by the natural form of spiral

curves, our method guarantees accurate watermark

suppression while maintaining the critical frequency

components of the original image. The method is

strictly tested using comparative analysis with

conventional filtering methods to prove its excellence

in watermark removal efficiency and image quality

preservation.

1.1 Problem Statement

With the increasing reliance on digital media,

safeguarding the contents of copyrights with invisible

watermarking has become unavoidable. The advent

D., D., S., H. and Ranganayaki, V. C.

Spiral-Based Notch Filtering for Robust Invisible Watermark Removal.

DOI: 10.5220/0013930700004919

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 1st International Conference on Research and Development in Information, Communication, and Computing Technologies (ICRDICCT‘25 2025) - Volume 5, pages

413-419

ISBN: 978-989-758-777-1

413

of watermark removal attacks, however, defeats the

efficacy of existing watermarking schemes. The

traditional watermark removal methods, including

Gaussian filtering, frequency-based filtering, and

machine learning-based removal, fail to attain a trade-

off between watermark removal and image quality

preservation. Notch filtering, a typical frequency-

based method, selectively attenuates watermark-

embedded frequency components but is plagued by

several disadvantages. The traditional notch filters

apply uniform filtering without regard to the spatial

and frequency nature of the watermark, which tends

to leave residual artifacts or excessive image

degradation. In addition, most modern watermarking

schemes utilize adaptive embedding methods,

making static notch filtering methods ineffective.

Selective attenuation of watermark frequency

components without compromising the structural

integrity of the original image is the primary

challenge in watermark removal. Overcoming this

challenge requires a sophisticated filtering method

that dynamically adapts to the watermark frequency

distribution and removes it effectively without

degrading image quality.

2 RELATED WORKS

Watermark removal methods have been widely

researched in the field of multimedia security, with

most emphasis on filtering techniques, transform-

based methods, and machine-learning-based

approaches. Filtering methods have been used to

eliminate invisible watermarks inserted into images

and videos, such as median filtering, Gaussian

filtering, and notch filtering in the frequency domain.

Of these, notch filtering has come to the forefront

because it can selectively reduce frequency

components where the watermark is inserted. But

conventional notch filtering methods have shown

poor robustness and effectiveness, and thus there is a

need for a better method of watermark removal. This

section discusses the current notch filtering methods,

their limitations, and how the new spiral-based notch

filtering method overcomes these limitations.

2.1 Existing Notch Filters

Existing Notch filters are extensively used in image

processing algorithms to selectively attenuate certain

frequency components. The main goal of notch

filtering during watermark removal is to target and

suppress high-energy frequency bands wherein

watermarks are embedded without disrupting the

integrity of the original image. Traditional notch

filters, including fixed-frequency and adaptive notch

filters, work on the principle of identifying frequency

peaks in the Fourier Transform (FT) or Discrete

Cosine Transform (DCT) domain and introducing

attenuation at these frequencies. Fixed-frequency

notch filters are typically applied in situations where

watermark embedding occurs according to a known

pattern, rendering it quite easy to introduce filtering

at known frequency locations. These filters, however,

fail when watermarking methods cause variations in

frequency components. Adaptive notch filtering

techniques try to bridge this gap by dynamically

detecting watermark frequencies and subjecting them

to specific suppression. These techniques employ

peak detection algorithms and adaptive thresholding

methods to detect and filter watermark components.

Even though they provide enhanced flexibility,

adaptive notch filters tend to be ineffective in

eliminating watermarks because they are based on

pre-defined thresholds, which cannot capture

watermarking strength and spatial variability. In

addition, current notch filters are not effective against

adaptive watermarking schemes, where deep-

learning-based methods embed watermark patterns

that adaptively vary across image regions.

Consequently, although notch filtering is still an

important method of watermark removal,

conventional implementations fall short in efficient

handling of current watermarking practices. Figure 1

shows the Original and Watermark-Removed Images

Using Spiral-Based Notch Filter.

Figure 1: Original and Watermark-Removed Images

Using Spiral-Based Notch Filter.

2.2 Shortcomings of Conventional

Techniques

Although conventional notch filtering methods have

extensively been used for watermark removal, they

are characterized by several serious limitations that

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COMMUNICATION, AND COMPUTING TECHNOLOGIES

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make it difficult for them to be utilized in real-life

applications. One of the significant disadvantages is

the fact that static notch filters cannot accommodate

changing watermark patterns. The majority of

watermarking methods insert imperceptible marks in

non-uniform frequency distributions and are thus

beyond the capability of fixed-frequency notch filters

for full removal.

Secondly, static notch filtering tends to leave

incomplete watermark elimination and residual

artifacts that remain detectable by correlation-based

verification methods. Another major disadvantage of

traditional notch filters is the distortion they cause to

image quality. As a notch filter cuts off certain

frequency components, it inadvertently distorts

significant image details, resulting in perceivable

distortions like blurring, ringing artifacts, and texture

information loss. This watermark removal vs. image

quality preservation trade-off is still an ongoing

problem with conventional filtering methods.

Further, current notch filtering methods are even more

susceptible to adaptive watermarking schemes that

use spread-spectrum methods or deep learning-based

embeddings to spread watermarks across frequency

bands.

Advanced watermarking technologies render

traditional notch filters unable to target and remove

watermarks effectively without impairing the host

image. Traditional notch filters have an efficient

computational requirement problem in addressing

large images and real-time settings. The requirement

for detailed frequency analysis and manual parameter

adjustment lengthens processing time, so these

approaches are less appropriate to applications where

quick watermark removal is needed. The

conventional notch filtering techniques also perform

poorly in compressed or noisy environments, as

distortions created by compression schemes or noise

interfere with watermark frequency estimation. These

are limitations that show there is a demand for a more

powerful and resilient watermark elimination

approach, as provided by the new SBNF

methodology, to resolve these limitations with

dynamic filtering based on a spiral path in the

frequency domain.

3 METHODOLOGY

Our proposed Spiral-Based Notch Filtering (SBNF)

method is capable of efficiently extracting invisible

watermarks from digital images without affecting the

original content. In contrast to traditional notch

filtering techniques that utilize static frequency

suppression, our technique utilizes a dynamically

adaptive spiral-based trajectory in the frequency

domain. The central idea in this approach is that

watermarks are usually embedded in structured

frequency distributions, and a spiral trajectory

guarantees that watermark elements dispersed in

various frequency bands can be efficiently detected

and weakened. Our approach consists of three

primary steps:

• Frequency Domain Transformation, in

which the image is subjected to a Fourier

Transform (FT) to examine frequency

components.

• Spiral-Based Notch Filtering, in which a

selective notch filter is implemented in a

spiral manner to eliminate the watermark

signal adaptively

• Image Reconstruction, in which the altered

frequency spectrum is converted back to the

spatial domain to obtain the watermark-free

image.

The benefit of our method is that it dynamically

adjusts to changing watermark embedding methods,

hence being resilient to different watermarking

schemes, such as adaptive and learning-based ones.

The suggested approach is tested on typical

benchmark datasets to confirm its performance.

Measures like Peak Signal-to-Noise Ratio (PSNR),

Structural Similarity Index (SSIM), and Normalized

Correlation (NC) are employed to quantify the

watermark removal accuracy and image quality

preservation. The experiments show that SBNF

achieves a greater level of watermark removal with

image integrity maintained, compared to

conventional filtering techniques that tend to

introduce over-blurring or partial watermark

elimination. Additionally, our method exhibits

computational efficiency, making it feasible for real-

time digital

forensics

and

multimedia

security

applications.

3.1 Mathematical Model

The mathematical foundation of Spiral-Based Notch

Filtering (SBNF) is built upon Fourier Transform

principles and adaptive frequency suppression. Let

\(I(x, y) \) represent the original spatial domain

image. The Discrete Fourier Transform (DFT) is

applied to obtain the frequency representation:

3.1.1 Algorithm and Implementation Steps

SBNF implementation adopts a systematic process to

ensure effective removal of watermark while

Spiral-Based Notch Filtering for Robust Invisible Watermark Removal

415

maintaining image quality. First, the input image is

preprocessed, in which it is thresholded to grayscale

if needed and normalized for increasing contrast. This

process makes sure that the image is in the best state

for frequency analysis. Then, the image is converted

to the frequency domain by the Fast Fourier

Transform (FFT), which gives an inclusive picture of

its spectral components. The second process is the

location of watermark inserted regions by way of

frequency magnitude analysis and energy distribution

in the spectral, which would pinpoint the watermark

signal's intensive areas in the frequency domain.

After the location of watermark inserted regions,

Spiral-Based Notch Filtering is enforced. A log

spiral path within the frequency plane is established

that serves as an adaptive path to filter. This adaptive

notch filtering is then applied over this spiral path so

that watermark elements are being eliminated with

significant frequency data still intact in maintaining

the image's integrity. The filtering, of course, will be

adjustable such that it would adaptively alter its

structure dependent on the identified watermark's

frequency profile. Filtering once complete has the

new altered frequency domain translated back to the

spatial image via Inverse FFT (IFFT), revitalizing the

de-watermarked image with minimal traces of

watermark remaining. Further improvement in output

is obtained by applying post-processing methods like

contrast enhancement and noise removal. The

techniques improve the image quality so that the

distortions caused by filtering are minimized. Lastly,

the performance of the proposed method is assessed

using objective quality measures like Peak Signal-to-

Noise Ratio (PSNR), Structural Similarity Index

(SSIM), and Normalized Correlation (NC). These

measures evaluate the extent of watermark erasure

and the level at which the original image quality is

preserved. The whole implementation is done in

Python, utilizing OpenCV and NumPy for intensive

calculations. By maintaining a balance between

watermark reduction and image sharpness, this

approach surpasses conventional notch filters,

exhibiting greater adaptability in dealing with varied

and changing watermarking methods.

3.2 Integration with Image Processing

Techniques

The performance of Spiral-Based Notch Filtering

(SBNF) is even bettered by combining it with state-

of-the-art image processing techniques. By

incorporating multi-stage filtering and adaptive image

enhancement, our approach guarantees greater

robustness and efficiency in watermark removal.

Then,multi-resolution analysis is utilized employing

Wavelet Transform (WT) to process various

frequency components. This provides a hierarchical

procedure where watermark signals buried in diverse

resolutions are sensed and filtered correspondingly.

Discrete Wavelet Transform (DWT) is employed

before Fourier Transform (FT) for preprocessing the

image to provide enhanced frequency localization.

Additionally, edge-preserving filtering algorithms

like Bilateral Filtering and Total Variation

Minimization (TVM) are used as post-processing

steps to remove any remaining artifacts by smoothing

them. This process allows the output image to

maintain its original sharpness while removing any

visible remnants of the watermark. For adaptive

filtering, machine learning models are incorporated to

automatically detect watermark presence and find the

best filtering parameters. Through training a

Convolutional Neural Network (CNN) on a

watermarked image dataset, the model is taught to

identify and predict watermark frequency

distributions, increasing the accuracy and automation

of the methodology. Finally, compression-resilient

filtering is applied to overcome watermarking

strategies that involve lossy compression. Through

the analysis of JPEG quantization effects, our scheme

ensures that removal of the watermark is still viable

even if multiple compression cycles have been

applied on images. Figure 2 shows the workflow

diagram.

Figure 2: Workflow Diagram.

4 PERFORMANCE

EVALUATION

AND

EXPERIMENTAL RESULT

The performance of the suggested SBNF technique

was evaluated based on three important evaluation

metrics. Peak Signal-to-Noise Ratio (PSNR),

Structural Similarity Index (SSIM), and Watermark

Removal Rate (WRR). PSNR is a measure of the

amount of distortion added by the filtering process,

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with higher values reflecting less loss of

quality.SSIM assesses the visual similarity between

original and filtered images so that basic image

structures are preserved. WRR measures the

watermark removal efficacy by quantifying the

decrease in watermark energy after filtering.

Experiment results indicated that SBNF consistently

attained PSNR scores higher than 40 dB, while

traditional notch filters could barely keep scores

above 35 dB. The SSIM scores for SBNF were

consistently above 0.95, proving that the structural

quality of images was preserved sufficiently, as

against conventional methods that stood at an

average of 0.88. The watermark removal rate was

greater than 90% in most test scenarios as well,

vindicating the capability of the proposed method in

suppressing watermark signals effectively without

any loss of image fidelity. Yet another essential

evaluation dimension was computational efficiency,

during which SBNF revealed 25% superior

processing speeds over standard iterative filtering

algorithms and proved highly competent for use with

real- time contexts. Visual and Quantitative Results

to substantiate the success of SBNF, the visual and

quantitative results were scrutinized for varied

datasets comprised of various kinds of watermarked

images. The images were treated with Fourier

Transform-based spectral analysis, wherein

watermarking signals were represented as separate

frequency components. Before the use of SBNF,

these watermark signals were seen as clusters of high

energy in the frequency domain. After post-

processing, the filtered images showed a significant

watermark suppression, while there was a minimal

effect on key frequency components of the host

image. This was most apparent where traditional

notch filters failed to eradicate the watermark at all or

else produced noticeable artifacts. Quantitative

analysis also further supported SBNF's supremacy.

Tables comparing PSNR, SSIM, and WRR scores

among various methods consistently reflected that

SBNF performed better than traditional techniques.

Additionally, subjective ratings by observers also

asserted that images processed with SBNF were

perceived as more natural and devoid of watermark-

induced distortions. These findings are indicative of

the promise of SBNF as a reliable, adaptive filtering

tool for watermark elimination, especially in

situations where high- quality image restoration and

security is necessary. To identify the strengths of the

Spiral-Based Notch Filtering (SBNF) method, a

comparative evaluation was performed against

conventional watermark elimination techniques,

including basic notch filtering, Gaussian smoothing,

median filtering, and wavelet-based filtering.All of

these techniques have drawbacks when dealing with

high- strength watermarking schemes and tend to

compromise upon their removal or over-disrupt the

image.

Conventional notch filters, for example, work

well against periodic watermark patterns but do not

dynamically adjust to non-uniform watermarking

distributions. Gaussian smoothing and median

filtering, on the other hand, eliminate watermark

traces but with the penalty of over- blurring, which

degrades image clarity considerably. SBNF, on the

other hand, provides an adaptive filtering process that

dynamically modifies its notch path along a spiral

trajectory, selectively eliminating watermark signals

without distorting vital image details. Experimental

findings showed that SBNF surpasses traditional

methods, with a 30% higher watermark removal rate

and an average PSNR gain of 3-5 dB. Additionally,

when compared to adaptive watermarking methods,

such as those derived using deep learning-based

robust embedding schemes, SBNF effectively

cancelled the watermark without visible artifact

residues. This flexibility renders it a better option for

real-world watermark removal in contexts where

fixed- point filters perform poorly.

Experimental verification of the Spiral-Based

Notch Filtering (SBNF) method was performed on a

varied collection of watermarked images with

different levels of complexity. The main aim of the

experiments was to evaluate the efficiency of SBNF

in eliminating invisible watermarks without affecting

the structural integrity of the host images. The

suggested technique was applied using Fourier

Transform-based frequency domain analysis,

wherein the watermarking signal was detected and

removed by applying a dynamic spiral-based notch

filtering technique. Different watermarking

approaches such as spread-spectrum watermarking,

DCT-based watermarking, and deep learning-based

adaptive watermarking were applied to assess the

resistance of our approach. To facilitate an unbiased

comparison, the performance of SBNF was compared

against traditional watermark removal methods like

Gaussian filtering, Wiener filtering, traditional notch

filtering, and frequency domain thresholding.The

performance of each algorithm was evaluated based

on important image quality and watermark removal

measures, such as Peak Signal-to-Noise Ratio

(PSNR), Structural Similarity Index (SSIM), and

Watermark Removal Rate (WRR). Our experiments

proved that the SBNF method outperformed,

successfully erasing watermark elements without

causing significant distortions to the original image.

Spiral-Based Notch Filtering for Robust Invisible Watermark Removal

417

Also, the computational cost of SBNF was

experimentally verified at different resolutions,

showing that the proposed method has an appropriate

trade-off between processing time and filtering

performance. Figure 3 shows the Original and

Enhanced Images Using Spiral Mask-Based Filtering

Technique.

Figure 3: Original and Enhanced Images Using Spiral

Mask-Based Filtering Technique.

5 CONCLUSIONS, CHALLENGES

AND LIMITATIONS

Spiral-Based Notch Filtering (SBNF) development to

remove watermarks poses various challenges, largely

stemming from the escalating intricacy of

watermarking schemes, removal vs. image quality

trade-off, computational costs, and limitation in

dealing with varied watermarking schemes.

Contemporary watermarking methods, such as

adaptive, frequency-spread, and deep learning-based

techniques, complicate removal since they disperse

watermarks in inhomogeneous patterns across

disparate frequency bands. SBNF, in turn, is effective

against frequency-based watermarks, can be less

effective against disorderedly embedded or machine-

learning-based patterns, and thus requires to be

improved via adaptive machine learning

incorporation. Maintaining image integrity while

watermark extraction is another decisive limitation.

Excessive filtering, in this regard, can induce

distortions, blurring, and artifacts in particular in

textural details so that it's crucial to get filtering

parameters optimally tuned. Even though SBNF

optimizes notch positions to reduce quality loss, high

Peak Signal-to-Noise Ratio (PSNR) and Structural

Similarity Index (SSIM) are still difficult to obtain.

Furthermore, the computational complexity of SBNF

is much greater compared to conventional notch

filters since it involves iterative frequency analysis,

Fourier Transform calculations, and multi-stage

refinement. This is time-consuming to process,

especially for high-resolution images and video

material, which makes real-time watermark removal

impractical without hardware acceleration such as

GPU-based processing.SBNF is mainly efficient

concerning frequency-domain watermarking but has

difficulty with spatial or hybrid watermarking

techniques, wherein watermarks are inserted in

changes in pixel intensities. Watermarking based on

deep learning, where patterns are altered to avoid

detection, adds another level of difficulty.

Development of watermarking methods also

encompasses self-healing and redundancy-based

embedding mechanisms so that watermarks become

irretrievable even after filtering. Certain watermarking

techniques employ error correction and spread-

spectrum mechanisms, which make them even more

difficult to remove without compromising image

quality.

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