# MATLAB - Ideal Highpass Filter in Image Processing

The principle of an optimal highpass filter is applied to image processing to boost high-frequency elements while suppressing low-frequency ones. It's crucial to remember, though, that the qualities of an ideal highpass filter make it theoretical and impractical. Other highpass filter types with finite cutoff frequencies are utilized in practice because they are easier to implement.

### Steps:

Your method is a well-organized breakdown of the processes needed to use MATLAB to create an optimum highpass filter for image processing.

Permit me to talk briefly about each step:

Step 1 The first step is input, which involves reading a picture. It's crucial to pick the right image to bring out the highpass filter's effects.

Step 2: It's a good idea to save the size of the input image because it will be useful for further calculations and operations.

Step 3: The Fourier Transform of the input

Step 4: It's crucial to assign the Cutoff Frequency D0. Which frequency components are regarded as "high" frequencies are determined by this parameter. The results of the filtering will change if this value is changed.

Step 5: The mask for the frequency domain image is created while designing the filter. This is a binary mask with 1 for high frequencies and 0 for low frequencies in the case of a perfect highpass filter.

Step 6: Convolution of the Fourier transforms in The filtering mask and the transformed input image are a frequency-domain multiplication of elements. Low-frequency components are suppressed while the high-frequency components are emphasized.

Step 7: Taking the Inverse Fourier at The image is transformed to restore the spatial domain while maintaining the high-frequency accent.

Step 8: The last step is to display the completed image, step eight. This lets you visually compare the image and the filtered output and see how the highpass filter has affected the image.

Note:

### Implementation:

output:

The IHPF algorithm is implemented step-by-step in this code using MATLAB. It takes in an input image, filters it in the frequency domain, and outputs sharpened images for display. [Name of input image file] can be changed. Put [file format] in place of your input image's real filename and file format.

• To modify the highpass filtering's strength, change the D0 value. Even though this code represents the optimum highpass filter, real-world applications generally employ more sophisticated filters, such as Gaussian and Butterworth highpass filters, due to their improved results and smoother transitions.

Output:

• Remember that the MATLAB code above illustrates the fundamental principle of an ideal highpass filter.
• Due to the shortcomings of the ideal filter, you would employ more practical filters in real-world situations, such as Gaussian or Butterworth highpass filters.
• The cutoff frequency and other parameter tweaking would also depend on the particular image and application.

## Benefits and Limitations of Highpass: filter

Even though the ideal highpass filter is rarely employed in actual image processing because of its idealized characteristics and related artifacts, knowing its advantages and disadvantages might help us comprehend more practical filtering methods.

Benefits of considering the optimum highpass filter in image processing:

Simple implementation and conceptual understanding make The ideal highpass filter an effective educational tool for introducing the ideas of frequency domain filtering and Fourier transformations in image processing.

Understood theoretically: The impact of high-frequency components in images can be understood theoretically using the ideal highpass filter as a point of comparison. It draws attention to how different frequency ranges affect certain aspects of an image.

Visualization of Artifacts: Although ringing and noise amplification artifacts are known to be produced by the ideal highpass filter, they can be used to illustrate the difficulties in quickly deleting low-frequency information.

• Implementing the ideal highpass filter makes it simple to compare it to other highpass filter types, like Butterworth or Gaussian filters,
• This comparison aids in understanding the compromises and enhancements that more complex filters provide.

Finding Edge Information: The optimal highpass filter highlights edges and distinct transitions in the image, making it beneficial for emphasizing characteristics and structures crucial in particular applications, such as edge identification.

Artistic Effects: The artifacts produced by the perfect highpass filter can be used in creative applications to develop artistic effects, giving images a distinctive texture or stylized appearance.

• The qualities of the ideal highpass filter can be utilized as a foundation to develop better filters that keep high-frequency information while decreasing.

Exploration of Limitations: The shortcomings of the ideal highpass filter highlight the difficulties in practical image processing, leading to the development of more complex filters that address problems like ringing artifacts and noise amplification.

• Although the optimal highpass filter offers many advantages, it is crucial to remember that some of its shortcomings, including ringing artifacts and noise amplification, are significant and can produce unfavorable or unrealistic results.
• Due to their controllable cutoff characteristics and smoother transitions, edge-preserving filters like Butterworth, Gaussian, and others are frequently used in practice.

The perfect highpass filter has several severe drawbacks when it comes to actual image processing despite having some theoretical characteristics that may appear appealing:

Ringing Artifacts: The ideal highpass filter's frequency response has a sharp transition, which causes ringing artifacts in the spatial domain.

• These distortions appear as oscillations or ripples at the margins in the filtered image. The quality of the processed image may suffer due to these artifacts.
• The ringing artifacts above exemplify the Gibbs phenomenon, characterized by overshoots near image edges.
• Reduced visual quality and an unnatural appearance may result from this.

Aliasing: The ideal highpass filter must consider the idea of aliasing, which happens when high-frequency data collapses back into lower frequencies due to undersampling.

Sensitivity to Noise: The optimum highpass filter enhances edges and high-frequency noise. As a result, noise in the filtered image may be amplified, making it less appropriate for real-world noisy photos.

Loss of Low-Frequency Information: A good highpass filter strips the image of all low-frequency elements. Important nuances and textures in the low-frequency region may need to be recovered.

Unrealistic Assumptions: The ideal highpass filter erroneously assumes that it is possible to accomplish sudden changes in the frequency domain without effects on the spatial domain.

• Real-world images, however, are not precisely discontinuous; therefore, making such assumptions yields inaccurate findings.

Unnatural Appearance: The filtered image may appear too crisp and unnatural due to the amplification of high-frequency components. This can produce an unpleasant visual result.

Implementation Challenges: The optimal highpass filter necessitates complex mathematical processes that are challenging to execute in real life. The usage of infinite values is required due to the sudden shift in the frequency domain, which cannot be directly realized in discrete systems.