Draft:High Boost Filter

The High Boost Filter is a non-linear digital filtering technique. The High Boost Filter, also known as High Boost Filtering, is a fundamental concept in the field of digital image processing. It is a technique utilized to enhance the sharpness and details of an image by accentuating its high-frequency components while preserving its low-frequency components.

Algorithmic description
The fundamental concept behind the High Boost Filter involves selectively amplifying high-frequency components within an image while preserving its low-frequency details. Analogous to traditional linear filters, the High Boost Filter operates on a non-linear paradigm, accentuating image sharpness by enhancing edges and fine details. This process begins with the extraction of high-frequency components through high-pass filtering, followed by amplification and integration with the original image. Unlike traditional filters that rely on weighted averages, the High Boost Filter's emphasis on frequency manipulation enables precise enhancement without sacrificing edge integrity. The filter's versatility extends to various dimensions, accommodating both one-dimensional and multidimensional data, ensuring comprehensive detail enhancement across diverse image types.

= Formula = HPF = Original image - Low frequency components LPF = Original image - High frequency components HBF = A * Original image - Low frequency components = (A - 1) * Original image + [Original image - Low frequency components] = (A - 1) * Original image + HPF Here,


 * HPF = High pass filtering, which means the higher frequency components are allowed to pass while low-frequency components are discarded from the original image.
 * LPF = Low pass filtering, which means the lower frequency components are allowed to pass while high-frequency components are discarded from the original image.
 * A = Amplification factor, determining the extent to which high-frequency components are enhanced relative to the original image.

Question:
Given an original grayscale image with pixel values ranging from $$0$$ to $$255$$, apply a High Boost Filter with an amplification factor $$A = 2$$ and a kernel size of $$3 \times 3$$. The low-pass filtering operation is performed using a simple averaging filter. If a specific pixel in the original image has a value of $$100$$ and its neighboring pixels within the $$3 \times 3$$ kernel have the following values:$$[ 110, 90, 120, 95, 105, 115, 85, 125, 100 ]$$, compute the corresponding pixel value in the resulting High Boost Filtered image.

1. Compute the average value of the neighboring pixels:
$$Average \, value = \frac{9}$$

$$Average \, value =  \frac{935}{9} $$

$$Average \, value \approx 103.89$$

2. Compute the high-pass filtered value:
$$High \, pass \, filtered \, value=Original \, pixel \, value \, - \, Average \, value \, $$

$$High \, pass \, filtered \, value=100 - \, 103.89 $$

$$High \, Pass \, filtered \, value \approx -3.89$$

==== 3. Apply the amplification factor:$$Amplified \, High \, Pass \, filtered \, value=(2-1)\times Original \, pixel \, value \, + \,  High \, Pass \, filtered \, value$$$$Amplified \, High \, Pass \, filtered \, value=(2-1)\times 100, + \, (-3.89)$$$$Amplified \, High \, Pass \, filtered \, value=100 - \, 3.89 $$$$Amplified \, High \, Pass \, filtered \, value \approx 96.11$$ ==== 4. Compute the resulting pixel value in the High Boost Filtered image:$$High \, Boost \, Filtered \, pixel \, value=Original \, \, value \, + \,  Amplified \, high \, pass \, filtered \, value $$$$High \, Boost \, Filtered \, pixel \, value= 100 +96.11 $$$$High \, Boost \, Filtered \, pixel \, value \approx 196.11$$