🖼️ Custom Gaussian Image Blurring (Octave/MATLAB)

Project Overview

This project provides a from-scratch implementation of a 2D Gaussian blur filter written in Octave/MATLAB script files. The primary goal is to demonstrate the manual construction of a convolution kernel and its application to an image for smoothing/blurring, without relying on built-in functions like fspecial or imgaussfilt.

The system takes an input image and a specified standard deviation ($\sigma$) to control the degree of blurring.

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⚙️ Key Functions

The implementation is split into three core functions:

1. domaci1v3(s) (Main Execution)

• Role: Loads the image, executes the filtering, and displays the results.
• Steps:
  1. Loads a test image (testpattern1024.tif) and converts it to double precision.
  2. Calls f_linFilt to generate the Gaussian kernel based on the input standard deviation (s).
  3. Applies the kernel to the image using the built-in 2D convolution function (conv2(img, gf, 'same')).
  4. Displays the Original Image and the Blurred Image side-by-side using subplot and imshow.

2. f_linFilt(n, s) (Kernel Builder)

• Role: Constructs the 2D Gaussian convolution kernel (gf).
• Parameters:
  • n: The size of the kernel (e.g., 61x61).
  • s: The standard deviation ($\sigma$) of the Gaussian distribution.
• Process: Iterates over an $N \times N$ matrix, calculating the Gaussian value for each point based on its distance from the center. Finally, it normalizes the kernel by dividing all elements by their sum, ensuring the image's overall brightness remains unchanged.

3. gaus(x, y, s) (Gaussian Formula)

• Role: Calculates a single value of the Gaussian distribution at coordinates $(x, y)$.
• Formula: Implements the 2D Gaussian function: $$K \cdot e^{-\frac{x^2 + y^2}{2 \sigma^2}}$$ where $K = \frac{1}{2\pi \sigma^2}$ is the normalization constant before the final kernel normalization.

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🚀 Usage

1. Ensure the image file specified in the imread function (C:/Users/nvuji/Downloads/testpattern1024.tif) is correctly located.
2. Run the main function domaci1v3 in your Octave or MATLAB environment, passing the desired standard deviation ($\sigma$) as the argument.

% Example usage with a standard deviation (sigma) of 5
domaci1v3(5);