Digital Image Processing Course - Homework Solutions

This repository contains my solutions to six homework assignments from the Digital Image Processing course. Each assignment focuses on different aspects of image processing, including signal processing, transformations, and machine learning techniques applied to images. The solutions are implemented in Python using Jupyter notebooks, with a combination of theoretical explanations and practical algorithm implementations.

Table of Contents

1. Homework 1: Image Kernels & Fourier Series
2. Homework 2: Quantization Techniques
3. Homework 3: Convolution & DCT Compression
4. Homework 4: CLAHE & Filter Comparison
5. Homework 5: Hough Transform, Segmentation & K-Means
6. Homework 6: Compression & Morphological Operations

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Homework 1: Image Kernels & Fourier Series

Part 1: Image Kernels

In this task, I applied the provided kernel to the image image1. Additionally, I experimented with two other kernels and compared the resulting images to understand how different kernels affect image processing.

Part 2: Fourier Series

I explored Fourier transformations by calculating the Fourier coefficients of image2 and visualizing the transformed image. I then reconstructed the image step by step by summing sinusoidal signals, demonstrating the power of Fourier synthesis.

Visualization of reconstructed image using the fourier synthesis.

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Homework 2: Quantization Techniques

This homework focused on various quantization methods, including:

• Part a: I explained the concept and purpose of quantization in digital image processing.
• Part b: I applied uniform quantization with 4 levels to a given set of values, visualized the results, and calculated the Mean Squared Error (MSE).
• Part c: I implemented a custom quantizer function to quantize an image using decision and reconstruction levels.
• Part d/e: I implemented Lloyd-Max and uniform quantization methods and analyzed their effects on a given image, comparing histograms and MSE.

Visual comparison of the original image, uniform quantization, and Lloyd-Max quantization, alongside their corresponding histograms, highlighting differences in compression and detail retention.

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Homework 3: Convolution & DCT Compression

Part 1: Convolution

I implemented both standard and circular convolution on images, experimenting with different kernels and observing the resulting transformations.

Part 2: DCT Image Compression

I utilized the Discrete Cosine Transform (DCT) to compress images, experimenting with different compression ratios and assessing the visual quality and efficiency of the compression.

Visualization of DCT compression and decompression with varying coefficients (n = 1, 2, 4, 6, 8, 10), illustrating the impact on image quality.

(a)

(b)

Plot (a) shows the MSE of the decompressed image versus DCT coefficients (n), while plot (b) compares the PSNR of the decompressed image as a function of n.

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Homework 4: CLAHE & Filter Comparison

Part 1: CLAHE Implementation

I implemented Contrast Limited Adaptive Histogram Equalization (CLAHE) from scratch and applied it to image1.jpg. CLAHE enhances image contrast while preventing over-amplification in high-contrast areas by processing small tiles in the image.

Comparison of the original image and the CLAHE-enhanced image, highlighting improved contrast and detail preservation in the enhanced version.

Part 2: Wiener vs. Inverse Filtering

I compared the performance of Wiener and inverse filters on an image that was both blurred and noisy, evaluating which method provided better restoration.

(a) Noise-free situation

(b) Noisy situation

Comparison of inverse and Wiener filters for noise-free image restoration in (a) and noisy image restoration in (b), with PSNR values in the titles indicating image quality relative to the original.

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Homework 5: Hough Transform, Template Matching & K-Means Segmentation

Part 1: Hough Transform

I implemented the Hough transform from scratch to detect lines on a chessboard image (chess.jpg). I developed an algorithm to remove non-relevant lines and identified chessboard corners.

Visualization of detected lines on chess image using Hough transform.

Part 2: Image Template Matching

I applied template matching techniques to the image birds.jpg, aiming to detect the birds without using external libraries.

Detected birds in the image using template matching techniques.

Part 3: K-Means Clustering

I described the K-Means clustering algorithm and used it to quantize the image sight.jpg. I determined the optimal number of clusters based on image analysis.

Output of 4-bin quantization using K-means algorithm.

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Homework 6: Compression & Morphological Operations

Part 1: Image Compression

I compressed the cameraman.jpg image using both the Walsh-Hadamard and Discrete Cosine Transforms (DCT) with identical compression ratios. I evaluated the quality of the compressed images using multiple metrics and performed arithmetic coding on the DCT-compressed result.

Comparison of Walsh-Hadamard and Discrete Cosine Transform (DCT) at identical compression ratios (5, 10, 15, 20, 25), illustrating the differences in image quality and information retention across both methods.

Table: Comparison of WHT and DCT compression results.

Ratio	WHT_MSE	WHT_PSNR	WHT_SSIM	DCT_MSE	DCT_PSNR	DCT_SSIM
5	0.001399	28.541886	0.959120	0.001108	29.552790	0.974540
10	0.002148	26.680216	0.917958	0.001623	27.897143	0.936990
15	0.002814	25.506035	0.887582	0.002203	26.569549	0.905004
20	0.003434	24.641524	0.858834	0.002781	25.558190	0.877347
25	0.004397	23.568252	0.822654	0.003902	24.086957	0.833458

Part 2: Morphological Image Processing

I implemented custom morphological operations to complete the following tasks:

• Isolating stars in andromeda-galaxy.png.

Result of morphological processing on andromeda-galaxy.png, isolating and retaining only the tiny stars in the grayscale image.

• Segmenting organs in MRI.png.

Segmentation of organs in MRI.png, where distinct organs are separated, defined, and colored uniquely after binarization and morphological processing.

• Coloring the letter "I" red in text.jpg.

Result of morphological processing on text.jpg, highlighting every instance of the letter 'I' in red.