Digital-Image-Processing

Assignments for Digital-Image-Processing course at ECE AUTH

Digital Image Processing – Assignment 1

Histogram Equalization & Matching

Overview

In this project, I implemented histogram processing techniques for grayscale images in Python.

Specifically, I implemented:

• Histogram Equalization
• Histogram Matching

Each method was developed using three different modes:

• Greedy
• Non-Greedy
• Post-Disturbance (noise-based approach)

Files

• hist_utils.py – Histogram computation and transformation utilities
• hist_modif.py – Core implementation of equalization and matching algorithms
• demo.py – Demonstration script that loads images, runs all modes, and displays results
• report.pdf – Analysis and experimental results

Usage

Run:

python demo.py

The program asks for:

• Input image path
• Reference image path

It then performs histogram equalization and histogram matching in all three modes and displays the results with their corresponding histograms.

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This project demonstrates the implementation and comparison of different histogram modification strategies and their effect on image contrast and distribution.

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Digital Image Processing – Assignment 2

Edge & Circle Detection

Overview

In this project, I implemented edge detection and circle detection algorithms from scratch using FIR convolution.

Specifically, I implemented:

• 2D FIR convolution
• Sobel edge detection (with threshold analysis)
• Laplacian of Gaussian (LoG) edge detection
• Circular Hough Transform for circle detection

Implemented Methods

• Sobel Operator
  Computes first-order gradients (Gx, Gy) and detects edges via thresholding on gradient magnitude.

• Laplacian of Gaussian (LoG)
  Applies Gaussian smoothing and Laplacian filtering, detecting edges through zero-crossings.

• Circular Hough Transform
  Detects circles in binary edge images using a 3D voting accumulator (center_x, center_y, radius).

Demo

The demo.py script:

• Analyzes Sobel for multiple threshold values
• Plots threshold vs detected edge points
• Compares Sobel and LoG edge maps
• Detects circles using:
  • Sobel + Hough
  • LoG + Hough
• Evaluates different voting thresholds (V_min)

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This project demonstrates implementation of convolution-based edge detection and parametric shape detection using the Hough Transform.

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Digital Image Processing – Assignment 3

Image Segmentation

Overview

In this project, I implemented graph-based image segmentation methods.

Specifically, I implemented:

• Image-to-graph representation (fully connected affinity graph)
• Spectral Clustering for image segmentation
• Normalized Cuts (n-cuts)
  • Non-recursive version
  • Recursive version with stopping criteria

Implemented Methods

• Image as Graph

  • Each pixel is treated as a node
  • Edge weights are defined as: A(i, j) = 1 / exp(d(i, j))
  • d(i, j) is the Euclidean distance between pixel color vectors
  • Produces a fully connected affinity matrix

• Spectral Clustering

  • Laplacian: L = D − W
  • Solve eigenproblem: Lx = λx
  • Use k smallest eigenvectors
  • Apply KMeans (random_state=1) in spectral space

• Normalized Cuts (n-cuts)

  • Solve generalized eigenproblem: Lx = λDx
  • Cluster using KMeans on eigenvectors
  • Compute Ncut metric to evaluate partition quality

• Recursive n-cuts

  • Repeatedly splits graph into 2 clusters
  • Stops when:
    • Cluster size < T1
    • Ncut value > T2
  • Produces hierarchical segmentation

Demo

The demo scripts:

• demo1.py – Spectral clustering on a predefined affinity matrix
• demo2.py – Spectral clustering on RGB images
• demo3a.py – Non-recursive n-cuts (k = 2,3,4)
• demo3b.py – Single-step binary partition with Ncut evaluation
• demo3c.py – Full recursive n-cuts (T1=5, T2=0.2)

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This project demonstrates graph-based segmentation using spectral methods and highlights the differences between spectral clustering and normalized cuts, including recursive hierarchical splitting.