IACV Homework 2024/25

Computer Vision homework for reconstructing 3D geometry from a single image

Overview

This project implements a complete computer vision pipeline to reconstruct the 3D geometry of a rectangular parallelepiped (cabinet) from a single uncalibrated image. The implementation includes feature extraction, camera calibration, geometric rectification, and 3D model reconstruction.

Problem Statement

Given a single image of a rectangular cabinet with:

• Known width (1 unit along X-axis)
• Unknown depth (m) and height (h)
• Visible horizontal circumference and planar curve
• Multiple sets of parallel lines in X, Y, and Z directions

Goal: Reconstruct the complete 3D geometry and camera parameters.

Input image with extracted features (lines, circumference, and curve S)

Key Features

1. Feature Extraction

• Line Detection: Advanced edge detection using PCA on RGB+HSV channels, Canny edge detection, and Hough transform
• Conic Extraction: Circumference detection and parameterization
• Curve Extraction: Horizontal planar curve identification

2. Geometric Reconstruction

• Vanishing Point Detection: Robust intersection finding for parallel line sets
• Metric Rectification: Euclidean rectification of horizontal planes
• Camera Calibration: Intrinsic parameter estimation from vanishing points
• 3D Measurements: Height and depth calculation from rectified geometry

3. 3D Model Generation

• Complete parallelepiped reconstruction
• Camera localization in 3D space
• Multiple view visualization

Project Structure

├── Code/
│   ├── 1-FeatureExtraction/      # Edge detection, line/conic extraction
│   ├── 2.0-ManualLineExtraction/  # Manual line picking tools
│   ├── 2.1-Vanishing_Line_Extraction/  # Vanishing point computation
│   ├── 2.2-Metric_Rectification/  # Geometric rectification
│   ├── 2.3-Intrinsic_Calibration/  # Camera parameter estimation
│   ├── 2.4-Height_Calculation/    # 3D measurements
│   └── 2.5-2.6-Curve_S_and_Camera_Localization/  # Final reconstruction
├── Report/                        # LaTeX technical report
├── Assignment/                    # Original homework specification
└── IACV_Homework_2024_Report_Paolo_Ginefra.pdf

Technical Approach

1. Feature Extraction: PCA-based preprocessing, Canny edge detection, Hough line transform
2. Vanishing Geometry: SVD-based robust intersection for vanishing points and lines
3. Rectification: Homography computation for metric reconstruction
4. Calibration: Camera matrix estimation from orthogonal vanishing points
5. 3D Reconstruction: Height/depth measurement and complete model generation

Results

Feature Extraction Pipeline

Left: Detected lines using Hough transform. Right: PCA-based feature extraction

Geometric Rectification

Metric rectification of the horizontal plane

3D Model Reconstruction

Reconstructed 3D model from different viewpoints

Requirements

• MATLAB with Computer Vision Toolbox
• Image Processing Toolbox

Author

Paolo Ginefra (ID: 10765882)
Politecnico di Milano - Image Analysis and Computer Vision Course 2024/25
Supervisor: Prof. Vincenzo Caglioti

Documentation

See the complete technical report (IACV_Homework_2024_Report_Paolo_Ginefra.pdf) for detailed methodology, mathematical formulations, and results analysis.