LA Mini Project - Image Color Manipulation

Problem Statement

Matrix Multiplication - Manipulate image colours similar to Photo Filters for Images

Tech Stack

• FastAPI backend for image processing API
• Custom HTML/CSS/JavaScript frontend with KaTeX for LaTeX rendering
• NumPy + Pillow for matrix-based transformations

Core Matrix Operations

• Color Matrix Transforms (3×3 RGB multiplication): 9 filter presets + custom blending
• Hue Rotation: YIQ color space basis change for rotation math
• Tone Controls: Exposure, contrast, saturation via matrix operations
• Grayscale Projection: Orthogonal projection onto luminance vector
• Vibrance Boost: Selective saturation amplification
• Least Squares Color Correction: Solves min_X ||AX - B||²_F for optimal color mapping
• PCA Compression: Eigendecomposition + reconstruction at reduced rank (k=1,2,3)
• Covariance Analysis: Full color covariance matrix from pixel distribution

Dashboard & Analysis

• Transformation Diagnostics: Rank, nullity, determinant, condition number, invertibility
• Matrix Properties: Trace, Frobenius norm, RREF via Gaussian elimination
• Eigenanalysis: Dominant eigenvector, explained variance per component
• Color Statistics: Mean RGB, standard deviation, dynamic range

UI Features

• Live Preview: Real-time split/original/edited view modes
• Interactive Controls: Sliders for all 14 parameters with smart tooltips
• Formula Rendering: KaTeX + safe math parser for tooltip formulas

Setup & Run

Requirements: Python 3.8+

Installation:

python -m venv venv

# On Windows:
venv/Scripts/activate          
# On Unix/Mac
source venv/bin/activate

pip install -r requirements.txt

Start the App:

python app.py

The server will start on http://127.0.0.1:8000 with hot-reload enabled. Upload an image and adjust controls to see live matrix transforms and LA metrics update in real-time.

Project Structure

• app.py: Single app entrypoint + FastAPI routes
• src/filter_matrices.py: Filter presets, hue rotation, tonal/enhancement controls
• src/la_core.py: Matrix operations, RREF, rank, determinant, structure analysis
• src/analysis.py: Least squares correction, eigendecomposition, PCA, color statistics
• src/image_pipeline.py: Full pipeline orchestration + response payload
• frontend/index.html: UI layout (images left, controls right)
• frontend/styles.css: Professional dark theme with modern gradients
• frontend/app.js: Live controls, KaTeX formula rendering, smart tooltips