Description

This repository contains the source code for a university assignement, based on some Numerical Linear Algebra tasks (mainly image processing operations) performed by using LIS library and Eigen3 to solve sparse linear systems and produce output images, being the images in this case stored as matrices onto which different linear algebra operations are made, such as the application of kernels/convolution matrices.

The quest represented the first NLA challenge of the semester, hence the main program is denoted as challenge1.cpp.

For the way in which the Makefile is written, the program will take the uma.jpg image as an argument

and apply the image processing operations to this image.

Requirements

Before building the code, make sure the following are available on your system:

• A C++17 compiler (e.g. g++)
• make
• Eigen3 headers installed system-wide
  (for example, on Debian/Ubuntu: sudo apt install libeigen3-dev)

The LIS library source (lis-2.1.10/) is downloaded from the original source and installed, hence the first compilation of the program may take some minutes.
There is no need to install it manually: the Makefile takes care of all required LIS build commands automatically.

Building

From the project root directory, run:

make

This will:

1. Download and configure the LIS library (inside lis-2.1.10/) with the required options.

2. Compile challenge1.cpp with the appropriate include and library paths.

3. Link against LIS and Eigen.

4. Produce the executable ./challenge1.

So make handles both the LIS build process and the compilation of the program in a single step.

Running

After building, simply run:

make run

Cleaning up

To remove all compiled files and reset the directory to a clean state:

make clean

Or, to remove also the lis directory:

make distclean

This setup ensures that anyone with Eigen and gcc installed can compile and run the project using just make and make run, without needing to install LIS separately.

Repository Structure

ImageProcessing/
├── Makefile                        # Build script (compiles LIS and challenge1)
├── README.md
├── src/                            # C++ sources
│   ├── challenge1.cpp              # Main C++ source code
│   ├── stb_image.h                 # Header to read images
│   └── stb_image_write.h           # Header to write images (PNG)
├── Outputs/                        # Directory including the outputs
└── data
    └── uma.jpg                     # Input image

Output

The output obtained by the execution of this program is:

Task 1. Image size: 500 x 456 (rows x cols)
Task 2. Noise image saved to Outputs/noise.png
Task 3. v size = 228000, ||v||_2 = 62506.566799
Task 4. Non-zero entries in A1 = 1592178
Task 5. Smoothed image saved to Outputs/smoothing.png
Task 6. Non-zero entries in A2 = 1138088, A2 symmetric? true
Task 7. Sharpened image saved to Outputs/sharpening.png
Task 8. Exported A2.mtx and w.mtx under /Outputs
Task 8. LIS iterations = 11, final residual = 9.35333117183e-16
Task 9. LIS solution image saved to Outputs/lis_solution.png
Task 10. A3 symmetric? false
Task 11. Edge detection image saved to Outputs/edge_detection.png
Task 12. Eigen solver iterations = 57, final residual = 4.98074833471e-09
Task 13. Eigen solution image saved to Outputs/eigen_solution.png