ofxRadonTransform

Radon Transform (Sinogram) addon for OpenFrameworks.

Overview

ofxRadonTransform is an OpenFrameworks addon that implements the Radon Transform for image processing. The Radon transform is a fundamental tool in tomographic reconstruction and has applications in computer vision, pattern recognition, and image analysis.

What is Radon Transform?

The Radon Transform represents an image as a collection of projections along different angles. The result is often visualized as a sinogram - a 2D image where:

• Each row corresponds to a projection at a specific angle
• Each column corresponds to a specific position in the original image

This transformation provides a different representation of the image that highlights certain features and can be particularly useful for:

• Feature extraction
• Rotation-invariant pattern recognition
• Tomographic reconstruction
• Line detection

Features

• Fast implementation of Radon Transform for grayscale images
• Adjustable angle resolution
• Computation time measurement
• Simple integration with existing OF projects
• Interactive example application with GUI controls

Dependencies

• OpenFrameworks 0.10.1+
• ofxCv
• ofxOpenCv
• ofxGui

Installation

1. Download or clone this repository into the addons folder of your OpenFrameworks installation:

   cd openFrameworks/addons
   git clone https://github.com/bemoregt/ofxRadonTransform.git
   

2. Open the example project in Project Generator, update it, and open in your IDE.

3. Alternatively, add ofxRadonTransform to your existing project using the Project Generator.

Usage

Basic usage example:

#include "ofxRadonTransform.h"

ofxRadonTransform radonTransform;
ofImage inputImage, outputImage;

// In setup()
inputImage.load("test.png");

// Compute Radon transform with 360 angle steps
radonTransform.compute(inputImage, outputImage, 360);

// In draw()
inputImage.draw(0, 0);
outputImage.draw(inputImage.getWidth(), 0);

// Get computation time
float time = radonTransform.getElapsedTime();

Algorithm

• Sinogram is the Radon Transform for Grayscale Image.
• Sinogram is a kind of Reciprocal Transform, like a Fourier Transform.
• From Fourier Slice Theorem, Sinogram can be implemented from Polar 1D FFT.
• Like the Fourier space, Phase space, and Hough space, these second spaces are very important to get more detailed features by post processing.
• The implementation is based on rotating the image at various angles and summing pixel values along columns.
• The resulting sinogram is a 2D representation where:
• Horizontal axis represents angle (0-360 degrees)
• Vertical axis represents distance from center
• Pixel intensity represents sum of pixels along each projection line

Applications

• Image feature extraction
• Dataset transformation and augmentation for deep learning
• Data compression
• Invariance achievement
• Second space image processing
• Tomographic reconstruction

Future Plans

• Inverse Radon Transform for image reconstruction
• Fast Hough Transform implementation using Radon Transform
• 1D Entropy Plot for analyzing projection patterns
• Peak detection for identifying significant features in the sinogram
• Performance optimizations for real-time usage

Reference

• Original implementation based on: OpenCV-Radon
• Theoretical background: Radon Transform - Wikipedia

License

MIT License

Author

bemoregt