Image feature detection using Phase Stretch Transform in MATLAB

Phase Stretch Transform (PST) is an operator that finds features in an image. PST takes an intensity image I as its input, and returns a binary image out of the same size as I, with 1's where the function finds sharp transitions in I and 0's elsewhere. PST function is also able to return the detected features in gray scale level (i.e. without thresholding).

In PST, the image is first filtered by passing through a smoothing filter followed by application of a nonlinear frequency-dependent phase described by the PST phase kernel. The output of the transform is the phase in the spatial domain. The main step is the 2-D phase function (PST phase kernel) which is typically applied in the frequency domain. The amount of phase applied to the image is frequency dependent with higher amount of phase applied to higher frequency features of the image. Since sharp transitions, such as edges and corners, contain higher frequencies, PST emphasizes the edge information. Features can be further enhanced by applying thresholding and morphological operations

Overview of Phase Stretch Transform (PST)

The Phase Stretch Transform is a non-linear, non-iterative transform that can be applied to 1D or 2D signals, including images. It was first proposed by Dr. Gonzalo R. Arce in 2014. PST has shown promising results in feature extraction, edge detection, and pattern recognition due to its ability to enhance structures with varying orientations and frequencies.

The basic idea behind PST is to stretch the phase of an input signal in such a way that its low-frequency components get compressed, while the high-frequency components remain stretched. This unique stretching and compression behavior allow PST to capture structures and patterns with varying scales and orientations, making it an effective tool for feature detection.

Implementation of Phase Stretch Transform in MATLAB

To implement the Phase Stretch Transform in MATLAB, we'll need the following steps:

1. Load the input image.
2. Preprocess the image (if necessary) to enhance features.
3. Compute the phase stretch transform of the image.
4. Enhance the features in the transformed image.
5. Threshold the transformed image to detect features.
6. Display the results.

% Step 1: Load the input image
input_image = imread('input_image.jpg');
gray_image = rgb2gray(input_image);

% Step 2: Preprocess the image (Optional)
% You can apply filters or other preprocessing techniques to enhance features.

% Step 3: Compute the Phase Stretch Transform
% Assuming you have a function that calculates the PST of a 2D signal.
pst_image = phase_stretch_transform(gray_image);

% Step 4: Enhance features in the transformed image (Optional)
% You can further process the pst_image to enhance features based on your specific requirements.

% Step 5: Threshold the transformed image to detect features
threshold_value = 0.5; % Adjust this value based on your image and feature requirements
binary_image = pst_image > threshold_value;

% Step 6: Display the results
figure;
subplot(1, 2, 1); imshow(gray_image); title('Original Image');
subplot(1, 2, 2); imshow(binary_image); title('Detected Features');

Keep in mind that the implementation may vary depending on the specifics of the Phase Stretch Transform algorithm you are using or any enhancements you want to add. Additionally, tuning parameters like the threshold value may significantly impact the quality and accuracy of the detected features.