Edge detection identifies boundaries within images by locating abrupt changes in intensity or color, which correspond to object outlines and structural details. This process is fundamental for tasks like object recognition and image segmentation.

Wavelet transform serves as a time-frequency analysis method, decomposing signals into linear combinations of wavelet basis functions. These functions exhibit localization and oscillatory properties, enabling precise capture of local variations in signals.

In image edge detection, wavelet transform leverages these characteristics through a multi-step approach:

1. Wavelet Decomposition: The image undergoes wavelet decomposition, producing a set of wavelet coefficients that represent different frequency components.
2. Edge Enhancement: Coefficients corresponding to edges are amplified using techniques such as:
   • Thresholding: Coefficients above a defined threshold are retained, while others are set to zero.
   • Non-Maximum Suppression: Local maxima along gradient directions are preserved, suppressing non-maximal coefficients to thin edges.
3. Edge Linking: Enhanced coefficients are connected to form a continuous edge map, often through morphological operations or contour tracing.

Key advantages of this method include:

• Localization: Wavelet basis functions provide precise spatial localizatino of edges.
• Multi-Scale Analysis: Different decomposition scales allow detection of edges at varying levels of detail.
• Noise Resilience: Wavelet transforms inherently suppress noise, improving robustness in noisy images.

Applications span numerous fields, such as medical imaging for tissue boundary identification, remote sensing for land feature extraction, and computer vision for object detection.

function detectEdgesWithWavelet()
    imgData = imread('sample_image.jpg');
    grayImg = rgb2gray(imgData);
    imgMatrix = double(grayImg);
    
    rows = 250;
    cols = 250;
    decompositionLevel = 6;
    thresholdValue = 7;
    smoothRegions = 20;
    edgeRegions = 40;
    
    waveletCoeffs1 = zeros(rows, cols);
    waveletCoeffs2 = zeros(rows, cols);
    waveletCoeffs3 = zeros(rows, cols);
    
    for rowIdx = 1:rows
        waveletCoeffs1(rowIdx, :) = cwt(imgMatrix(rowIdx, :), 1, 'bior4.4');
        waveletCoeffs2(rowIdx, :) = cwt(imgMatrix(rowIdx, :), 2, 'bior4.4');
        waveletCoeffs3(rowIdx, :) = cwt(imgMatrix(rowIdx, :), decompositionLevel, 'bior4.4');
    end
    
    % Edge enhancement and linking steps follow
end