1. Wavelet transform application – edge detection
電子所 .
蘇伯恩 .

2. Capable of analyzing the fluctuations of image grayscale levels.
Extract features isolate the edges.
* The Wavelets have the capacity to locally analyze the fluctuations of image grayscale levels.
* The analysis of images by wavelets makes it possible to extract a new image from which we can isolate the edges .

3. Define ‘edge’
Contour across an image which the brightness of the image changes abruptly.
Data from digital images are discrete
discrete filters ( which can be applied by discrete convolutions. )
Often defined as the local maxima of the gradient.
An edge in an image is a contour across which the brightness of the image changes abruptly.
Data from digital images are discrete. So to deal with such image data, we need discrete filters, which can be applied by discrete convolutions.
Image data is discrete, so edges in an image often are defined as the local maxima of the gradient.

4. Define ‘edge’

5. Characteristics of edges
Some are more significant, and some are blurred and insignificant.
Insignificant edges are removed by wavelet transforms.
In an image, all edges are not created equal. Some are more significant, and some are blurred and insignificant.
The edges of more significance are usually more important and more likely to be kept intact by wavelet transforms.
The insignificant edges are sometimes introduced by noise and preferably removed by wavelet transforms.

6. Characteristics of edges

7. noise An additive contamination of an image. Not predictable.
An image signal has a power spectrum that concentrates on the lower frequencies.
The noise has a bounded uniform distribution in its power spectrum.
Noise is broadly defined as an additive (or possibly multiplicative) contamination of an image.
It is reasonable to assume that the image signal has a power spectrum that concentrates on the lower frequencies, and the noise has a bounded uniform distribution in its power spectrum.

8. Noise reducing Smoothing Approximate the image with a smooth function.
Filtering with the Gaussian function.
Gaussian wavelet
Filtering the images with the Gaussian before edge detection.
If the Gaussian is used as the smoothing function, this class of wavelets is called a Gaussian wavelet.

9. steps Choose a suitable wavelet function.
Transform images into decomposition levels.
Filter out noise.
Edges are detected from the filtered detailed coefficients.
Choose a suitable wavelet function.
Use the function to transform images into decomposition levels.
The wavelet detailed coefficients containing significant energy at noise scales are filtered out.
* Finally edges are detected from the filtered detailed coefficients.

10. examples

11. examples

12. Thank you