Multi Scale Wavelet Based Edge Detection

8/8/2019 Multi Scale Wavelet Based Edge Detection

1/29

Multiscale wavelet based

edge detection

Presented by

Venugopala Rao ASGuide

Mrs Shubha Bhat


2/29

Contents What Edge?

How to identify edge?

Different methods to find edge

Limitations of existing methods

Introduction to wavelets

Multiscale method

Results

Scope for future work.


3/29

What is edge detection?

Edge is a set of connected pixels that lie on the boundary

between two regions

A process of detecting such edge points is edge detection.

The result will be conversion of 2D image to set of curves.


4/29

Identifying edges

Edges are identified by sudden change in color intensity.

Change is measured by derivative in 1D

Biggest change, derivative has maximum magnitude

Or 2nd derivative is zero.


5/29

Edge Detection

Edge detectionusing derivatives

cont.


6/29

Image gradient The gradient of an image:

The gradient points in the direction of most rapid change inintensity

The gradient direction is given by:

how does this relate to the direction of the edge?

The edge strength is given by the gradient magnitude


7/29

The discrete gradient

How can we differentiate a digitalimage f[x,y]?

: take discrete derivative (finite difference)

How would you implement this as a cross-correlation?


8/29

Different methods to find edges

Based on the mask used to find gradient there aredifferent methods for edge detection

Sobel edge detection

Prewitt Edge detection

LOG Edge detection

Roberts

Canny edge detection etc.

Each of these have their own masks Gx and Gy forcomputing gradients.

Then a threshold is defined. If the gradient is above

threshold that is retained else it is made zero.


9/29

Limitations of existing methods

These methods are well suited for the clear images. In the presence of noise the performance degrades.

As noise intensity increases the methods fail to eliminate

noise

Even noise will be seen in the edge detected image.

To overcome this, wavelet transform can be used as the

edge detecting tool.


10/29

Wavelet transform

Limitations of F.T. Complex exponentials stretch out to infinity in time

They analyze the signal globally, not locally

Hence, FT can only tell what frequencies exist in the entire

signal, but cannot tell, at what time instances these frequenciesoccur

In order to obtain time localization of the spectral components,

the signal need to be analyzed locally, this requires window

Wavelet transform can be one solution for this problem!!


11/29

Wavelet transform Overcomes the preset resolution problem of the FT by

using a variable length window Analysis windows of different lengths are used for

different frequencies:

Analysis of high frequencies Use narrower

windows for better time resolution Analysis of low frequencies Use wider

windows for better frequency resolution This works well, if the signal to be analyzed mainly

consists of slowly varying characteristics with occasionalshort high frequency bursts.

The function used to window the signal is called thewavelet


12/29

Wavelet Transforms

wavelet transforms are based on small waves, calledwavelets, of limited duration.

The strength of W.T. lies in the process called Multi-

resolution analysis (MRA)

In this the image is represented in more than oneresolution or scale.

Features that might go undetected at one resolution

may be easy to spot in another resolution.


13/29

Image Pyramids


14/29

Image Pyramids

At each level we have an approximation image and a

residual image.

The original image (which is at the base of pyramid) and

its P approximation form the approximation pyramid.

The residual outputs form the residual pyramid. Approximation and residual pyramids are computed in

an iterative fashion.

A (P+1) level pyramid is build by executing the

operations in the block diagram P times.


15/29

Image pyramids

During the first iteration, the original 2Jx2J image is

applied as the input image.

This produces the level J-1 approximate and level J

prediction residual results

For iterations j=J-1, J-2, , J-p+1, the previous

iterations level j-1 approximation output is used as

the input


16/29

Each iteration is composed of three sequential steps:

Compute a reduced resolution approximation of the input

image. This is done by filtering the input and

downsampling (subsampling) the filtered result by a

factor of 2. Filter: neighborhood averaging, Gaussian filtering

The quality of the generated approximation is a function

of the filter selected

Image pyramids


17/29

2. Upsample output of the previous step by a factor of 2and filter the result. This creates a prediction image with

the same resolution as the input.

3. Compute the difference between the prediction of step 2and the input to step 1. This difference can be later used

to reconstruct progressively the original image.

Image pyramids


18/29

Three Steps:

Decompose the image into wavelet domain

Alter the wavelet coefficients, according to

your applications such as denoising,

compression, edge detection, etc.

Reconstruct the image with the altered

wavelet coefficients.

Image processing with wavelets transforms


19/29

The wavelet transform

The wavelet coefficients are named as approximation,vertical, horizontal and diagonal coefficients.

Normally Diagonal coefficient is high frequency

component and next step of wavelet decomposition uses

only approximation coefficients.


20/29

Wavelet transform for edge detection

Scale of the wavelet transform controls the edges to beshown in the output.

Edges of lower significance will get disappeared as scale

increases.

Wavelet filter with small scale- gives precise location of

edge but fail to eliminate noise.

Wavelet filter with large scale- removes noise but

uncertainty about edge locations Wavelet coefficients are used to measure Lipschitz

regularity ( mathematical model which helps to detect

edges)


21/29

At higher scale, wavelet coefficients tend to increase when

Lipschitz regularity is positive.

At lower scale, wavelet coefficients tend to decrease when

Lipschitz regularity is negative.

locations with lower Lipschitz regularities are more likely to be

details and noise and hence can be neglected. We use a larger-scale wavelet at positions where the wavelet

transform decreases rapidly as scale increases to remove the

effect of noise

Also we use a smaller-scale wavelet at positions where thewavelet transform decreases slowly across scale to preserve the

precise position of the edges.

Wavelet transform for edge detection


22/29

Filter implementation of DWT

Approx. coefficients at any level j can be obtained by

filtering coefficient. at level j-1 (next finer level) by

h[n] and downsampling by 2

Detail coefficients at any level j can be obtained by

filtering approximation coefficients at level j-1 (next

finer level) by g[n] and downsampling by 2


23/29

Results and conclusion

For a noise free image the proposed method gives the

results as good as canny edge detector. But the performance of proposed method is found better

in the presence of noise.

As scale is increased the effect of noise will be reduced

but at the same time higher scales will result in someedges being undetected.

So there must be a trade off between noise elimination

and correct edge detection for the better result.


24/29

Scope for the future work

The existing system can perform significantly well for a

certain level of noise. But if the noise level is more then

this method fails to eliminate the noise and more

number of false edges will be detected. This can be addressed at the beginning itself and

filtering can be made use of before applying edge

detection which can eliminate the noise level

significantly.


25/29

Result ImagesComparison of edge detection with Gaussian Noise


26/29

Comparison of edge detection with Poisson Noise


27/29

Comparison of edge detection with Salt & pepper Noise


28/29

Comparison of edge detection with Speckle noise


29/29

Thank you

Multi Scale Wavelet Based Edge Detection

Documents

Transcript of Multi Scale Wavelet Based Edge Detection