edge and boundary detection

8/9/2019 Edge and Boundary Detection

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EDGE /BOUNDARY

DETECTIONSobelLaplacian

Canny

pB


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Edge detection

Goal: Identify sudden changes

(discontinuities) in an image

Intuitively, most semantic and

shape information from the imagecan be encoded in the edges

More compact than pixels

Ideal: artists line drawing (but artist

is also using object-level knowledge


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Why do we care about edges?

Extract information, recognize objects

Recover geometry and viewpoint


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Origin of edges

Edges are caused by a variety of factors


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Closeup of edges


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Closeup of edges


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Closeup of edges


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An edge is a place of rapid change in the image intensity function

Characterization of edges


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Consider a single row or column of the image

Plotting intensity as a function of position gives a signal

Effects of noise


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Difference filters respond strongly to noise

Image noise results in pixels that look very different from their neighbors

Generally, the larger the noise the stronger the response

What can we do about it?

Effects of noise


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Solution: smooth first

Effects of noise


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Tradeoff between smoothing and

localization

Smoothed derivative removes noise, but blurs edge. Also finds edges at

different scales.


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Designing an edge detector

Criteria for a good edge detector:

Good detection:

the optimal detector should find all real edges, ignoring noise or other artifacts

Good localization:

the edges detected must be as close as possible to the true edges

the detector must return one point only for each true edge point

Cues of edge detection

Differences in color, intensity, or texture across the boundaryContinuity and closure

High-level knowledge

Source: L. Fei-Fei


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Edge detection

An edge is the boundary between two regions with relatively distinct gray-

level properties.

Assumption: The regions in question are sufficiently homogeneous so that

the transition between two regions can be determined on the basis of gray-level discontinuities alone.

The idea underlying most edge-detection techniques is the computation of a

local derivative operator.


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Edge detection

Edge detection by derivative operators:

(a) light strips on a dark background; (b)dark strip on a light background. Note that

the second derivative has a zero crossing

at the location of each edge.


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Profile of gray-level at the edge is modelled as a smooth change of gray-level.

First derivative of the gray level profile is positive at the leading edge of a

transition, negative at the edge, and zero in areas of constant gray level.

The second derivative is positive for that part of the transition associated withthe dark side of the edge, and negative for that part of the transition

associated with the light side of the edge.

Hence, the second derivative can be used to determine whether an edge pixel

lies on the dark or light side of an edge.

Edge detection


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The gradient of an image f(x, y) at location (x,y) is given by :

Gradient Operators

The gradient vector points in the direction of maximum rate of change.

In edge detection, an important quantity is the magnitude of , which is referredto simply as gradient, where


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Gradient Operators

Gradient is commonly approximated by the absolute values:

Where angle is measured with respect to thex-axis.


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Derivatives may be implemented in digital form in several ways.

Sobel operators have the advantage of providing both a differencing and a

smoothing effect.

As differencing or dervatives in digital image processing enhance noise, thesmoothing effect of Sobel operators is an attractive features.

Sobel


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Sobel


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Sobel

Derivatives based on Sobel masks are

Computation of the gradient at the central location of the mask then uses eqn

(4) & (5) to give one value of the gradient.

The mask in then moved to the next location, and the process is repeated. We

will obtain a gradient image which is of the same size as the original image.

Mask operations on the image border are implemented by using the

appropriate partial neighbours.


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Sobel


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Laplacian

Laplacian of a 2-D function f(x,y) is

The mask used in this case must have a positive central pixel, and the outer

pixels must be negative. In addition, the sum of the coefficients must be zero.


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Laplacian responds to transition in intensity, but is seldom used in practice for edge

detection, because

1. As a second order derivative, it is unacceptably sensitive to noise.

2. It produces double edges (See previous Fig).

3. It is unable to detect edge direction.

Laplacian usually play a secondary role of detector for establishing whether a pixel

is on the dark or light side of an edge.

A more general use of Laplacian is in the finding the location of edges using its

zero crossing property


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Laplacian

The concept is based on convolving an image with the Laplacian of a 2-DGaussian function of the form.


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Laplacian

The average value of the Laplacian operator h^2 is zero, so as the image

obtained by convolving with it.

This operator will blur the image with the degree of blurring being

proportional to . It can be used for noise-reduction, but its usefulness lies in

its zero-crossing.


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Fig. 9 shows an example of edge detection with the ^2h operator, with = 4.

Laplacian


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Some Remarks on Gradient Operations in Edge Detection

1. They tend to work well in cases involving images with sharp intensity

transitions and relatively low noise.

2. *Zero-crossings offer an alternative in cases when edges are blurry or when a

high noise content is present.

*They offer reliable edge location, and the smoothing properties of ^2h reduce

the effect of noise.

*Computational complex & intensive.


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Canny Edge detector

This is probably the most widely used edge detector in computer vision

Theoretical model: step-edges corrupted by additive Gaussian noise

Canny has shown that the first derivative of the Gaussian closelyapproximates the operator that optimizes the product of signal-to-noise ratio

and localization

J. Canny, A Com putat ional Appro ach To Edge Detect ion, IEEE Trans. Pattern Analysis and

Machine Intelligence, 8:679-714, 1986.


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Canny Edge detector


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Canny Edge detector


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Canny Edge detector


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Canny Edge detector


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Canny Edge detector


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Canny Edge detector


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Canny Edge detector


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Hysteresis thresholding

Threshold at low/high levels to get weak/strong edge pixels

Do connected components, starting from strong edge pixels

Canny Edge detector


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Canny Edge detector


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Canny Edge detector

Final Canny Edges


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1. Filter image with x, y derivatives of Gaussian

2. Find magnitude and orientation of gradient

3. Non-maximum suppression:

Thin multi-pixel wide ridges down to single pixel width

4. Thresholding and linking (hysteresis):

Define two thresholds: low and high

Use the high threshold to start edge curves and the low threshold to continue

them

MATLAB: edge(image, canny)

Source: D. Lowe, L. Fei-Fei

Canny Edge detector


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Effect of (Gaussian kernel spread/size)

The choice of depends on desired behavior

large detects large scale edges

small detects fine features


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Where do humans see boundaries?


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pB Boundary detector


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edge and boundary detection

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