14-Feature Extraction 2

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CSC412-Image Processing

Bishops University

Department of Computer Science

Fall 2007

Lecture 14:Lecture 14: Feature_Extraction_2Feature_Extraction_2

M. ALLILI


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11/19/2007 M. ALLILI, Image Processing Slide 2

Todays Agenda

Detection of Discontinuities

Point Detection

Line Detection

Edge Detection

Gradient

Laplacian


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Detection of Discontinuities

Detect the three basic types of gray

level discontinuities in a digital image

points , lines , edges

The common way is to run a mask

through the image


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Point Detection


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Point Detection: Examples


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Line Detection


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Line Detection: Example


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Edge Detection

Isolated points and thin lines do not occur frequently in most practical

applications.

For image segmentation, we are mostly interested in detecting the boundary

between two regions with relatively distinct grey-level properties.

We assume that the regions in question are sufficiently homogeneous so that the

transition between two regions can be determined on the basis of grey-level

discontinuities alone.

An edge in an image may be defined as a discontinuity or abrupt change in grey

level.


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Edge Detection

In practice the edges in an image are blurred. So instead of being represented by

an ideal step function, they are represented by a curve with a ramp-like profile.

The slope of the ramp is inversely proportional to the degree of blurring in theedge.


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Edge Detection

The ideal situations do not frequently occur in practice.

Also, in two dimensions edges may occur at any orientation.

Edges may not be represented by perfect discontinuities.

Therefore, the task of edge detection is much more difficult than what it looks

like.

A useful mathematical tool for developing edge detectors is the first and secondderivative operators.

The magnitude of the first derivative can detect the presence of an edge.

Similarly, the sign of the second derivative can be used to determine whether an

edge pixel lies in the dark or light side of an edge.


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Edge Detection


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Edge Detection

The second derivative produces

two values for every edge pixel in an image

An imaginary line between the extreme positive and negative values of the

second derivative would cross zero near the midpoint of the edge.

This property is useful to find the centers of thick edges.

In practical situations, edges are not free of noise.

The first derivative and second derivative operators are very sensitive to noise.

Thus, to qualify as an edge point, the transition in grey level associated with that

point has to be significantly stronger than the background at that point.


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Edge Detection


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Edge Detection

We define a point in an image as being an edge point if the magnitude of the

gradient of the image at that point isgreater than a specified threshold.

A set of such points that are connected according to a predefined criterion of

connectedness is by definition an edgeor an edge segment.

An alternate definition of an edge point is simply to define the edge points in a

given image as the zero crossings of its second derivative.

The definition of an edge segment is obtained in a similar way as before.


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Edge Detection

The techniques of computation of magnitude of gradients and Laplacian using

convolution masks are discussed in the image sharpening section.

One can design special masks to compute directional derivatives instead of only using

derivatives in x and y directions.

Because derivatives enhance noise, the direct operators may not give good results if

the input image is very noisy.

One way to combat the effect of noise is by applying a smoothing mask.

This becomes very important to use the derivatives of Gaussian as masks to compute

the gradient and the Laplacian.


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Edge Detection: Example


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Edge Detection


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Edge Detection


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Edge Detection: Example


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Edge Detection


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Edge Detection


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Edge Detection


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Edge Linking

Edge detection algorithms are followed by linking procedures to assemble edge

pixels into meaningful edges.

Basic approaches Local Processing

Global Processing via the Hough Transform

Global Processing via Graph-Theoretic Techniques

Well study local processing:

analyze the characteristics of pixels in a small neighborhood (say, 3x3, 5x5)

about every edge pixels (x, y) in an image.

all points that are similar according to a set of predefined criteria are linked,

forming an edge of pixels that share those criteria.


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Edge Linking

Criteria:

the strength of the response of the gradient operator used to produce the

edge pixel

an edge pixel with coordinates (x0,y0) in a predefined neighborhood of

(x, y) is similar in magnitude to the pixel at (x, y) if

where E is a non-negative threshold.


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Edge Linking

Criteria:

the direction of the gradient vector

an edge pixel with coordinates (x0,y0) in a predefined neighborhood of

(x, y) is similar in angle to the pixel at (x, y) if

where A is a non-negative angle threshold.


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Edge Linking


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Edge Linking

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