IP seminar for Fall semester in 2004
IMAGE SEGMENTATION Xiaoheng Yang Nakajima Lab, Titech October 29, 2004 CONTENTS
Problem Preview
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Detection of Discontinuities 1.1 Point Detection 1.2 Line Detection 1.3 Edge Detection
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Edge Linking and Boundary Detection 2.1 Local Processing 2.2 Global Processing Processing via Hough Trans form 2.3 Global Processing via Graph-Theoretic Techniques
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Thresholding 3.1 3.2 3.3 3.4 3.5 3.6
Foundation The Role of Illumination Basic Global Thresholding Basic Adaptive Threshloding Optimal Global and Adaptive Thresholding Use of Boundary Characteristics for Histogram Improvement and Local Thresholding 3.7 Thresholds Based on Several Variables 4
Segmentation subdivides an image into it’s constitute regions or objects. The level to which the the su bdivision is carried depends on the problem being solved. That is, segmentation should stop when the objects of interests in an application have been isolated.
Image segmentation algorithms generally are based on one of two basic properties of intensity values: discontinuity and similarity.
1 Detection of Discontinuities The most common way to look for discontinuities is to run a mask through the image. n
R = ∑ wi zi i
Region-Based Segmentation 4.1 Basic Formulation 4.2 Region Growing 4.3 Region Splitting and Merging
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5.1 5.2 5.3 5.4
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Figure.1
Segmentation by Morphological Watersheds Basic Concepts Dam Construction Watershed Segmentation Algorithm The Use of Markers
1.1 Point Detection
| R |≥ T 1.2 Line Detection
The Use of Motion In Segmentaion 6.1 Spatial Techniques 6.2 Frequency Domain Techniques
Summary References and Further Reading
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IP seminar for Fall semester in 2004 1.3 Edge Detection
2 Edge Linking and Boundary Detection
A point is is being an edge point if its two --dimensi --dimensional onal first-order derivative is greater than a specified threshold. A set of such points that are connected according to a predefined criterion of connectedness edge . is by definition an edge.
Edge detection algorithms typically are followed by linking procedures to assemble edge pixels into meaningful edges. (for example, breaks caused by noise.) 2.1 Local Processing
In practice, optics, sampling, other image acquisition imperfections yield edges that are blurred. The slope of the ramp is inversely proportional to the degree of blurring blurring in in the edge. edge. The The “ thicknes thickness” s” of edge edge is determined by the length of the ramp. ramp. First-order derivatives of a digital image are based on various approximations of the 2-D gradient. Second-order derivative is defined as digital approximations to the Laplacian of a 2-D function. Conclusion : The first derivative can be used to detect the presence of an edge at a point in an image. Similarly, the sign of the second derivative can be used to determine whether an edge pixel lies on the zero-crossing ). dark or light side of an edge ( zero-crossing
Criteria: the strength of the resp onse of the gradient operator / the direction of the gradient vector A point in the predefined neighborhood is linked to the pixel if both magnitude and direction criteria are satisfied. 2.2 Global Processing via Hough Transform
Computational attractiveness Approach based on the Hough transform is as follow: a. Compute the gradient of an image and threshold it to obtain a binary image. b. Specify subdivisions in the ρθ − plane c. d.
Problem: Derivatives are sensitive to noise.
Examine the counts of the accumulator cells for high pixel concentrations. Examine the relationship between pixels in a chosen cell.
2.3 Global Processing via Graph-Theoretic Techniques
This representation provides a rugged approach that performs well in the presence of noise. Some terms used here Graph G = ( N , U )
arc for each pair ( ni , n j ) successor / parent
level
Figure.4 Figure.3
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IP seminar for Fall semester in 2004
Figure.6. 3.5 Optimal Global and Adaptive Thresholding
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Thresholding 3.1 Foundation
T = T [ x, y, p( x, y ), f ( x, y)] Classification for threshold: local, global, dynamic or adaptive 3.2 The Role of Illumination The image resulting from poor illumination could be quite difficult to segment.
A method for estimating thresholds that produce the minimum average segmentation error PDF PDF ( probability density function ) 3.6 Use of Boundary Characteristics for Histogram Improvement and Local Thresholding
The chanc es of sel ecting a good thre shold are enhanced considerably considerably if the histogram peaks are tall, narrow, symmetric, and separated by deep valleys. One approach for improving the shape of histogram is to consider only those pixels that lie on or near the edges between objects and the background.
3.3 Basic Global Thresholding
The success of this method depends entirely on how well the histogram can be partitioned. Heuristic approach based on visual inspection of the histogram. 3.4 Basic Adaptive Threshloding
Issues: how to subdivide the image and how to estimate the threshold for each resulting subimage
Figure.7
IP seminar for Fall semester in 2004 3.7 Thresholds Based on Several Variables Multispectral thresholding The concept of thresholding now becomes one of finding clusters of points in multi-dimension space.
(In general, segmentation problems requiring multiple thresholds are best solved using region growing methods. ) 4
Region-Based Segmentation
The objective of segmentation is to partition an image into regions. 4.1 Basic Formulation 4.2 R egion Growing Region growing is a procedure that groups pixels or subregions into larger regions based on predefined criteria. Seed region 4.3 Region Splitting and Merging
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Segmentation by Morphological Watersheds
Segmentation by watersheds embodies many of the concepts of the other three approaches and, as such, often produces more stable segmentation results, including continuous segmentation boundaries. 5.1 Basic Concepts
The concept of watersheds is based on visualizing an image in three dimensions: two spatial coordinates versus gray levels.
Figure.9 5.2 Dam Construction
The simplest way to construct dams separating sets of binary points is to use morphological dilation.
IP seminar for Fall semester in 2004 A marker is a connected component belonging to an image.
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Figure.13 Figure.10
6 The Use of Motion In Segmentaion 5.3 Watershed Segmentation Algorithm
6.1 Spatial Techniques
Figure.14 6.2 Frequency Domain Techniques
Referen ce: Digital Image Processing, Rafael C. Gonzalez & Richard E. Woods, second edition 2002, Prentice Hall Figure.11 5.4 The Use of Markers Problem: oversegmentation
