R-snakes Lyubomir Zagorchev, Ardeshir Goshtasby, Martin Satter Speaker: HongxingShi 2007.11.01 Image...
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Transcript of R-snakes Lyubomir Zagorchev, Ardeshir Goshtasby, Martin Satter Speaker: HongxingShi 2007.11.01 Image...
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R-snakesLyubomir Zagorchev, Ardeshir Goshtasby,
Martin Satter
Speaker: HongxingShi
2007.11.01
Image and Vision Computing 25 (2007) 945–959
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Author
• Ardeshir Goshtasby· Postion
Professor of Department of Computer Science and
Engineering, Wright State University
· Education
B.E. Electronics Engineering, University of Tokyo
M.S. Computer Science, University of Kentucky
Ph.D. Computer Science, Michigan State University
· Journal Special Issues Edited
Pattern Recognition on Image Registration
Computer Vision and Image Understanding
Information Fusion on Image Fusion
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Introduction and background
• What is snake?· An energy minimizing countours
· Continuously deform to minimize its energy
· Slither while deforming, like snake
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Energy
• Contours
• Internal force · Constrain the smoothness of contours
• External force · Push the contours toward image features
( ) ( ( ), ( )), here [0,1]Q u x u y u u
int ( ( ))E Q u
ext ( ( ))E Q u
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Situations of curves’ definition
• DiscreteDefined by a sequence of points
• ContinuousDefined by a parametric curve, such as B-Splines ,
NURBS,RaG curves, and so on…
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Energy definition
• Total energy
• Internal energy
• External energy
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Compute
• From the calculas of variations, obtain:
• After discrezing….
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Result
• The equations can be written
where A is a pentadiagonal matrix.
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B-snakes
• Definition
• Energy function
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B-snakes
• Minimize the total energy
• Obtain
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Rational Gaussian curves
• Definition
• Control points
• Blending functions
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Rational Gaussian curves
• Where is the weight, and
• are standard deviation
• are nodes
• The blending function can be varied.
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RaG curves
• are (a)0.05 (b)0.1 (c)0.15
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Closed RaG curves
• Replaced the Gaussian function with
• are (a) 0.045 (b) 0.06 (c) 0.085
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RaG snakes
• As the situation of discrete snakes:
• Let
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RaG snakes
• Discrete, and obtain
• The extern energy( ( )) ( ( ), ( ))ext j x j y jE Q u f u f u
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Synthetical images
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Parameters in synthetic image
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CT images
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Parameters in CT images
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Parameters analyse
• Standard deviation and the number of nodes n – bigger , smoother shapes– larger n ,smoother shapes
• Experientially, we let
1/ 2n
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Standard deviations: (c)-(h)0.015, 0.025, 0.035, 0.045, 0.055, 0.065
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Standard deviations: (c)-(h)0.015, 0.025, 0.035, 0.045, 0.055, 0.065
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Standard deviations: (c)-(h)0.015, 0.025, 0.035, 0.045, 0.055, 0.065
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Standard deviations: (c)-(h)0.015, 0.025, 0.035, 0.045, 0.055, 0.065
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Coarse-to-fine segmention
• How to select the n, number of nodes?– First, with a small n and a large , find a co
arse boundary
– Then, increase n until the finest resolution image is segmented
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Conclusions
• Advantages over B-snakes– The stiffness can be varied to recover shapes co
ntaining smooth as well as detailed parts– The stiffness can be continuously varied to track a
boundary from coarse to fine
• Disadvantage– Complexity
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References
• [1] L Zagorchev, A Goshtasby, M Satter, R-snakes, Image and Vision Computing, 2007
• [2] M. Kass, A. Witkin and D. Terzopoulos, Snakes: Active contour models, International journal of computer vision. 321-331, 1988
• [3] A. Goshtasby, Geometric modelling using rational Gaussian curves and surfaces, Computer Aided Design 27 (5) (1995) 363–375
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Q&A