4/6/2009

Computational Geometry of Contour Extraction

Contour extraction Image

Contours

Pedro Tejada Advisor: Dr. Minghui Jiang

Utah State University Department of Computer Science April, 2009

Contour extraction Image

Contours

Computational Geometry Convex Hull

Voronoi Diagram

Metamorphosis of the Cube http://erikdemaine.org/metamorphosis/

Algorithm

Algorithm

General stages

Geometric algorithms

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4/6/2009

Pre-processing

Clustering

• Extract “edge” pixels from digital image

• Clean up – Reduce number of points – Prevent multiple parallel lines for a single contour

– Using Sobel edge detector – Based on intensity difference with neighbor pixels

• Merge close points with similar angle

• Convert pixels to “directed” points

– “Parallel” (blue) but not “collinear” (red) – Average out coordinates and angles

– Each pixel has an angle associated with it (direction of change)

• Continue until minimum distance is at least some value.

Linking

Simplification

• Connect points based on distance and angle

• Simplified path: subset of original path, including extreme points • Optimize ratio of original path length to simplified path length • Keep as many points as possible without letting the distance from simplified paths to original paths be too large

– Closer and similar angle is better

• Start with “good” pair of points and extend in both directions • Repeat until there are no more good pairs

Example Clustered points

Simplified contours

Results: binary images (avg. error: 0.0085 / std: 0.0063)

Original image

Extracted contours

Image size: 256 x 256

78 points / 4 paths (Error: 0.0134)

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Results: real images

Results: real images

Original image

Extracted contours

Original image

Extracted contours

Image size: 512 x 512

7500 points -> 485 points / 123 paths

Image size: 512 x 512

57017 points ->5885 points / 1699 paths

Applications • Image segmentation • Object recognition and classification • Computer vision • Image compression • Maps • Animation Original video: Metamorphosis of the Cube http://erikdemaine.org/metamorphosis/ Used with permission

3

Image contour extraction

Apr 6, 2009 - Based on intensity difference with neighbor pixels. • Convert pixels to “directed” points. – Each pixel has an angle associated with it (direction.

547KB Sizes 3 Downloads 307 Views

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