Geometric Computing Notes

Mark Jajeh

September 14, 2015

1 Lecture 2: Shape Analysis

1.1 Shape Analysis

How, as a computer do you define shapes?There are many questions about shape you can ask...Medial Axes(MA) Simple and elegant mathematical definition: Given any shape, the medial axes is made up of allthe points that have 2 or more nearest neighbors on the boundary. So there is an equal distance between 2 points onthe boundary to the interior point, and these 2 points are the closest boundary points ( could be more than 2)... TheMA is not a closed set it is open.Properties

• ThinIn N dimensions, the MA is at most N-1 dimensions

• Preserve objects shapebuild a circle for every point on medial axes with radius as distance to boundary. Take union of all circles toget shape back

• Preserve objects topologyDoes not break connectivity ( topology).

• Not stable under boundary pertubation.MA gets complicated from addition of ’bumps’.

Grassfire analogy

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