Skeletons In Images

Skeletons Presentation By Adam Metro CIS 467 – Image Processing

What are Skeletons? „ „ „ „

Morphological Operation Skeletons define the “Structure” of an object within an image. Can also be considered the “Wire Frame” of the object. Only works with Binary Images (to my knowledge), use Threshold function to convert.

What are Skeletons?

What are Skeletons Con’t. „

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The Skeleton S(A) of a set A can be expressed in terms of a series of erosions and openings. Each iteration k of erosions and openings creates a subset Sk(A)

Lets Refresh Your Memory „

Erosion „ „

Removal of pixels from edges objects within an image A. Uses a structuring element B to define custom erosion.

Lets Refresh Your Memory „

Opening „

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Opening smoothes the outer edges of an object within an image. Opening is defined as applying Erosion on an Image A with a Structuring Element B then applying Dilation on the resulting erosion.

Back to Skeletons „

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Formal Definition of a skeleton of an object within an image A: Formal Definition of a Subset k of a skeleton of an object within an image A with structuring element B:

K

S ( A) = U S k ( A)

S k ( A) = ( AΘkB) − ( AΘkB) • B k =0

Sk ( A) = ( AΘkB) − ( AΘkB) • B

In English Please… „ „ „ „

K equals the level of erosions performed on the image before opening is performed. S ( A) Each subset equals the result of the erosion minus the result of the opening. The final skeleton will be the union of the Kmax subsets found. Kmax equals the maximum number of S ( A)erosions before no more pixels exist in the object. k

k

Example

My Project „ „ „ „

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Take in binary image. Perform skeletonization on the image. Return and display the resulting image. Will use matlab functions imerosion() and imdialate() to perform the various erosions and openings. Will also use image subtraction function used in a previous homework assignment.

Questions?