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Binary MorphologyConnected Component LabelingRegion Props

Lecture 1317-10-02

Binary Image Morphology

InputsBinary Image BStructuring Element STypically, S is also a binary image of small size

OutputS is applied to B

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Structuring Elements

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

BOX(3,5)

1 1 1

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

1 1 1

DISK(5)

1 1 1

1 1

1 1

1 1

1 1 1

RING(5)

1 1

1 1

1 1 1 1

1 1 1 1

1 1

1 1

1 1

1 1

1 1

1

1

1

1 1

1

1

1

1

1

1

1

Dilation Example

1 1 1 1

1 1

1 1

1 1 1

1 1

1 1

1 1

1 1

1 1 1 1

1 1

1

1

1

1 1

1 1

1 1

1

1

1

1 1

1 1

1 1

1 1 1 1

1 1 1

1 1 1

1 1 1

1 1

1 1

1 1

1 1

1 1 1 1

1 1

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Example –Dilation by BOX(3,3)

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

1 1 1 1

1 1 1 1

1 1

1 1

1 1

1 1

1 1

1 1 1 1 1 1

1 1 1 1 1 1

1 1 1 1

1

1

1

1

1

1

1

1 1 1 1

1 1

1 1

1 1 1

1 1

1 1

1 1

1 1

1 1 1 1

1 1

Real Example

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Erosion Example

1 1 1 1

1 1

1 1

1 1 1

1 1

1 1

1 1

1 1

1 1 1 1

1 1

1

1

1

1 1

1 1

1 1

1

1

1

1 1

1 1

1 1

1 1 1 1

1

1

1

1 1

1 1

1 1

1 1

1 1 1 1

1 1

Example –Erosion by BOX(3,3)

1 1 1 1

1 1

1 1

1 1 1

1 1

1 1

1 1

1 1

1 1 1 1

1 1

1

1

1

1

1

1

5

Real Example

Closing / Opening Operations

Closing: B ● S = (B ⊕ S) ө SOpening: B ◦ S = (B ө S) ⊕ SEffect?

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Closing (Dilation followed by Erosion)

1 1 1 1

1 1

1 1

1 1 1

1 1

1 1

1 1

1 1

1 1 1 1

1 1

1 1 1 1

1 1 1

1 1 1

1 1 1

1 1

1 1

1 1

1 1

1 1 1 1 1

1 1

Opening(Erosion followed by Dilation)

1 1 1 1

1 1

1 1

1 1 1

1 1

1 1

1 1

1 1

1 1 1 1

1 1

1 1

1 1

1 1

1 1

1 1

1 1

1 1

1 1

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Opening/Closing Example

Original Closing Opening

Logical Subtraction

A – B = A ∩ (NOT B)

A

B

A - B

B - A

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Application Example

Problem: To find defects in manufactured gear heads for watches

Threshold - 140

Detection of Holes

RL RS RL- RS

Structuring Element

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Covering of Holes

Dilate

Covering of Holes

OR

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OPEN

Er + Di

A = Dilate to make same size as diskB = Dilate a little to cover teethB-A

AND

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Dilation Subtraction, Dilation, OR

Connected Components

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Connected Components

Definition: Connected Pixels A pixel [r,c] is connected to pixel [r’,c’] if there

exists a sequence[r,c]=[r0,c0], [r1,c1], …, [rn,cn] = [r’,c’]in which B[ri,ci]=1 and [ri, ci] and [ri-1, ci-1] are neighbors for 1 ≤ i ≤ n

Definition: Connected ComponentA connected component is a set of pixels C such

that every pair of pixels in C is connected.

Connected Component Labeling

Find all connected components, give unique label to eachRecursive Code

For each unlabeled ON pixel, assign it a unique labelFollow neighbors (4 connected or 8 connected) recursively, and assign each unlabeled ON pixel assign it the same label

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Connected Component Labeling

Non recursive algorithms, parallel algorithms also existIdea for Non-recursive code:

Process only two rows at a timeIf connected pixels are found, assign them same labelsIn the end, find equivalences

Region Properties

AreaCentroidBounding BoxPerimeter (connectivity definitions)Perimeter LengthCircularity Definitions2nd Moments, relation with elliptical shapes