Image Segmentation and Morphological Processing

Digital Image Processing in Life- ScienceAviad Baram 4-4-2012

Image In Attributesout

Image In Image out

Processing vs Analysis

Image processing:

Image analysis:

EnhancecontrastSmooth

RegionEdges“meaning”

Part I - Segmentation

Subdivide the image into constituent regions or objects (sets)

Based on properties of intensity values

▪ Discontinuity – changes (e.g. edges)

▪ Similarity – partition into similar regions

∑i=1

n

Ri=R Q (Ri )≠Q (R j )

Basic set operations

Union (Rr∪Rg)Complementary (Rrgc)Intersect (Rr∩Rg)Exclusive or (Rr⊕Rg)

Synonyms in set operations

Selection

ROI

Make Inverse

OR (Combine)

AND

XOR

Mathematical

Set (Ri)

Complementary (Ric)

Union (Ri∪Rj)

Intersect (Ri∩Rj)

Exclusivedisjunction (Ri⊕Rj)

BinaryMask

Inverse

OR

AND

XOR

Automatic approaches

■ Discontinuity – Edge based methods■ Classical gradient detectors (Sobel, Prewitt...)■ Canny edge detector

■ Similarity - threshold

Why?Human comprehension is far superior UnbiasedHigh throughput – ImageJ macros

Edge detection

Find the boundary of a region by identifying points, lines and edges

Tools:

▪ Second derivatives (Laplacian) operators

▪ Very sensitive to noise

▪ Double line detection (show example)

▪ First derivative

▪ Smoother

▪ Less sensitive

Derivatives noise

First derivative Second derivative

Derivatives noise

First derivative Second derivative

Derivatives noise

First derivative

Second derivative

Laplacian double edge

Prewitt and Sobel

Derivative Sobel

-1

-2 0

1

210

0

-1

Laplacian of Gaussian - LoG

Laplacian LoG

Canny edge detector

angle

norm

Nonmaxima suppression along gradient

Double threshold → use TH edge pixelsas seeds to connect TL edges

Edge detection Summary

1st derivative 2nd derivative Source

LoGSobel Canny

Similarity - Threshold

Partition Image into regions

▪ Global threshold

▪ Adaptive threshold

▪ Smaller image blocks

▪ Threshold for each blocks

▪ Interpolate results for each pixels

Global threshold - noise

g ( x,y )={a iff ( x,y )>T 2b ifT1<f ( x,y )≤T 2

c iff ( x,y )≤T 1}

T1

T2

abc

Global threshold - background

Automatic global threshold

Example 1 - mean:

Initial estimatefor T

Segment into G1 and G2

Compute meanfor G1 and G2

Compute new thresholdT=

12 ( ⟨G1⟩+ ⟨G2⟩ )

G1 G2

⟨G1⟩ ⟨G2⟩

Repeat until no significant change

Automatic global thresholdExample 2 – Otsu: minimize error in pixelassignment to groups

Global mean: mG

Global variance: σ2G

mean1 mean2

Between-class variance: σ2B

η=σ B

2

σG2

“goodness” of TH:

Calculate for allthresholds and choosethe max σ2

B

smoothing imagesimproves auto segmentation

Local thresholding

Calculate T from “subimage” histogram (e.g. edges...) ⇒ apply to full image

Variable thresholding

For each pixel, f(x,y), compute a threshold, Txy, based on mxy and σxy of neighborhood Sxy

Meanm - mean σ - variance

T xy=aσ xy+bm xy

T xy=aσ xy+bmG

g ( x,y )={1 iff ( x,y )>T xy0 iff ( x,y )≤T xy }

Part II - Morphology

Processing of region shapes

Structuring Elements

Erosion

A B⊖

Erosion

Remove connecting linesShrink regions

Dilation

A B⊕

Dilation

Bridge gapsGrow regions

Dilate⇔ErodeC

Open

A◦B

Smooth contourBreak narrow bridgesEliminate protrusions

nX Erode → n X dilate

Close

A•B

Smooth contourFuse narrow breaksEliminate small holesFills gaps

nX dilate → n X erode

Open⇔CloseC

Boundary extraction

Subtract the eroded image from original

Skeletons

Minimal set required for reconstruction

ImageJ built in function – erode to single pixel

Fill holes

Hole – background region surrounded by a foreground connected border

Hit or Miss

A B=(A B⊛ ⊖1)∩(AC B⊖

2)

Shape detection

Probe for object

Probe for background

Watershed

ImageJ built inSegmentationGray level

ImageJ Set Measurement...

Gray level morphology

Erode DilateOpen Close

Examples

Yael Mutsafi Ayelet Tetelboim