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A MATLAB Tour ofBinary Image Analysis

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Image Topology: Connectivitya and ! are connected if t"ere e#ists a $at" from a to !

%o& do &e define t"e $at" for discrete images'

4(neig"!ors)(neig"!ors

De$ending on t"e selection of 4(neig"!ors or )(neig"!ors*

&e mig"t "a+e different connecti+ity result

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Example

$

-

$ . - no matter

4(neig"!ors or )(neig"!ors

$

-

$ . - only &"en )(neig"!ors

is considered

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Component Labeling

If 4(neig"!ors*t"ree connected

com$onents

If )(neig"!ors*

t&o connected

com$onents

original

!inaryimage

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MATLAB Function BWLABEL /"el$ !&la!el B0LABEL La!el connected com$onents in !inary image L 2 B0LABEL3B0* returns a matri# L* of t"e same sie as B0* containing la!els for t"e connected com$onents in B0 can "a+e a +alue of eit"er 4 or )* &"ere 4 s$ecifies 4(connected o!7ects and ) s$ecifies )(connected o!7ects8 if t"e argument is omitted* it defaults to ) T"e elements of L are integer +alues greater t"an or e-ual to 9 T"e $i#els la!eled 9 are t"e !acground T"e $i#els la!eled 1 mae u$ one o!7ect* t"e $i#els la!eled mae u$ a second o!7ect* and so on

;L*

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Checkboar Image

4(neig"!ors

)(neig"!ors#

Ims"o&3la!elrg!3!&la!el3#*4

Ims"o&3la!elrg!3!&la!el3#*)

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Euler !umber

Euler um!er E2num!er of connected com$onents @ num!er of "oles

E2(,E29

E2(1

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Chain Coe"

4(directional c"ain code:

99,,,,,,,111191191

)(directional c"ain code:

9?666655,,11

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MATLAB Implementation

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!ormali#ation $trategy

,,9911

,,9911

,9911,

9911,,

911,,911,,99

1,,991

,,9911

,,9911

>ortro&s

9911,,

911,,9

11,,99

1,,991,,9911

,,9911

,,9911

,9911,

9911,,

irst ro& gi+es t"e

normalied c"ain code

MATLAB function: sortro&s

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$hape !umber"% !ormali#e

&i''erential Chain Coe"

Differential code:

d2c(c(13mod 4

,,9911

191911,1

,,9191

1911,119

91911,11 91911,11

differentiate

normalie

differentiate

normalie

MATLAB function: mod

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$keleton Fining via &i"tance

Tran"'orm

#

!&dist3.#*Ccity!locC8 !&dist3#*Ccity!locC8

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MATLAB Implementationfunction sk=skeleton_finding(x)

% calculate distance transform

dt=bwdist(~x,'cityblock');

% find the local maximum

n=! ";#" !;! #";" !$;

sk=dt!;for i="&

sk=sk(dt=circshift(dt,n(i,&)));

end