xla-lqn-tuan 9.pdf

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    X l nh s v video s nng caoTun9: Phn onnh

    TS. L QucNgc

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    Ni dung

    10.1. Pht biubi ton10.2. Region growing

    10.3. K-means

    10.4. HAC (Hierarchical Agglomerative Clustering)

    2TS. L Quc Ngc

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    10.1. Pht biu bi ton

    Giscnphn onnh thnh N vngCnxc nhlutphn on sao cho

    3TS. L Quc Ngc

    NRRR ,...,, 21I

    )(RP

    jiFalseRRPNiTrueRP

    jiRR

    RI

    ji

    i

    ji

    N

    ii

    ,)(,...,2,1,)(

    ,

    1

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    10.2. Region growing

    Nguyn lGeometrical proximity + homogeneity -> connected

    image regions.

    4TS. L Quc Ngc

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    10.2. Region growing

    Phngphp- Khinguntmtsimmm, lan tankhi phton bnh.

    -hinthcviclan tacnxc nh.immm

    . Lutlan tavvtr

    . Lutkimtra tnh thunnhtcavng sau mibclan ta.

    5TS. L Quc Ngc

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    10.2. Region growing

    Phngphp. Lutlan tavvtr

    Lan tatheo ln cn8.

    7TS. L Quc Ngc

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    10.2. Region growing

    Phngphp. Lutkim tra tnh thunnhtcavng sau mibclan ta.

    Tibcthk, vimivng

    Kimtra cc pixels chacphn lptrong ln cn

    8 camipixel thucbin cavng.

    Nu th ktnp

    pixel vo vng

    8TS. L Quc Ngc

    NiR ki ,...,2,1,)(

    TrueyxbRP kiki )}),({( )()( ),()( yxb ki

    )(kiR

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    10.2. Region growing

    Phngphp

    . Lutkim tra tnh thunnhtcavng sau mibclan ta.

    10TS. L Quc Ngc

    2/1

    )()()(

    )(2)()()1(

    )()()()1(

    ))(),())(1)(/()((

    )()())[1)(/(1()(

    )]()(),())[1)(/(1()(

    ki

    ki

    ki

    ki

    ki

    kik

    i

    ki

    ki

    ki

    ki

    RmyxfRNRN

    RRNRNR

    RmRNyxfRNRm

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    10.2. Region growing

    Phngphp

    . Lutmerge vng.

    11TS. L Quc Ngc

    )(|)()(|

    )(|)()(|

    )1()1()1(

    )1()1()1(

    ''

    '

    k

    i

    k

    i

    ki

    ki

    k

    i

    ki

    RkRmRm

    RkRmRm

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    10.3. K-means

    Nguyn lhomogeneity -> image regions.

    12TS. L Quc Ngc

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    Bahadir K. Gunturk EE 7730 - Image Analysis I 13

    10.3. K-means

    1. Partition the data points into K clusters randomly. Find thecentroids of each cluster.

    2. For each data point:

    Calculate the distance from the data point to each cluster.

    Assign the data point to the closest cluster.

    3. Recompute the centroid of each cluster.

    4. Repeat steps 2 and 3 until there is no further change in the

    assignment of data points (or in the centroids).

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    14

    10.3. K-means

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    15

    10.3. K-means

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    16

    10.3. K-means

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    17

    10.3. K-means

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    18

    10.3. K-means

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    Bahadir K. Gunturk EE 7730 - Image Analysis I 19

    10.3. K-means

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    Bahadir K. Gunturk EE 7730 - Image Analysis I 20

    10.3. K-means

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    21

    10.3. K-means

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    22

    10.3. K-means

    RGB vector

    xj

    i

    2

    jelements of i'th cluster

    iclusters

    K-means clustering minimizes

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    Bahadir

    K.Gunturk

    EE 7730 - Image Analysis I 23

    10.3. K-means

    Example

    Original K=5 K=11

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    10.3. K-means

    Phngphp

    24TS. L Quc Ngc

    changeslongerno

    membershipclusterortlysignificanchangenotdoesUntil

    ||

    :functionerrorheComputer t

    |C|/thatso,Cincurrently

    samplesallofcentroidthetoprototypethee Updat

    dok},{1,...,jwhere,Cclustereach For

    prototypenearestwithCclustertoAssign

    do

    n},{1,...,lwhere,orinput vecteach For

    Repeat

    prototypewithassociatedisCclusterEach

    n}{1,...,lk},{1,...,j,thatsuch),...,(sprototype

    ()

    1 C

    2

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    j

    **j

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    1

    j

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    wiE

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    wi

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    iwwwkInitialize

    meansKFunction

    k

    j i

    jl

    i lj

    j

    jl

    l

    j

    ljk

    l

    l

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    10.4. HAC

    Nguyn l

    homogeneity -> image regions.

    25TS. L Quc Ngc

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    10.4. HAC

    26TS. L Quc Ngc

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    10.4. HAC

    27TS. L Quc Ngc

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    10.4. HAC

    Phng

    php

    28TS. L Quc Ngc

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    10.4. HACPhngphp

    29TS. L Quc Ngc

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    10.4. HACPhngphp

    30TS. L Quc Ngc

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    10.4. HACPhngphp

    31TS. L Quc Ngc