Hiephv - Digital Image Processing - Chapter 4_2. Phan Vung Anh_Thresholding and Region Based

Hong Vn Hip

B mn K thut my tnh

Vin Cng ngh thng tin v Truyn thng

Email: [email protected]

X l nh

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Ni dung Chng 1. Gii thiu chung Chng 2. Thu nhn & s ha nh Chng 3. Ci thin & phc hi nh Chng 4. Pht hin tch bin, phn vng

nh Chng 5. Trch chn cc c trng trong

nh Chng 6. Nn nh Chng 7. Lp trnh x l nh bng

Matlab v C

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Chng 4. Phn vng nh

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Hai phng php chnh p dng trong phn vng nh Phng php da trn bin: pht hin bin

Phng php da trn vng nh

Phn vng nh da trn ngng

4

Segmentation

Detect discontinuity

Detect similarity

Edge detection

Gradient operator

Zero crossing (LoG)

Edge linking

edge Hough Transform

Optimal thresholding

Region growing

Boundary thresholding

Phn vng nh da trn ngng (tip)

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C s Khi i tng v nn c nhm li trong

cc vng

La chn mt ngng T c th phn tch cc vng

im nh p(x, y) o Nu f(x, y) > T p(x, y) thuc i tng

o Nu f(x, y) < T p(x, y) thuc nn

C th c nhiu ngng


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Ly ngng c th coi l bi ton xc nh hm T: T = T[x, y, p(x, y), f(x, y)]

f(x, y): biu din mc xm ca im nh (x,y)

p(x, y): hm m t thuc tnh cc b ca nh

nh sau ly ngng Hai cp (bi-level)

a cp (multi-level) o


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Vn : lm sao chn gi tr ngng T thch hp Nu T ch ph thuc f(x, y): php ly

ngng ton cc

Nu T ph thuc vo P(x, y) v f(x, y): php ly ngng cc b

Nu T ph thuc x, y: Php ly ngng thch nghi (adaptive thresholding)


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Cc phng php ly ngng Ly ngng cng

Ly ngng ton cc

Ly ngng cc b

Ly ngng thch nghi

Ly ngng da trn kim chng

Ly ngng da trn phn nhm (gom nhm)

Ly ngng cng

10

Ly ngng cng (tip)

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Ph thuc ch quan phn tch histogram

D b nh hng bi nhiu

nh hng bi thay i sng

nh hng ca nhiu

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nh hng ca sng

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nh hng ca sng

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Nhn xt nh c sng ng u ti cc vng s d

tm ngng hn

Ly ngng ton cc

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Cch tip cn heuristic Bc 1. Xc nh gi tr khi to ca T

(thng l gi tr trung bnh mc xm nh)

Bc 2. Chia nh thnh 2 vng: G1 (gm cc im nh mc xm >= T) v vng 2 (gm nhng im nh mc xm < T)

Bc 3. Tnh gi tr trung bnh mc xm ca G1 l m1, G2 l m2

Bc 4. Cp nht T = (m1 + m2)/2

Bc 5. Quay li bc 2 n khi no

Ly ngng ton cc (tip)

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Ly ngng thch nghi

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tng Ngng ton cc b nh hng bi

sng, nhiu

Chia nh nh thnh cc phn, sau p dng tm ngng khc nhau cho tng phn nh o Vn :

Chia nh th no l hp l

Tm ngng cho tng phn nh

Ly ngng thch nghi (tip)

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Ly ngng thch nghi (tip)

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Ly ngng ti u

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Gi s nh c 2 vng chnh r rt (vng i tng v nn)

Mt im (x, y) trong nh c 2 kh nng H0: Khng thuc vng i tng

H1: Thuc vng i tng

Gi z l gi tr mc xm trong nh (z coi nh bin ngu nhin)

Cc xc sut Xc sut tin nghim: P1= p(1); P2= p(0);

Ly ngng ti u (tip)

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p1(z): hm mt phn b xc sut ca cc pixel trn i tng

p2(z): hm mt phn b xc sut ca cnn (ch rng ta cha c p1(z) v p2(z))

Hm mt phn b xc sut p(z)

Ly ngng ti u (tip)

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T l ngng c chn phn vng nh (pixel > T nn v ngc li) Xc sut li khi phn vng cc pixel trn

nn l i tng

Xc sut li khi phn vng cc pixel trn i tng l nn

Xc sut li tng:

Ly ngng ti u (tip)

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Bi ton t ra l tm T , xc sut li nh nht

Gii, p dng lut leibniz cui cng thu c

Ly ngng ti u (tip)

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gii

Chng ta cn bit p1 v p2, tuy nhin thc t th p1 v p2 l cha bit

gii quyt c 2 cch o C1) Gi s phn b p1 v p2 l cc phn b

Gaussian (khng c gim st)

o C2) Xp x phn b p(z) l cc phn b Gaussian t histogram ca nh (c gim st) sao cho ti thiu ha:

Ly ngng ti u (tip)

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Phng trnh

Ly lograrit 2 v a phng trnh v

Ly ngng ti u (tip)

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Ch : c th ly ngng ti u bng cch xp x vi cc hm khc Gaussian Raleigh

Log-normal

Ly ngng ti u Otsu

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Hm graythresh trong matlab hin ang ci t theo phng php ny

Bi ton Cho nh a mc xm MxN

L mc xm {0, 1, 2, L-1}

ni: s pixel trong nh c mc xm I o MN = n0 + n1 + + nL-1

Histogram chun ha:

Tm ngng t ti u

Ly ngng ti u Otsu (tip)

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Vi ngng k, ta c 2 lp pixel

tng: Tm ngng sao cho minimizes the weighted within-class

variance tng t vi vic maximizing the between-class variance


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Weighed within-class variance

Trong :

w2(t) q1(t)1

2(t) q2 (t) 2

2(t)

q1(t) P(i)i1

t

q2 (t) P(i)i t1

I


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Class mean

Class variance

1(t) iP(i)

q1(t)i1

t

2(t)iP(i)

q2(t )it1

I

12(t) [i 1(t)]

2 P(i)

q1(t)i1

t

22(t) [i 2(t)]

2 P(i)

q2 (t)it1

I


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Total variance

V total variance = const

Minimize within-class tng ng vi maximize between-class

2w

2(t) q1(t)[1 q1 (t)][1(t) 2 (t)]

2

Within-class,

from before Between-class, B2(t)


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Thut ton: Bc 1. Tnh histogram, v xc sut ti mi

gi tr mc xm

Bc 2. Khi to Bc 3. Duyt ln lt cc gi tr ca t t 1

n L-1 o Tnh q1(t); 1 o Tnh

Bc 4. Cp nht ngng t ng vi ln nht

B2(t)

B2(t)


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Ch c th tnh bng cch qui Khi to:

qui:

B2(t)


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nh hng ca nhiu n ly ngng Otsu

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nh hng kch thc vng n ly ngng Otsu

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Ci thin ly ngng bng cch kt hp thng tin bin

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Thut ton Tnh gradient hoc laplacian ca nh ban

u

Ly ngng trn nh gradient hoc laplacian loi b cc im nhiu

Nhn nh ban u vi nh gradient hoc nh laplacian xy dng histogram

Ly ngng Otsu ca nh ban u da trn histogram va tm c

Ci thin ly ngng bng cch kt hp thng tin bin

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Phn vng nh da trn cc thut ton gom nhm

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Mi im nh c i din bi mt vector c trng

Cc c trng c th l Gi tr mc xm Gi tr thnh phn mu sc Cc o cc ln cn (v d gi tr trung bnh

trong ca s chy)

Phn nhm: tin hnh gom cc vector ging nhau vo cng mt nhm

Phn vng nh da trn cc thut ton gom nhm (tip)

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Cc phng php phn nhm K-means

ISODATA

Thut ton K-means Bc 1. Khi to k tm ca k nhm

Bc 2. Phn loi n im vo k nhm da vo khong cch n cc tm

Bc 3. Tnh li tm ca mi nhm (gi tr trung bnh), quay li bc 2 hoc sang bc 4

Bc 4. Thut ton dng khi tm cc nhm ln i + 1 so vi ln th i khng c thay i

Thut ton K-means

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Thut ton gom nhm ISODATA

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ISODATA l ci tin ca thut ton K-means

S lng cc nhm c th c iu chnh t ng o Nu 1 nhm qu tn mn tch lm 2 nhm

o Nu 2 nhm qu gn nhau gp vo mt nhm

Tnh khong cch t tt c cc phn t n tt c cc tm a ra quyt nh gom nhm hay tch nhm

Phn vng nh trc tip da trn min nh

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Gi s R biu din vng ca ton nh, chng ta c th chia R ra thnh nhiu vng con khc nhau R1, R2, , Rn tha iu kin:

RRa

n

i

i

1

)(

(b) Ri l mt vng lin thng, vi mi i = 1, 2, , n.

(d) P(Ri) = TRUE, vi mi i = 1, 2, , n.

(e) P(Ri Rj) = FALSE, vi mi i j

(c) Ri Rj = , i j.

Phn vng nh trc tip da trn min nh (tip)

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P(Ri) l mt hm logic c nh ngha trc trn cc im nh trong tp Ri v l tp hp rng.

iu kin (a) m bo vic phn vng l hon ton, mi im nh phi thuc vo mt vng no .

iu kin (b) R l mt vng lin thng.

iu kin (c) m bo cc vng phi ri nhau.

iu kin (d) m bo cc im nh trong vng phi tha mt tnh cht P no .

iu kin (e) m bo hai vng khc nhau v tnh cht P c nh ngha trc


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p dng khi nh c nhiu nhiu vic pht hin bin phc tp hoc khng th pht hin chnh xc

Tiu chun xc nh tnh ng nht ca min ng vai tr rt quan trng

Mt s tiu chun tnh ng nht Theo gi tr mc xm

Theo mu sc, kt cu nh

Theo hnh dng, theo m hnh


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Mt s phng php Phng php lan ta vng (gia tng vng

region growing)

Phng php phn chia v kt hp vng

Phng php lan ta vng

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Bt u ti nhng im ht ging

Pht trin vng bng cch thm vo tp cc im ht ging nhng im ln cn tha mn mt tnh cht cho trc (nh cp xm, mu sc, kt cu) Tha mn hm P

4 ln cn

8 ln cn

Phng php lan ta vng

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Tiu chun:

1. Gi tr sai khc

tuyt i gia cc

im nh phi nh

hn 65

2. Cc im nh phi

l 8 ln cn vi

nhau v c t nht

mt im nh nm

trong vng

Phng php lan ta vng (tip)

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V d: Phn vng p dng lan ta vng cho nh sau (s sai khc < 3, seed point l nhng im c gi tr ln nht)

0 0 1 2 5 7 1 0 1 1 1 1 1 0

0 0 1 6 6 7 1 0 0 0 0 0 0 0

0 1 2 1 2 1 1 0 0 7 7 7 1 1

1 2 1 1 1 2 0 0 0 6 6 7 1 1

1 2 7 6 6 6 5 5 1 6 7 7 1 1

2 3 1 1 1 6 6 1 1 6 6 7 1 1

0 0 0 1 1 1 1 1 1 6 6 7 1 1

0 0 0 0 0 0 1 1 0 0 0 0 1 1

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0 0 1 2 5 7 1 0 1 1 1 1 1 0

0 0 1 6 6 7 1 0 0 0 0 0 0 0

0 1 2 1 2 1 1 0 0 7 7 7 1 1

1 2 1 1 1 2 0 0 0 6 6 7 1 1

1 2 7 6 6 6 5 5 1 6 7 7 1 1

2 3 1 1 1 6 6 1 1 6 6 7 1 1

0 0 0 1 1 1 1 1 1 6 6 7 1 1

0 0 0 0 0 0 1 1 0 0 0 0 1 1

Cc im nh ht ging

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0 0 1 2 5 7 1 0 1 1 1 1 1 0

0 0 1 6 6 7 1 0 0 0 0 0 0 0

0 1 2 1 2 1 1 0 0 7 7 7 1 1

1 2 1 1 1 2 0 0 0 6 6 7 1 1

1 2 7 6 6 6 5 5 1 6 7 7 1 1

2 3 1 1 1 6 6 1 1 6 6 7 1 1

0 0 0 1 1 1 1 1 1 6 6 7 1 1

0 0 0 0 0 0 1 1 0 0 0 0 1 1

Pht trin vng.

Phng php phn chia v kt hp vng

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tng: Xc nh mt lut P(Ri) m mi vng phi

tha mn

Mt vng Ri s c chia thnh cc vng nh hn nu P(Ri) = FALSE

Hai vng Ri v Rj s c gp vo nhau nu P(Ri Rj) = TRUE

Thut ton dng khi khng chia v gp c na

Phng php phn chia v kt hp vng (tip)

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C nhiu k thut tch v hp vng Xem xt k thut tch v hp vng theo cu

trc cy t phn

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K THUT TCH VNG V HP VNG T PHN

P(Ri) = TRUE nu c t nht 80% cc im trong Ri c tnh cht |zj m| 2i.

Trong :

zj: l cp xm ca im nh th j trong vng Ri.

m: l gi tr trung bnh ca vng Ri.

i: l lch chun ca cc cp xm trong Ri.

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TNH LCH CHUN

Khi cc vng c gp: tt c cc pixel trong vng nhn gi tr trung bnh ca vng

Phng sai:

lch chun:

1

1

2

2

n

zzn

j

j

1

1

2

n

zzn

j

j

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Hiephv - Digital Image Processing - Chapter 4_2. Phan Vung Anh_Thresholding and Region Based